1 Introduction
Graphene, a two-dimensional crystal composed of a single atomic layer of carbon arranged in a honeycomb hexagonal lattice, has drawn substantial attention over the past two decades. It is the first fabricated two-dimensional material that contradicts the long-standing theoretical prediction stating that thermodynamic fluctuations do not permit two-dimensional crystals to exist stably at finite temperatures [
1]. Since its discovery by Novoselov
et al. [
2] at the University of Manchester, UK, graphene has opened a new chapter in the field of low-dimensional materials and has garnered widespread attention across diverse disciplines [
2]. The unique planar two-dimensional crystal structure confers upon graphene a series of outstanding physical properties, such as exceptional mechanical strength [
3], excellent thermal conductivity [
4], and extremely high charge carrier mobility [
5,
6]. These properties, taken together, form the basis for its extensive application potential [
7−
9]. In particular, a fundamental aspect of the electronic properties of graphene is the appearance of massless Dirac fermions [
10,
11], which has enabled the observation and exploration of novel quantum phenomena, including the integer quantum Hall effect (IQHE), the fractional quantum Hall effect (FQHE) [
12−
20], and Klein tunneling [
21,
22].
Graphene multilayers, namely, a finite number of graphene layers stacked vertically via van der Waals interactions, can yield a wide range of stacking configurations. The specific stacking configuration fundamentally dictates the electronic properties of the multilayer graphene [
23−
39]. For instance, while both monolayer and AA-stacked bilayer graphene are semi-metals with zero band gaps, Bernal (AB-stacked) bilayer graphene can be tuned into a semiconductor under an external electric field [
40−
45]. A particularly intriguing scenario arises when two monolayer graphene sheets are stacked and twisted to form twisted bilayer graphene (tBG) [
46−
52], resulting in electronic properties markedly different from those of their constituent monolayer graphene or Bernal/AA-stacked bilayer graphene. Recently, a variety of flat-band-induced strongly correlated phenomena have been revealed in tBG when the twist angle approaches the so-called magic angle of approximately 1.1° [
53−
73]. Most notably, Cao
et al. [
54,
55] reported the observation of superconducting and correlated insulating states in magic-angle tBG, which ignited intense research interest in the correlation physics driven by these twist-induced flat bands [
74]. Subsequent theoretical works predicted that such flat bands, capable of hosting emergent correlated phenomena, were not exclusive to tBG [
75] but also existed in other twisted multilayer graphene systems [
76], including twisted monolayer-bilayer graphene (tMBG) [
77], twisted trilayer graphene (TTG) [
78], and twisted double-bilayer graphene (tDBG) [
79]. Indeed, a series of strongly correlated states arising from low-energy flat bands have been experimentally observed across various twisted platforms [
80−
86]. The emergence of these remarkable strongly correlated effects at small twist angles highlights the twist angle as a crucial and versatile degree of freedom for exploring and engineering electronic properties in graphene systems.
The predominant technique for fabricating twisted multilayer graphene is the “tear-and-stack” method [
87]. This approach, however, inevitably introduces impurities, wrinkles, and inhomogeneous strain [
88−
91], which can degrade sample quality and complicate the interpretation of transport measurements, thus impeding the investigation of strongly correlated effects [
92,
93]. Given these challenges, scanning tunneling microscopy (STM) [
94,
95] emerges as a powerful tool for investigating moiré physics and strong correlations in these systems. STM offers several critical advantages: Firstly, it can characterize surface topography from the macroscopic scale down to the atomic level, directly providing detailed surface information of the twisted graphene samples, such as local strain, wrinkles, and defects. Moreover, by directly imaging the moiré pattern, STM allows the twist angle to be accurately determined locally. Secondly, scanning tunneling spectroscopy (STS), a key functionality of STM, enables the measurement of the local density of electronic states in real space. This capability is pivotal for unraveling the microscopic origins of strongly correlated phases. In this article, we review the recent experimental advances in the study of magic-angle twisted multilayer graphene investigated using STM and STS measurements.
2 Atomic structures and band structures of twisted multilayer graphene
Twisted graphene systems typically consist of two or more individual graphene layers, primarily including tBG, tMBG, TTG, tDBG, and other similar multilayer configurations. We begin by introducing the atomic and electronic band structures of tBG, as shown in Fig. 1(a) [
75,
96,
97]. The tBG structure comprises two monolayer graphene layers rotated relative to each other by a specific twist angle
θ, which gives rise to a clearly observable moiré superlattice. In the model image, the bright regions correspond to AA stacking sites, while the darker surrounding regions are composed of AB and BA stacking sites — both of which exhibit identical density of states (DOS). In 2011, Bistritzer
et al. [
75] investigated the electronic band structures of tBG at different twist angles using a continuum model. For large twist angles, the low-energy band structures of tBG resemble that of isolated graphene sheets. As the twist angle decreases, the Fermi velocity is renormalized and progressively decreases, causing the low-energy bands to gradually flatten. When the twist angle is reduced to approximately 1.05° (the so-called first magic angle), the Fermi velocity vanishes and the low-energy bands become maximally flat, thereby inducing various strongly correlated phenomena. In addition, it has been proposed that the Fermi velocity vanishes at a series of angles, such as
θ ~ 1.05°, 0.5°, 0.35°, 0.24°, and 0.2°, collectively referred to as magic angles.
tMBG can be formed by twisting and stacking a monolayer graphene sheet on top of a Bernal-stacked bilayer graphene. Its lattice and electronic band structures are shown in Fig. 1(b) [
77,
98−
103]. The brightest regions correspond to ABB stacking sites, surrounded by darker ABC stacking sites and the darkest ABA stacking sites. Park
et al. [
77] investigated the band structure of tMBG using a continuum model. They predicted that tMBG hosts isolated flat bands at specific, wider magic-angle regions within the range of approximately 0.3° to 1.5°, thus offering greater tunability compared to tBG. Within the minimal model (neglecting remote hopping terms), the bandwidth of these flat bands in tMBG is smaller than those in tBG under the same system parameters within the magic-angle range, implying stronger electronic correlations. Furthermore, they discovered that the topological valley Chern numbers of the low-energy bands in tMBG are highly tunable by applying a perpendicular electric field [
77].
TTG consists of three monolayer graphene sheets, with the middle layer twisted at the same (or different) angles relative to the top and bottom layers. The atomic and electronic band structures of TTG are shown in Fig. 1(c) [
78,
104−
106]. The TTG structure features AAA, ABA, and BAB stacking sites. According to Khalaf
et al. [
78], TTG exhibits two sets of flat bands at a magic angle of 1.53°. The electronic properties of these flat bands are similar to those in tBG at the corresponding magic angle. A key distinguishing feature of TTG is the coexistence of these flat bands with a Dirac-like dispersing band, unlike in tBG where the low-energy bands are isolated and both become flat at the magic angle.
tDBG is formed by twisting two Bernal-stacked bilayer graphene sheets relative to each other. The atomic and electronic band structures of tDBG are shown in Fig. 1(d) [
79,
107−
110], featuring ABAB, ABCA, and ABBC stacking sites. Using a continuum model, Chebrolu
et al. [
79] demonstrated that tDBG hosts flat bands with bandwidths approximately half of those in tBG, suggesting a potential for stronger electron correlations than in tBG. Furthermore, they showed that applying vertical pressure can increase the magic angle (from ~1.05° at zero pressure) to up to ~1.5° under ~2.5 GPa of pressure, primarily due to the pressure-induced enhancement of the interlayer coupling. Their work also predicted the emergence of topological flat bands with electrically tunable valley Chern numbers in this system.
3 Twisted bilayer graphene
tBG has emerged as a prominent material system that has attracted widespread attention, particularly following the discovery of flat-band-induced unconventional superconductivity and correlated insulating states. These discoveries have significantly advanced the fields of strongly correlated physics and twistronics. The introduction of a small twist angle between the two layers serves as a novel degree of freedom, enabling profound modifications of the electronic structure via the formation of the moiré pattern. At the specific “magic angles”, notably around 1.1°, the resulting flat electronic bands give rise to a rich array of strongly correlated phenomena, including unconventional superconductivity, correlated insulating states, and magnetic ordering. Research on tBG not only deepens our understanding of fundamental condensed matter physics but also holds considerable promise for future applications in quantum computing and novel electronic devices. In the following section, we will review the progress in understanding these strongly correlated phenomena in magic-angle tBG through STM/STS studies.
3.1 Basic topographic and spectroscopic characterization
In recent years, tBG has emerged as a prominent research focus, primarily driven by the discovery of strongly correlated phenomena arising from its flat electronic bands. This interest extends beyond the study of correlation-driven physics itself and encompasses fundamental investigations into the structural and spectroscopic properties of the moiré superlattice. Accordingly, this section begins with a review of the basic topographic and spectroscopic characterization of tBG.
Zhou
et al. [
111] investigated the evolution of the basic topography of tBG with different twist angles, focusing on those near the magic angle. Figure 2(a) shows schematics and STM topographic images of two distinct structural phases of tBG, referred to as the unreconstructed and reconstructed structures. The unreconstructed structure comprises two rigid monolayer graphene sheets that are simply rotated with respect to each other and do not undergo spontaneous structural reorganization. In contrast, the atomic lattice in the reconstructed structure undergoes significant spontaneous reorganization [
112]. In the reconstructed structure, to minimize the system’s total energy, AB and BA stacking regions expand at the expense of the AA stacking regions, which are separated from each other by a network of narrow domain walls (DWs) [
45,
52]. These reconstruction-induced stacking DWs can generate one-dimensional topological transport and tunable plasmonic photonic crystals in tBG, offering a versatile platform for engineering quantum phases and nano-optical devices without the need for complex nanofabrication [
112−
115].
STM offers an effective approach that not only distinguishes between the unreconstructed and reconstructed structures in tBG but also directly visualizes the moiré superlattice at the atomic scale. Furthermore, the twist angle θ can be determined using the relationship L = a/[2sin(θ/2)], where L represents the period of the moiré superlattice and a is the graphene lattice constant. The study demonstrated that STM could provide two methods for distinguishing between the unreconstructed and reconstructed structures of tBG. As shown in Fig. 2(b), the unreconstructed and reconstructed structures of tBG could coexist when the twist angle is 1.09°. A key distinguishing feature is the presence of DWs in the reconstructed structure, which are absent in the unreconstructed one. By quantitatively comparing the height ratio between the DW and AA stacking regions, the authors determined the twist angle ranges corresponding to each structure, as shown in Fig. 2(c).
Additionally, the unreconstructed and reconstructed structures could be distinguished by comparing the relative sizes of the AA and AB/BA stacking regions. In the unreconstructed structure, the size of the AA regions increased rapidly as the twist angle decreased. In contrast, the size of the AA regions in the reconstructed structure exhibited a much weaker dependence on the twist angle, as they were significantly reduced during reconstruction to minimize the total energy of the system by avoiding unfavorable high-energy stacking configurations. To quantify the size of the AA stacking regions, the authors performed STS mapping at the Van Hove singularity (VHS) energy and determined the size of each AA region from the standard deviation (σ) of a Gaussian curve fitted to the profile line. The average value of σ was then plotted as a function of twist angle for a series of tBG devices, providing a clear metric to distinguish between the two structures. Using these two approaches, the authors established the prevalence of each structure across different twist angles. The unreconstructed structure was found to exist predominantly at angles above approximately 1.80°, whereas the reconstructed structure was exclusively observed below angles of about 0.9°. A transition region was identified between 0.9° and 1.8°, where both reconstructed and unreconstructed domains were found to coexist within the same sample. This coexistence was attributed to a delicate balance between the interlayer stacking energy and intralayer elastic energy.
The unreconstructed and reconstructed structures of tBG can not only coexist within the same magic-angle tBG sample but also be switched to each other, as investigated by Liu
et al. [
116]. The authors observed coexisting unreconstructed and reconstructed structures in magic-angle tBG (~1.15°) within a STM topographic image, which were directly distinguishable by the presence of DWs in STS mapping acquired at the flat-band energy. Critically, the authors controllably switched between these two structures by applying a voltage pulse from the STM tip. As shown in Fig. 2(d), the reconstructed structure was transformed into the unreconstructed one after applying a 3 V pulse for 0.1 s, which was verified by the disappearance of the characteristic height corrugation at the DW regions. Remarkably, the lattice reverted to its original configuration when an additional tip pulse was applied. Furthermore, this structural transformation was accompanied by modifications to the low-energy flat bands, as shown in Fig. 2(e). First, the flat bands were shifted from fully empty to fully occupied states, a transition potentially driven by tip-induced charge transfer from the substrate. Second, the reconstructed phase exhibited a broader overall bandwidth, as evidenced by the larger full width at half maximum (FWHM) for its subpeaks (~105 meV vs. ~70 meV). Third, a distinct negative differential conductance signature was observed, indicating a gap between the flat bands and the high-energy conduction bands [
36].
We now discuss the single-particle electronic properties of tBG, beginning with its characteristic VHSs. Li
et al. [
120] identified two sharp DOS peaks on either side of the Fermi level in large-angle tBG by STS, which was attributed to twist-induced VHSs. Subsequent works established the relationship between the energy separation of these VHSs (Δ
EVHS) and the twist angle
θ [
118,
121,
122]. As shown in Fig. 2(h), Δ
EVHS was found to increase linearly with the twist angle. This trend can be described by the following expression:
where ΔK = 2|K|sin(θ/2) and |K| = 4π/(3a). Here a ~ 0.246 nm is the lattice constant of graphene, θ is the twist angle, K is the reciprocal-lattice vector, vF is the Fermi velocity of graphene, tθ is the interlayer hopping parameter, and is the reduced Planck constant.
In 2015, Yin
et al. [
117] expanded on this topic by systematically tracking the evolution of these low-energy VHSs with small angles using STM/STS. A key finding was that as the twist angle decreased, the two VHSs moved toward the Fermi level and eventually merged into a single, sharp peak, signaling the formation of flat bands near the Fermi level, as shown in Figs. 2(f) and (g). This peak was narrowest at approximately 1.1° and then re-broadened as the angle was further decreased, leading the authors to identify this angle as the first magic angle. This work provided crucial experimental verification of the predicted single-particle electronic spectrum of magic-angle tBG, showing good consistency with theoretical predictions [
75]. The 1.1° magic angle was later further confirmed in 2018 by transport measurements, which revealed superconductivity at this angle [
55]. Although Yin
et al. [
117] confirmed the evolution of VHSs around the magic angle, the flat-band peak in their study did not exhibit the splitting later observed by Kerelsky
et al. [
123] at the magic angle, a difference that may be attributed to the screening effect of their metallic substrate.
The flat bands in magic-angle tBG are influenced by multiple factors, including defects, strain, and substrate effects. Among these, the formation of the moiré superlattice is the most fundamental origin of the flat bands. Yin
et al. [
119] systematically investigated the flat-band characteristics in magic-angle tBG with reduced structural symmetry. They found that the low-energy flat bands remained stable even if the translational symmetry of the moiré superlattice was broken in one direction. However, the flat-band state was remarkably broken in the incomplete moiré spots, as shown in Fig. 2(i). In other words, the more incomplete the moiré superlattice was, the more severely the flat bands were degraded or even completely suppressed. Thus, the authors demonstrated that a single, complete moiré spot was indispensable for generating effective moiré flat bands in magic-angle tBG, indicating a moiré quantum well picture.
3.2 Strong electron interactions in tBG
Flat-band-induced strong electronic interactions in magic-angle tBG have attracted extensive interest. A series of strongly correlated phenomena have been successively discovered in various magic-angle twisted multilayer graphene systems. This section reviews the strongly correlated effects investigated experimentally by STM in magic-angle tBG. Early work by Li
et al. [
124], using STS mapping, visualized the spatial symmetry breaking of electronic states around the VHSs in a tBG sample with a twist angle of 1.2°. In 2019, detailed spectroscopic signatures of strong electronic correlations were reported in magic-angle tBG through STM/STS measurements by several groups [
123,
125−
127]. Among these studies, Kerelsky
et al. [
123] provided direct spectroscopic evidence of strongly correlated effects in magic-angle tBG. As shown in Figs. 3(a) and (b), by varying the doping level at an AA-stacking site, the authors observed the opening of a gap (~6.5 meV) at the shoulder of the conduction VHS at half-filling in 1.15° tBG, which was interpreted as evidence of a correlated insulator. Notably, the insulating gap was reduced at a twist angle of 0.79°, confirming the weakening of correlation effects away from the magic angle and indicating that the electronic correlations were strongest near 1.1°. Moreover, the spectral line shapes exhibited hallmarks of strong correlation: they sharpened when the flat band was near the Fermi level and developed strong asymmetries when doped away from it. Additionally, the doping- and energy-dependent STS maps, as shown in Figs. 3(c) and (d), revealed that the electronic structure of tBG exhibited strong nematicity — a breaking of rotational symmetry. This effect was most pronounced at the energy of the correlated insulator gap that opens at half-filling, in contrast to the more symmetric behavior observed at other doping levels. The findings suggested that the system entered a nematic phase near half-filling, potentially driven by electronic correlations, though the precise nature of this ordered state warranted further investigation.
Jiang
et al. [
125] also investigated the spectroscopic properties of magic-angle tBG and discovered strongly correlated effects by STM/STS. They found that strong electronic correlations in magic-angle tBG (~1.07°) led to a doping-dependent redistribution of spectral weight between two peaks as the Fermi level entered the flat bands, as shown in Figs. 3(e) and (f). This behavior, where spectral weight transferred from the lower to the upper band upon hole doping and vice versa for electron doping, closely resembled the phenomenology of doped Mott insulators in cuprates. The spectral weight ratio provided a sensitive local probe of charge filling, as validated against capacitive doping calculations. Furthermore, dynamical mean field theory (DMFT) simulations in Fig. 3(g) qualitatively reproduced this spectral evolution and confirmed its origin in interaction-driven broadening and the transfer of weight between Hubbard-like bands, thereby supporting a Mott-like interpretation in magic-angle tBG. Beyond these spectroscopic signatures, the study also revealed a correlation-driven electronic state that spontaneously broke the original C
6 rotational symmetry. STS mapping at charge neutrality showed a spatial redistribution of spectral weight within the AA stacking regions, indicating a localized charge order with a quadrupolar geometry — alternating electron- and hole-rich quadrants in Fig. 3(h). This local ordering coherently extended across the sample, forming global stripe patterns. The phenomenon was specifically tied to the correlated flat bands, as it disappeared at larger twist angles or when the Fermi level lay outside the flat band, ruling out extrinsic effects like strain or tip anisotropy. These results suggested the emergence of a robust, intrinsically correlated charge-ordered phase in the system.
At the same time, Xie
et al. [
126] explored strong electron-electron interactions in magic-angle tBG by examining the doping evolution of STS spectra. As shown in Fig. 3(j), they found that when the moiré flat bands were partially filled, the flat bands exhibited severe spectral broadening and distortion of the VHS peaks over an energy scale (30–50 meV) far exceeding the intrinsic bandwidth. Moreover, spectroscopic features, including a gap-like suppression of the DOS at half-filling of the conduction band in Fig. 3(i) — correlating with the correlated insulating state — and a significant enhancement of band separation near charge neutrality, both indicated strong many-body effects. Conversely, the flat bands in a non-magic-angle sample showed well-defined, symmetric peaks without doping-dependent broadening, confirming the unique correlated nature of magic-angle tBG. The stark contrast between spectra in the fully occupied/empty flat-band regime — which were well-described by a non-interacting model with strain — and those at partial fillings provided direct evidence for the dominant role of electronic interactions in magic-angle tBG.
Besides, spectroscopic signatures of correlation-induced insulating states and enhancement of the flatbands splitting have also been detected by the STM work of Choi
et al. [
127]. In a magic-angle tBG with
θ = 1.01°, the authors observed that the flat-band peaks (VHS) evolved with doping: they sharpened and intensified as they approached the Fermi level under both electron and hole doping. Furthermore, the splitting between the VHS peaks was significantly enhanced when the Fermi level lay within the flat bands. These phenomena were absent in a tBG with
θ = 1.92°, confirming their origin in electronic correlations unique to the magic-angle condition. Critically, the authors observed spectroscopic gaps originating from correlated insulating states when the flat bands were half-filled in a
θ = 1.01° magic-angle tBG. Additionally, they detected spontaneous breaking of C
3 rotational symmetry in the spatially resolved conductance maps. Subsequently, the same group (Choi
et al. [
128]) further investigated the evolution of the electronic bands and correlated phases across a range of twist angles. A key finding was the observation of significant filling-dependent band flattening, driven by electron−electron interactions, which occurred even at angles substantially larger than the magic angle. This flattening — inferred from changes in Landau level spacings in a magnetic field — maximized near integer fillings and led to a dramatic enhancement of the DOS. As the twist angle approached the magic value, this interaction-driven band flattening triggered the emergence of correlated gaps at integer fillings (
ν = ±2, ±3, +1). Moreover, they identified a broad, temperature-dependent soft gap in a filling range where superconductivity was anticipated, suggesting a potential connection to superconducting precursors or strong-coupling pairing. These results emphasized the essential role of interaction-induced band flattening — rather than single-particle bandwidth alone — in enhancing electronic correlations and stabilizing the diverse symmetry-broken phases observed in magic-angle tBG.
In 2020, Wong
et al. [
129] reported another typical spectroscopic characteristic of the strong electron–electron interactions in magic-angle tBG: a cascade of electronic transitions. This finding highlighted the interplay between correlation effects and the system’s degeneracies. Through STS measurements, they found a sequence of distinctive spectroscopic features near the Fermi level that evolved systematically with gate voltage, recurring at each integer filling of the moiré flat bands between
ν = +4 and
ν = −4, as shown in Figs. 3(k)–(n). These features — manifested as pronounced broadening, dispersion, and reorganization of spectral weight in the d
I/d
V spectra — were interpreted as direct signatures of strong electron−electron interactions. Moreover, d
I/d
V spectra measured at AB/BA stacking sites exhibited cusps in the chemical potential at every integer filling, indicating reduced compressibility and corroborating the interaction-driven restructuring of the electronic spectrum. The experimental findings were observed in multiple devices with twist angles near 1.1° but absent in non-magic-angle samples, confirming the existence of strong electronic interactions in magic-angle tBG. Furthermore, the cascade features were strongly suppressed under an applied perpendicular magnetic field of 9 T, suggesting that the magnetic field disrupts the interaction-driven electronic order.
These STM/STS studies collectively established the ubiquity of strong correlations in magic-angle tBG. Going beyond spectroscopy, the atomic resolution of STM enables the direct probing of the wavefunctions of correlated phases in real space at the atomic scale. A seminal work in this direction was reported by Nuckolls
et al. [
130], who observed spontaneously broken symmetry in magic-angle tBG using atomic-resolution STM and STS. The authors found that the squared wavefunctions of gapped phases, including correlated insulating, pseudogap, and superconducting states, exhibited significant broken-symmetry patterns. These patterns displayed a
×
super-periodicity relative to the graphene atomic lattice and showed complex spatial variation at the moiré scale, clearly revealing atomic-scale Kekulé patterns in magic-angle tBG. As shown in Figs. 4(a) and (b), when the carrier density was close to
ν = −2, the intensity of the unique
×
pattern reached its maximum, and the appearance of the related second-order peak 2
strongly confirmed the symmetry breaking at the atomic scale. This discovery established a clear link between this pattern and the formation of correlated insulators. The influence of strain on the ground state of magic-angle tBG correlated insulators was an important aspect of the research. Interestingly, high-strain samples exhibited asymmetric incommensurate Kekulé spiral (IKS) states, where the electron wavefunctions showed symmetry breaking at the moiré scale, with obvious stripe-like phase changes and vortex−antivortex structures; in contrast, ultra-low-strain samples tended to form time-reversal symmetric intervalley coherent (T-IVC) states, whose order parameters restored moiré periodicity — there were no vortex-antivortex pairs in the IVC bond phase diagram, and only isolated vortices existed in the IVC phase diagrams for site A and site B. This clearly indicated that strain was a key factor in determining the ground-state symmetry of magic-angle tBG correlated insulators. In addition, by tracking the evolution of order parameters during the doping process, the authors found that the IVC order was a common feature of insulating, pseudogap, and superconducting phases. However, when the superconducting phase formed, the phase stripes and vortex structures disappeared, and the symmetry of electron arrangement underwent a distinct change, showing an intervalley coherent mode that was fundamentally different from that of the insulating phase.
The above STM studies mainly focus on the first magic angle (i.e., around 1.1°) of tBG. Very recently, Nuckolls
et al. [
131] directly observed the fractal Hofstadter energy spectrum near the second magic angle of tBG, focusing on two devices with twist angles of
θ = 0.63° and 0.57°. STM topographies revealed a relaxed lattice structure (lattice reconstruction), while the gate-dependent d
I/d
V spectra at
B = 0 T showed numerous flat bands near the Fermi level, yet the correlated gaps were not observed at partial flat-band fillings. Theoretical calculations revealed dense flat electronic bands at these angles, with the 10 moiré bands near the Fermi level exhibiting bandwidths of less than 20 meV. Under a perpendicular
B-field, the zero-bias conductance at rational flux ratios Φ/Φ
0 ~ 1/6, 1/5, 1/4, 1/3 exhibited splitting of each moiré band into
q Hofstadter subbands and the opening of new gaps at
ν = ± 4/
q in Figs. 4(c) and (d), a manifestation of the band-folding effect central to Hofstadter’s original theory. However, the quasiparticle lifetime broadening limited spectroscopic resolution away from the Fermi level, necessitating careful doping to resolve individual subbands. Gate-dependent d
I/d
V spectra at Φ/Φ
0 = 1/6 and 1/3 enabled the identification of topological gaps, labeled by Chern number
t and integer
s. The density dependence of these gaps was remarkably well-captured by a theoretical model that incorporated strain and a filling-dependent Hartree potential. Signatures of fractal self-similarity were observed through discrete scaling transformations of the spectrum near
ν = ± 4 at integer Φ
0/Φ, a hallmark of the recursive construction of Hofstadter’s butterfly, although this scaling failed at non-integer flux ratios. Furthermore, the spectrum exhibited dynamic evolution with electron density and magnetic field, revealing strongly correlated effects, such as the anomalous closing of certain gaps, the
B-field-induced splitting and broadening of the zeroth Landau level. These phenomena were attributed to electron-electron interactions and quantum Hall ferromagnetism. Notably, correlation-induced features like the exchange gap at
ν = 0 weakened with increasing
B and vanished by
B = 3 T, illustrating the competition between Hofstadter subband broadening and interaction effects.
In addition, Zheng
et al. [
132] systematically investigated the electronic properties of tBG with various twist angles ranging from 0.075° to 1.2°, revealing the robust pseudo-Landau levels (PLLs) and emergent electronic kagome lattices. The authors demonstrated that an interlayer electric field induced by an Au-coated tip could open a band gap in the AB/BA stacking regions, leading to the emergence of one-dimensional topological edge states along the DWs and highly localized PLLs within them. These PLLs, observed consistently across all studied twist angles, formed a flat band in the hole-doped regime around 130 meV, in good agreement with theoretical predictions for rigidly tBG under similar electric fields. However, structural reconstruction in small-angle tBG caused the moiré lattice to relax into a triangular network of DWs, suppressing the formation of a structural kagome lattice and introducing electron-hole asymmetry that inhibits PLLs in the electron-doped side. Remarkably, the PLLs in real space organized into a sample-wide electronic kagome lattice, as shown in Fig. 4(g), directly visualized by STS map near the magic angle. The electronic kagome lattice was tunable and coexisted with other localized states, such as AA-stacked flat bands, at different twisted angles in Fig. 4(e). Figure 4(h) shows the evolution of the PLL energy in the DW region with the twist angle. It indicated that the PLL energy increased with the twist angle, a trend that was consistent with the theoretical calculation under different interlayer electric fields based on the rigidly tBG model. However, a quantitative deviation existed between the experimental values and the theoretical results, which could be reasonably attributed to the structural reconstruction not being considered in the theory. Figure 4(i) presents the evolution of FWHM of the flat bands in the AA-stacked region with the twist angle, demonstrating that the bandwidth of the flat bands was highly sensitive to the twist angle and reached a minimum near the magic angle of approximately 1.08°, which was consistent with the theoretical predictions. These findings established tBG as a versatile platform for realizing tunable electronic kagome lattices and exploring correlated phases in moiré systems.
The study of strong correlation effects in twisted graphene systems is influenced by multiple factors — such as the twist angle and strain — posing significant challenges for experimental and theoretical investigation. Recently, Li
et al. [
133] demonstrated experimentally that correlation-induced symmetry-broken states could be achieved in large-angle (3.45°) tBG — far from the magic angle — by engineering the ratio of the electron-electron interaction
U to bandwidth
W to exceed 1. They enhanced the electron−electron interaction by controlling the microscopic dielectric environment using a MoS
2 substrate, simultaneously reduced the width of the low-energy VHS peaks by enhancing the interlayer coupling via STM tip modulation, and drove the system into the strong correlation regime with
U/
W > 1. When the Fermi level partially filled the conduction VHS peak, a giant splitting (~76 meV) of the peak was observed, accompanied by a striped charge order in real-space LDOS mapping, signaling correlation-driven symmetry breaking. Comparative experiments on tBG on a graphite substrate (high screening,
U/
W < 1) showed no VHS splitting, underscoring the critical role of the substrate screening effect. This work provided a feasible pathway to explore correlated quantum phases in non-magic-angle tBG through the tailored engineering of the dielectric environment and interlayer coupling.
3.3 Topology and superconductivity in magic-angle tBG
Besides the correlation-induced insulating behaviors and symmetry breaking, STM/STS experiments have also revealed compelling signatures of topology and superconductivity in magic-angle tBG. The observed correlated phases in magic-angle tBG could have a non-zero Chern number, and their topological character can be determined by STM experiments. Nuckolls
et al. [
134] discovered a series of correlated topological phases in magic-angle tBG using STM/STS at millikelvin temperatures under perpendicular magnetic fields. As shown in Fig. 5(a), they observed nine gaps near the charge neutrality point (CNP) and six gaps far away from it; the filling factors at which these gaps occurred shifted with increasing magnetic field. First, the gaps near the CNP corresponded to eight Landau levels (LLs) originating from the eight Dirac cones (spin, valley, and moiré Brillouin zone corner) in the band structure. This eight-fold degeneracy was separated into two four-fold degenerate manifolds by single-particle effects. One four-fold degeneracy likely corresponded to the Landau fan observed in magnetotransport measurements, while the other underwent spontaneous symmetry breaking via exchange interactions to form quantum Hall ferromagnetic (QHF) states when the LLs crossed the Fermi surface. Second, the filling factors of these gaps away from the CNP exhibited a linear dependence on the magnetic field across all samples, as shown in Figs. 5(b) and (c). Each shaded region and line indicated a possible quantized Chern number for the corresponding gap, suggesting that these gaps originated from correlation-driven topological phases. In addition, the
C = +1 state near
ν = +3 was attributed to strong interactions spontaneously breaking the two-fold (C
2) rotational symmetry. Finally, theoretical modeling explained the full sequence of phases as a consequence of strong correlations breaking time-reversal symmetry, which led to the formation of Chern insulators that were stabilized by weak magnetic fields.
In another STM study, Choi
et al. [
136] also found topological phases in magic-angle tBG (~1.1°), where the tBG was placed on WSe
2 to improve sample quality without altering the magic-angle condition. They observed multiple gaps at various doping levels, and their behavior under magnetic fields closely resembled the findings reported by Nuckolls
et al. [
134]. These gaps near the CNP originated from the Dirac points, while other gaps away from the CNP were attributed to strong electron-electron interactions, which induced correlation-driven Chern insulating states. In addition, the filling factors at which the LL gaps near the CNP occurred remained fixed (independent of twist angle), consistent with their single-particle origin tied to the Dirac cone degeneracy. In contrast, the Chern insulating gaps shifted away from the CNP at larger twist angles, reflecting their dependence on the flatness of the bands and the strength of electronic correlations. Remarkably, Chern insulating gaps were only observed within a narrow range around the magic angle, underscoring the critical role of strong correlations and exceptionally flat electronic bands in the formation of these topological phases. This narrow angle dependence aligned with the theoretical expectation that strong interactions dominated only when the bandwidth was sufficiently reduced, which enabled correlation-driven symmetry breaking and topological order.
Superconductivity is one of the most remarkable discoveries in the twisted graphene system. Spectroscopic experiments could provide important microscopic results for exploring and understanding the superconducting behavior. Oh
et al. [
135] presented compelling evidence for unconventional superconductivity in magic-angle tBG through a combined approach of density-tuned and point-contact spectroscopy (DT-STS and DT-PCS). The authors observed multiple correlation-induced gaps, with a particular focus on the doping range –3 <
ν < –2 where transport studies had previously reported superconductivity. A clear transition was identified between a correlated insulating gap at
ν = –2 and a superconducting gap within –3 <
ν < –2, consistent with transport measurements, indicating a phase transition from a correlated insulator to a superconductor. To unambiguously distinguish the superconducting gap from insulating gaps, the authors complemented DT-STS with PCS. PCS probed Andreev reflection, a process where electrons are retro-reflected as holes while Cooper pairs entered the superconductor, resulting in a zero-bias conductance peak characteristic of superconductivity. Clear signatures of Andreev reflection were observed exclusively within –3 <
ν < –2 in Figs. 5(d) and (e), under magnetic fields
B < 50 mT and temperatures
T < 1.2 K, which confirmed the superconducting nature of the gap in this range. As shown in Fig. 5(f), the authors also directly contrasted the correlated insulating state and superconductivity using PCS and DT-STS. Low-temperature STS spectra in Figs. 5(g) and (h) exhibited a V-shaped density of states, which was incompatible with conventional s-wave pairing but consistent with a nodal superconductor with an anisotropic gap function, suggesting a non-BCS pairing mechanism driven by strong electronic correlations. Moreover, the tunneling gap far exceeded the BCS value and persisted even above the critical temperature and magnetic field, forming a pseudogap phase. Notably, both the superconducting and pseudogap phases were completely absent in hBN-aligned magic-angle tBG samples, indicating that the breaking of C
2 symmetry (which is prevented by hBN alignment) is crucial for stabilizing these phases.
3.4 Exotic quantum phases in tBG/h-BN heterostructures
Twisted graphene, as an important system for studying strongly correlated and topological physics, can form composite structures with hexagonal boron nitride (h-BN) that also exhibit abundant exotic quantum properties. Li
et al. [
137] investigated the magic-angle tBG aligned with h-BN using STM and STS, focusing on the interaction between moiré patterns at the graphene−graphene (G−G) and graphene−h-BN (G−h-BN) interfaces. As shown in Fig. 6(a), the STM topographic images revealed two sets of moiré patterns with similar wavelengths (~15 nm), where the G–h-BN moiré exhibited significant deformation into irregular hexagons — a phenomenon that was attributed to moiré pattern reconstruction (MPR) driven by incommensurate wavelength mismatch and inter-pattern coupling at a relative orientation of approximately 30°. Through Fourier and inverse Fourier analyses, along with molecular dynamics simulations, the authors demonstrated that this reconstruction led to the formation of short-range, nearly ordered “helical-flower-like” super-superstructures, rather than long-range quasicrystals, due to energy-driven atomic relaxation minimizing overlapping high-energy regions. This MPR introduced strong and non-uniform strain, particularly enhanced in the bottom graphene layer due to direct h-BN contact and more pronounced at AAA sites compared to AAB sites, as confirmed by simulated strain maps. Consequently, the strain induced spatially varying energy separations between VHSs in Figs. 6(b) and (c) — 41 meV and 25 meV at two different AA sites — by deforming Dirac cones, altering Fermi velocities, and shifting Dirac point wave vectors. Furthermore, gate-dependent STS measurements revealed that a correlated gap (~11.5 meV) emerged during doping at specific AA sites in Fig. 6(d), while absent at others, indicating that local electron correlations were modulated by the inhomogeneous strain and reconstruction. These findings highlighted the crucial roles of MPR and localized strain in shaping the electronic structure and correlation physics in tBG/h-BN heterostructures, providing key insights into the microscopic origins of spatially heterogeneous electronic behaviors and emerging quantum phases.
At the same time, Lai
et al. [
138] presented a detailed investigation of a rich variety of moiré periodic and quasiperiodic crystals in tBG on hBN (GG/GBN), where the interplay between two moiré potentials — graphene-on-graphene (GG) and graphene-on-hBN (GBN) — generated both commensurate and incommensurate structures. The authors illustrated the local stacking orders (AAB, AAN, AAC) and showed simultaneous imaging of GG and GBN moiré patterns, with the energetically favored AAB stacking leading to self-alignment even away from the rigid-lattice commensuration condition. Figures 6(e)−(g) show representative STM topographic images of diverse moiré configurations: the sample formed a 1:1 commensurate crystal with a triangular lattice of bright AAB sites and a six-fold symmetry, attributed to global alignment enabled by strain relaxation that allows commensuration over a wider range than theoretically predicted. Figure 6(f) exhibits moiré intercrystals (MICs) — quasiperiodic structures with more than two basis vectors but no forbidden symmetries — arising from incommensurate ratios between GG and GBN periods. Figure 6(g) reveals a dodecagonal moiré quasicrystal (MQC) with 12-fold rotational symmetry, forbidden in periodic crystals, resulting from specific combinations of reciprocal vectors
KGBN and
KMM. The phase diagram in Fig. 6(h) categorized these structures based on moiré wavelengths
LGG and
LGBN, highlighting a broad basin of attraction around the 1:1 commensuration line due to a self-alignment mechanism driven by van der Waals energy gain in AAB stacking outweighing the elastic cost of homogeneous strain. Finally, Figs. 6(i)−(k) show the electronic properties of the different moiré configurations from Figs. 6(e)−(g). Gate-dependent d
I/d
V spectra showed flat bands and correlation-induced gaps in crystals, MICs, and MQCs, respectively. Real-space LDOS maps demonstrated energy-dependent symmetry evolution in quasiperiodic structures — an effect attributed to electron scattering from the incommensurate potential, contrasting with the robust six-fold symmetry in commensurate crystals.
In addition, Wong
et al. [
139] investigated the electronic structure of magic-angle tBG in the intermediate regime of partial alignment to a hBN substrate. As shown in Fig. 6(l), they observed a small insulating gap (< 5 meV) at
ν = 0, attributed to weak sublattice symmetry breaking induced by hBN substrate, as well as strong conductance suppressions at fractional fillings
ν = ± 1/3 and weaker ones at
ν = ± 1/6 [inset in Fig. 6(l)]. Crucially, bias-resolved spectroscopy revealed that these fractional gaps were rigidly shifted with gate voltage and existed away from the Fermi level as the filling factor was tuned, indicating a single-particle origin. They proposed that this behavior stemmed from a long-wavelength moiré super-superlattice potential generated by the interference and superposition of the G−G (
λ ≈ 15.2 nm) and G−h-BN (
λ ≈ 7.4 nm) moiré patterns, rather than arising from many-body correlated states. This super-superlattice led to Brillouin-zone folding and secondary band gaps at specific fractional fillings. Furthermore, at filling beyond ±4, a series of LDOS peaks appeared in the dispersive remote bands, consistent with the VHSs generated by this Brillouin-zone folding. In contrast, spatially varying pseudogap-like features observed in Fig. 6(l) at other partial fillings were likely of many-body origin, as evidenced by their spontaneous appearance at the Fermi level. This work highlighted the crucial role of local spectroscopy in distinguishing single-particle effects from electron correlations.
4 Twisted monolayer-bilayer graphene
In recent years, tMBG has emerged as a highly attractive moiré system due to its wide magic-angle ranges and unique topological flat bands. Moreover, theoretical studies have predicted that the narrower flat bands could enhance electron-electron interactions, leading to richer strongly correlated phenomena. To date, a series of strongly correlated phenomena have been observed in transport and STM experiments [
140−
148].
4.1 Localization-delocalization coexisting flat bands
For tMBG, Tong
et al. [
149] first conducted spectroscopic studies in magic-angle tMBG using STM. The samples were fabricated on a highly oriented pyrolytic graphite (HOPG) substrate by surface exfoliation. Figure 7(a) showed a large-area STM topographic image (no clear native defects were observed in the studied region), which consisted of a tBG (middle region) and bilayer-side tMBG (right region), and displayed the moiré superlattice structures with the same periodicity and orientation. Moreover, the representative zoom-in STM topographic images of the tBG and tMBG were also shown in Fig. 7(b) (different stacking sites were indicated). By measuring the periodicity of moiré superlattices, the authors determined the twist angle of ~1.13° (magic angle) for both tBG and bilayer-side tMBG regions. Figure 7(c) presents the representative STS spectra of magic-angle tMBG, which directly displayed dispersionless flat bands (blue arrow) at the Fermi level and two remote bands (black arrow) away from the Fermi level in the hole and electron sides. In the magic-angle tBG region, it also exhibited three similar DOS peaks in the STS spectrum [inset in Fig. 7(c)], arising from the flat bands and remote bands in the magic-angle tBG, which was consistent with previous reports. In addition, the coexistence of tMBG and tBG in a single sample with exactly the same twist angle provided a unique opportunity to directly compare their flat-band electronic properties, which was particularly difficult for transport measurements, as they usually suffer from large variations among different samples. As shown in Fig. 7(d), the authors compared the bandwidth of the flat bands in these two twisted regions and found a smaller bandwidth for the flat band in tMBG than in tBG, which is also consistent with previous theoretical predictions.
Structurally, tMBG has two different surfaces: bilayer-side surface and twisted-side surface. STM mainly measures the electronic states of the sample surface, so the local electronic properties on the different surfaces of tMBG can be explored, as presented in the work of Tong
et al. [
149]
. As shown in Fig. 7(e), an almost uniform DOS of flat bands in the STS spectra was observed in the different stacking sites on the bilayer side of the 1.13° tMBG, suggesting delocalized flat-band states. Moreover, the STS maps indicated that the flat-band wave functions nearly extend over the whole moiré superlattice, further demonstrating the delocalized characteristic of the flat-band states in bilayer-side tMBG. On the other hand, the authors also investigated the spectroscopic feature on the twisted side of a tMBG with
θ ~ 0.7°. As shown in Fig. 7(f), the DOS of flat-band exhibited a clear site dependence — strongest at ABB sites, weaker at the ABC sites and weakest at the ABA sites — indicating a localization of the flat bands. In addition, the STS maps also supported the localized feature on the twisted-side tMBG. The authors also performed continuum model calculations which nicely reproduced the above experimental observations. These results established the unexpected coexistence of localized and delocalized flat-band electronic states, i.e., localization on the twisted-side and delocalization on the bilayer-side.
The localization and delocalization coexisting feature of the flat bands in tMBG is a distinctive property. In magic-angle tBG, the moiré flat-band electronic states are highly localized in the AA stacking sites. It demonstrated that the Coulomb repulsion between the localized electrons is expected to be responsible for the observed strongly correlated states in tBG [
150−
152]. However, in magic-angle tDBG, theoretical and experimental studies have demonstrated the spatially delocalized electronic states (see details in chapter 6), suggesting that the non-local exchange interaction may play an important role in this situation [
153]. Therefore, the experimental work of Tong
et al. [
149] suggested the potential coexistence of different interaction mechanisms in tMBG. It is worth noting that transport studies have observed the coexisting signature of tBG- and tDBG-like correlation effects in tMBG, where the correlation behaviors can be adjusted by a displacement electric field [
141]. This result can be well understood according to the localization-delocalization coexistence picture. Because localized and delocalized states are distributed across different layers in tMBG, the application of a displacement field lifts their degeneracy, thereby enabling a possible transition from localization-dominant correlated behavior characteristic of tBG to delocalization-dominant correlated behavior typical of tDBG. Therefore, tMBG provides an unprecedented platform to utilize their cooperation for investigating moiré physics and underlying mechanisms.
4.2 Correlated and topological phases
Due to the unique crystal symmetry, the flat bands in tMBG can host nontrivial topology, which has been demonstrated by theories and transport experiments. STM experiments also detected correlated and topological behaviors in tMBG as shown in Fig. 8(a). Li
et al. [
154] found correlation-induced electron crystal and topological torus structure in the twisted-side magic-angle tMBG (~1.04°). An obvious electron-hole asymmetry was observed, with no band splitting or correlated states detected under hole doping (
ν < 0). In contrast, under electron doping (
ν > 0), gate-dependent d
I/d
V spectra showed a distinct correlated gap only within the ABC stacking region in Fig. 8(b), where the CFB split into two branches separated by approximately 10 meV, indicating a spatially modulated Coulomb interaction in real space. Moreover, the authors directly observed concomitant spatial redistribution of electrons — manifested as downward energy bending of the CFB at the ABB sites — confirming electron puddles and a real-space electron crystal phase at integer fillings in Fig. 8(c). This charge order resulted in global suppression of DOS at the Fermi level and insulating behavior. Furthermore, the interplay between such correlation-driven charge order and the inherent non-trivial band topology of tMBG led to the emergence of a periodic array of topological boundary states, which were visualized as torus-shaped structures encircling specific stacking regions [as shown in Fig. 8(d)].
The topological properties of the flat bands in magic-angle tMBG can be tuned by the twist angles and perpendicular magnetic fields. Zhang
et al. [
155] systematically investigated the gate-tunable quantum anomalous Hall (QAH) effect in tMBG with a twist angle of approximately 1.25°. As shown in Fig. 8(e), the authors observed two correlated insulating states at
ν = 2 and
ν = 3, which exhibited distinct spectroscopic responses to a small out-of-plane magnetic field. The insulating gap at
ν = 2 remained fixed at the same filling level regardless of the
B field. In contrast, the gap at
ν = 3 split into two branches, identified as QAH insulating states with opposite Chern numbers
Ctot = +2 and
Ctot = –2. These branches followed the Středa formula, as shown in Figs. 8(f)−(h), confirming their topological nature and enabling electrostatic switching of the Chern number by varying
B and
v. Furthermore, they found that the gate-controlled switching occurred only within a narrow range of twist angles (1.25° to 1.28°) and under low hetero-strain conditions (< 0.15%). In regions with higher hetero-strain, only a single gap corresponding to
Ctot = +2 was observed, indicating suppressed switching. This phenomenon was explained by a continuum model highlighting the competition between the orbital magnetization of filled bulk bands and chiral edge states.
Recently, Zhang
et al. [
156] achieved spatial control over two correlated Chern insulating states with
Ctot = ±2 at
ν = 3. By exploiting naturally occurring charge density inhomogeneities, they stabilized neighboring domains of opposite Chern number. At the boundary between these domains, they spatially resolved one-dimensional chiral interface states, which were directly visualized in real space as bright one-dimensional conductive channels in zero-bias d
I/d
V maps, as shown in Fig. 8(i). They demonstrated reversible control over the spatial position of these chiral states by adjusting the global back-gate voltage. Moreover, they achieved the on-demand creation of such topological interfaces by using an STM tip pulse to fabricate electron- or hole-doped quantum dots, which generated the necessary charge density gradient. This method allowed them not only to observe but also to control the chirality of the one-dimensional interface states by reversing the polarity of the quantum dot.
Additionally, Wang
et al. [
157] introduced an innovative approach using a decorated STM tip as a local top gate to induce and manipulate correlated insulating states in tMBG. When combined with a global back gate, the decorated tip created a strong local displacement field that both fully lifted the eight-fold degeneracy of the flat bands and significantly enhanced the electron-electron interaction. This technique led to two major breakthroughs: it significantly expanded the observable twist-angle range for correlated insulators down to 0.92°, relaxing the strict “magic angle” requirement, and it enabled the first observation of these phases in the hole-doping regime, thereby addressing a key gap in previous transport studies. Furthermore, the method proved versatile, reliably inducing correlated phases in tMBG on different substrates such as hexagonal boron nitride and tungsten disulfide. It also allowed dynamic control over the flat bands’ degeneracy through gate voltage. Overall, this work provided a powerful new tool for the atomic-scale study and manipulation of correlated quantum phenomena in moiré systems.
5 Twisted trilayer graphene
TTG is another correlated electron platform, where interlayer twist angles can give rise to flat electronic bands that host a variety of emergent phenomena, including superconductivity and orbital magnetism [
81,
158−
165]. In the following, we will review the experimental progress in TTG based primarily on STM studies.
TTG typically consists of three monolayer graphene sheets. In the ideal AtA-type stacking, the top and bottom layers are rotationally aligned, while the middle layer is twisted at a specific angle relative to them. However, a twist angle is also often present between the top and bottom layers, resulting in the more general AtB-type structure. The AtA-type can thus be viewed as a special case of the AtB-type with a zero twist angle between the top and bottom layers.
5.1 Strongly correlated effects in magic-angle TTG
Similar to tBG, superconductivity has been observed in the magic-angle TTG system. Transport measurements demonstrated that the superconducting state in magic-angle TTG showed excellent electric field tunability and a higher Berezinskii-Kosterlitz-Thouless (BKT) transition temperature than magic-angle tBG, suggesting an unconventional nature [
165]. Subsequently, Kim
et al. [
166] provided direct spectroscopic evidence of unconventional superconductivity in TTG with
θ ~ 1.5° (AtA-type TTG) using STM/STS. The authors first established the foundational electronic structure, revealing correlation-driven band deformations — such as widely separated VHSs and cascades of symmetry-breaking transitions — which were theoretically attributed to strong electron-electron interactions similar to those in magic-angle bilayers. In addition, they explored the Landau fan diagram, where the observed Chern number shift of +2 and the presence of well-defined Landau levels from additional Dirac cones were explained by the unique mirror-symmetric A-tw-A band structure of magic-angle TTG, which hosted extra Dirac sectors in addition to the flat bands. Remarkably, a pronounced suppression of tunneling conductance at the Fermi level, accompanied by symmetric coherence peaks, was observed within the doping range −3 <
ν < −2 in Figs. 9(a)−(c). These spectroscopic gaps, which were gradually suppressed by temperature and magnetic field in Figs. 9(d)−(g), were identified as signatures of superconductivity. The exceptionally large ratio 2Δ/(
kBTC) ≈ 15−19 (
kB is the Boltzmann constant) indicated strong-coupling pairing beyond the conventional BCS mechanism. Furthermore, the doping-dependent transition from a U-shaped to a V-shaped gap profile was interpreted theoretically as a gate-induced evolution from a gapped Bose-Einstein condensate (BEC) phase to a gapless nodal BCS-like phase, suggesting a unified nodal order parameter throughout. Finally, the authors revealed peak-dip-hump structures adjacent to the coherence peaks, which were analyzed as bosonic mode signatures with an energy Ω that anticorrelates with Δ in the V-shaped regime; this trend, consistent with electronic pairing mechanisms in other unconventional superconductors, suggested that superconductivity in magic-angle TTG was likely mediated by bosonic modes of electronic origin rather than phonons.
Similar to tBG, a spontaneous broken-symmetry-induced IVC order was directly imaged in magic-angle TTG at the atomic scale by the STM experiments of Kim
et al. [
167]. The IVC order was manifested as a Kekulé distortion — a
superlattice pattern observed in real-space d
I/d
V maps, with its periodicity confirmed by Fourier analysis showing inner peaks at
of the graphene reciprocal lattice vectors rotated by 30° in Figs. 9(h)−(j). This distortion, indicative of intervalley coherence, emerged only within specific filling ranges (−3 <
ν < −2 and 2 <
ν < 3) where correlated gaps developed, and its intensity was bias- and temperature-dependent, confirming its electronic origin and ruling out structural or impurity effects. Furthermore, as shown in Figs. 9(k) and (l), large-scale d
I/d
V maps further showed that the Kekulé pattern varied between neighboring moiré sites. Auto-correlation analysis revealed a stripe-like modulation, suggesting breaking of moiré translation symmetry. Fourier analysis of these patterns identified an incommensurate wavevector
qKekulé that evolved with doping and aligned with the theoretically proposed incommensurate Kekulé spiral order, which resulted from intervalley nesting instabilities in the presence of small heterostrain. Additionally, sash-like features in Fourier maps and nematic bond order at charge neutrality further supported symmetry breaking. The robustness of IVC order under magnetic fields and its coexistence with superconductivity near
ν = −2 suggested that superconductivity in magic-angle TTG might emerge from an IVC parent state. It is worth noting that similar correlation-induced IVC order has been observed not only in twisted graphene systems, but also in other systems including bilayer and rhombohedral graphene [
168,
169].
5.2 Structure and band engineering in TTG
Due to the multiple twists between different layers, TTG can undergo rich structural reconstructions and band evolution. Turkel
et al. [
170] investigated the strong moiré reconstruction and correlated flat bands engineering in AtB-type TTG using STM/STS. As illustrated in Fig. 10(a), real TTG devices exhibited significant moiré lattice reconstruction (MLR) due to small interlayer twist mismatches (
δ0 ≈ 0.2−0.3°), which spatially segregated the sample into three distinct types of domains — uniform plaquettes, strained solitons, and high-twist-angle twistons — each exhibiting unique electronic properties due to their local structural parameters. Spectroscopic measurements revealed that the flat bands were most pronounced in the low-angle, low-strain plaquettes, became heavily suppressed in the high-strain solitons due to heterostrain disrupting the band structure, and were both split and shifted in the high-twist-angle twistons, a behavior consistent with theoretical calculations for unstrained TTG at larger angles, thereby illustrating how nanoscale structural disorder directly tailors the electronic landscape. Furthermore, spectroscopic measurements in the plaquette regions in Fig. 10(b) revealed strongly renormalized flat bands with broad VHSs that were poorly described by single-particle models; instead, Hartree−Fock calculations incorporating electron interactions successfully reproduced the large VHS separation (~18 meV) and width (~23 meV), indicating strong electronic correlations and band renormalization. Notably, correlated insulating gaps were absent in the plaquette but emerged selectively at twistons and moiré solitons, suggesting spatially confined strong correlations in these regions. Furthermore, a gate-tunable flat-band resonance occurred near |
ν| ≈ 2−3 in Figs. 10(d) and (e), where the electronic states from the plaquette and twiston regions align, enhancing the global density of states and suppressing spatial inhomogeneity. This resonance condition coincided with the doping range where superconductivity is most robust, implying that the superconducting dome might be disorder-limited, with the homogeneity of the parent state facilitated by the flat-band resonance. The persistence of superconductivity in TTG, despite significant structural disorder, underscored the critical interplay between local lattice reconstruction, electronic correlation, and emergent order in moiré systems.
Hao
et al. [
171] demonstrated the existence of robust flat bands across multiple magic-angle pairs in AtB-type TTG, revealing that the atomic and electronic structures are highly sensitive to the twist angles
θTM and
θBM. The authors measured five TTG samples with different twist angle pairs and divided the TTG into two cases. The first case (the samples 1 and 2) featured at least one relatively large twist angle, resulting in weak coupling between the moiré lattices; the second case (the samples 3, 4 and 5) lay in the magic angle region with relatively strong coupling. Due to the existence of
θTM and
θBM, two moiré superlattices could be observed, further forming a moiré-of-moiré (MoM) pattern as shown in Figs. 10(f) and (g). The MoM pattern exhibited distinct high-symmetry regions such as AA-MoM and AB/BA-MoM, where the local C
3z symmetry was preserved in central regions of AA-MoM, but broken in areas deviating from AA-MoM due to different domain wall stackings (DW-MoM). STM topographic images of sample 1 further revealed that the central region of AA-MoM (region 1) preserved the C
3z rotational symmetry, whereas the region deviating from the center (region 2) underwent C
3z symmetry breaking. STS measurements detected pronounced low-energy DOS peaks in all samples, confirming the existence of flat bands and verifying the theoretically predicted magic-angle phase as shown in Figs. 10(h)−(j). Energy-fixed STS maps showed that the flat bands were concentrated in the AAA stacking regions in the central area of AA-MoM with preserved C
3z symmetry, while in the deviated regions, they were distributed in the AAA-BR and DW-AA-2 stacking regions with broken symmetry. The authors also found that the bandwidth of the flat bands was sensitive to the twist angle pairs, with magic-angle samples exhibiting narrower bandwidths than non-magic-angle ones — a result further explained by continuum model calculations and attributed to inter-moiré coupling strength. Additionally, the layer LDOS distribution depended on the coupling strength: the electronic properties of weakly coupled samples were approximately a superposition of two independent twisted bilayer graphene, while the flat bands in strongly coupled samples were uniformly distributed across the three layers as shown in Fig. 10(k).
Ren
et al. [
172] presented a novel approach for real-space mapping of local subdegree lattice rotations in small-angle tBG by utilizing a top-layer large-angle moiré pattern as a magnifying lens to amplify the subtle atomic-scale reconstructions of the underlying tBG by approximately two orders of magnitude. The characteristic “double-moiré” superlattice of TTG was clearly identified in STM topographies, and spatial variations in the topmost moiré period were observed across different stacking regions. In the experiment, local lattice rotations in the underlying small-angle tBG caused significant spatial variations in the topmost moiré period at different positions. Applying the relation
L =
a/[2sin(
θ/2)], the local twist angles
and
were derived, revealing a local relative rotation
that directly reflected the underlying reconstruction. Systematic measurements across 15 samples showed a consistent hierarchy
, and the statistical results showed that as
θ23 approached 0,
approached approximately 1.0°, and extrapolation indicated that reconstruction began when
θ23 was below about 1.7°. In electronic properties, the spatial distribution of Δ
EVHS of topmost tBG closely followed the moiré pattern of the underlying tBG, a phenomenon well reproduced by tight-binding calculations that account for the full trilayer stacking order. The energy-fixed STS mappings further confirmed the influence of the underlying interfacial reconstruction on the spatial variation of VHSs in the topmost tBG, including new peaks strongly localized at DWs, which might be related to the predicted pseudo-Landau levels.
6 Twisted double-bilayer graphene
tDBG possesses electrically tunable flat bands that host strong correlations and topologically nontrivial states. Gate-dependent spectroscopy and magnetic field responses have revealed numerous strongly correlated phenomena in this system [
173−
187]. In the following, we will review the strongly correlated effects of tDBG measured by STM.
Through gate-tunable STS spectroscopic measurements, Zhang
et al. [
185] investigated correlated electronic states in magic-angle tDBG (
θ ~ 1.08°). Figure 11(a) presented a representative STM topographic image, identifying the different stacking sites within the moiré unit cell. Their STS measurements of the flat bands revealed highly delocalized electronic character across the moiré unit cell, which stood in contrast to the localized behavior observed in tBG. At half-filling of the conduction flat band (
ν = 2), a correlation-induced splitting of the CFB of approximately 20 meV was observed across all three stacking sites, as shown in Figs. 11(c)−(e). The splitting reached its maximum at
ν = 2, signaling the formation of a correlated insulator. Theoretically, self-consistent Hartree−Fock calculations attributed this phenomenon to spontaneous symmetry breaking driven by non-local exchange interactions within the flat bands. The excellent agreement between the experimentally observed band splitting, spatial LDOS profiles, and theoretical predictions underscored the dominance of these exchange-driven correlations in magic-angle tDBG.
Liu
et al. [
186] investigated the electronic properties of tDBG (
θ ~ 1.48°), directly demonstrating its electrically tunable band structure and revealing spectroscopic signatures of both strong correlations and non-trivial band topology. Through atomic-resolution imaging, they directly visualized the broken C
2 symmetry and identified distinct stacking configurations within the moiré unit cell. Spatially resolved STS maps at the four VHSs of the first and second conduction/valence bands (C1, C2, V1, and V2) further confirmed this broken C
2 symmetry. Most notably, the STS spectroscopy revealed pronounced correlation effects near half-filling of the C1 band, characterized by a sudden jump in the VHS energy near the Fermi level. The magnitude of this jump, ranging from 0.38 to 1.3 meV depending on twist angle, was interpreted as a direct spectroscopic signature of the correlated insulating state previously detected in transport measurements. As shown in Figs. 11(f)−(h), under a perpendicular magnetic field (
B), the C1 peak split into two peaks. This splitting increased linearly with
B and persisted over a wide range of doping. The extracted effective g-factors were very large (
g ~ 13 at half-filling,
g ~ 21 at 3/4-filling), unequivocally ruling out a spin Zeeman origin. The authors attributed this splitting to the valley Chern number
C = ± 2 carried by the C1 band in each valley. The large orbital magnetic moments associated with these topological bands led them to couple strongly to
B, resulting in energy shifts of states in opposite valleys in opposite directions.
Rubio-Verdu
et al. [
187] investigated the electronic structure of tDBG and reported the emergence of a moiré nematic phase, a state characterized by the breaking of the system’s three-fold rotational (C
3) symmetry. Experimentally, the authors observed pronounced unidirectional stripe patterns at the valence flat band (VFB) over a wide range of doping (0.3 to 0.7 electrons per moiré unit cell) away from CNP, while the remote bands largely preserved C
3 symmetry across all doping levels, as shown in Figs. 11(i)−(k). They systematically ruled out heterostrain and displacement fields as extrinsic causes through detailed comparisons across samples with varying strain and via theoretical modeling. These findings indicated that the anisotropy was doping-dependent and aligned with a principal moiré axis, providing key evidence for an intrinsic origin. Their theoretical analysis revealed a dominant nematic instability driven by electron-electron interactions on the moiré scale. Continuum model simulations further demonstrated that the experimentally observed site-dependent splitting of the VFB and the spatial structure of the LDOS were consistent with a moiré-scale nematic order parameter, rather than atomic-scale graphene nematicity. These results established the nematic phase in tDBG as an intrinsic, correlation-driven phenomenon, underscoring the role of long-range interactions in spontaneously breaking rotational symmetry in moiré flat-band systems.
7 Conclusions and perspectives
In this review, we have summarized recent research progress in the STM experiments on magic-angle twisted multilayer graphene systems — including tBG, tMBG, TTG, and tDBG — in which strong correlation effects and rich emergent quantum phenomena are induced by moiré flat bands. The discovery of various strongly correlated phenomena in these systems by STM and STS measurements, such as unconventional superconductivity, correlated insulating states, topological phases, and moiré nematic phases, demonstrates that moiré flat bands provide an excellent platform for studying a wide range of strongly correlated quantum states. These findings have significantly advanced the fields of strongly correlated physics and twistronics. However, spectroscopic research on the electronic properties and strongly correlated phenomena in magic-angle twisted multilayer graphene still faces considerable challenges, and various issues remain to be addressed.
1) The observed strongly correlated states in twisted graphene systems are highly sensitive to multiple factors closely related to the fabricated samples, such as local variations in twist angle and strain. However, the controllable fabrication of samples with specific twist angles and strain remains a great challenge. It has been demonstrated that some correlated quantum states are transient and cannot be reliably reproduced, making it difficult to investigate their origins. STM measurement can directly detect the evolution of the quantum states with varying twist angles and strains in a single sample from a local-by-local or region-by-region point of view, which could offer important evidence for revealing the intrinsic and exotic properties of twisted graphene.
2) The discovery of unconventional superconductivity in twisted graphene systems, which defies explanation by conventional BCS theory, has garnered significant attention. Yet, the microscopic mechanism behind this superconductivity remains unclear, necessitating further experimental studies and the development of new theoretical frameworks. STM/STS experiments are expected to provide essential microscopic information to advance the understanding of this superconducting behavior.
3) The flat bands in tMBG exhibit a unique characteristic of coexisting localization and delocalization, sharing spatial distribution features with both tBG and tDBG. As a result, some strong correlation phenomena in tMBG resemble those observed in tBG and tDBG. Furthermore, tMBG’s lower symmetry and narrower flat-band bandwidth, compared to other twisted graphene systems, may stabilize even more exotic quantum states. Therefore, further exploration of the intriguing properties of tMBG is warranted. The local probing capability of STM/STS is intrinsically suited to exploring these intriguing layer-dependent properties in tMBG, as well as in broader twisted monolayer-multilayer structures.
4) Twisted multilayer graphene, such as alternating twisted graphene heterostructures and twisted thick graphene [
83−
85,
188−
192], has emerged as a highly tunable platform for investigating strong electron correlations. Owing to the increased number of coupled moiré potentials, these systems exhibit exceptionally flat bands and enhanced electronic interactions, leading to robust correlated insulating states, orbital magnetism, and robust superconductivity. This enhanced tunability, afforded by additional layers and twist angles, provides unprecedented control over the band structure and symmetry, thereby stabilizing exotic quantum phases inaccessible in simpler bilayers. Nevertheless, STM studies on these more complex multilayer systems remain limited, underscoring the need for further investigation to elucidate their moiré and flat-band physics from a local perspective.
5) Integrating magic-angle tBG with transition metal dichalcogenide (TMD) substrates has become a powerful strategy for engineering novel quantum states. The TMD primarily imprints its strong spin−orbit coupling onto the adjacent graphene layer and breaks inversion symmetry via proximity effects. This fundamental alteration dramatically expands the correlated phase diagram beyond that of pristine magic-angle tBG. A landmark achievement is the robust emergence of ferromagnetism and Chern insulators at integer fillings, demonstrating the stabilization of topologically nontrivial, spin- and valley-polarized states [
64,
136,
188,
193,
194]. Furthermore, the TMD substrate also acts as a tuning knob, potentially stabilizing and modifying the superconducting phase in magic-angle graphene [
82,
178]. Given these developments, detailed microscopic and spectroscopic measurements in magic-angle graphene/TMD heterostructures are also highly desirable at present.
The existence of a narrow magic-angle regime in twisted graphene gives rise to exceptionally flat electronic bands, where the dramatic enhancement of electron–electron interactions over kinetic energy creates a strong-correlation landscape. These systems not only provide an ideal platform for investigating novel quantum phenomena, such as unconventional superconductivity, correlated insulators, and topological phases, but also serve as an excellent reference for exploring and designing other moiré and two-dimensional flat-band materials. As research on magic-angle graphene systems continues to advance, more surprising and novel quantum states are anticipated in the broader family of twisted two-dimensional quantum materials.
PDF
(10587KB)
