Progress of ambient-pressure superconductivity in bilayer nickelate thin films

Abstract

This review summarizes recent progress of ambient-pressure superconductivity in bilayer nickelate La₃Ni₂O₇ thin films, a major advancement following the discovery of high-pressure superconductivity in bulk La₃Ni₂O₇. First, we explain how epitaxial strain engineering enables ambient-pressure superconductivity in La₃Ni₂O₇ thin films, with compressive strain from substrates like SrLaAlO₄ stabilizing superconductivity. Next, we review experimental characterizations of related systems, with particular emphasis on ARPES measurements that have shown conflicting Fermi surface topologies. We then discuss progress in increasing the superconducting transition temperature T_c. Finally, we summarize theoretical studies of the electronic structure and pairing symmetry of La₃Ni₂O₇ thin films. Together, these advances establish bilayer nickelate thin films as a highly tunable and promising platform for exploring high-T_c superconductivity.

Graphical abstract

Keywords

nickelate superconductors / thin films / ambient pressure / transition temperature / electronic structure / pairing symmetry

1 Introduction

Since the discovery of superconductivity (SC) in copper oxides with a transition temperature (T_c) of up to 164 K [1, 2], many efforts have been devoted to finding more high-T_c superconductors. One of the promising candidates predicted to be a high-T_c superconductor is nickel oxides, as nickel is located next to copper in the periodic table and is therefore believed to possess similar properties [3]. In 2019, the prediction was finally confirmed with the discovery of SC in an infinite-layer nickelate [4]. In 2023, Sun et al. [5] found SC with T_c near 80 K in bilayer nickelate La₃Ni₂O₇ under high pressure, marking nickelates as the second class of high-T_c superconductor to enter the liquid-nitrogen temperature range, following copper oxides. In 2024, Zhu et al. [6–8] observed SC with T_c = 20−30 K under high pressure in trilayer nickelate La₄Ni₃O₁₀, further expanding the family of nickelate superconductors. However, the requirement of high pressure has significantly limited the use of specific key experimental techniques for directly investigating the superconducting phase. Consequently, considerable research has focused on achieving ambient-pressure SC in nickelates.

Recently, using pulsed laser deposition (PLD), Ko et al. [9] reported ambient-pressure SC with a T_c exceeding 40 K in La₃Ni₂O₇ thin films grown on SrLaAlO₄ (SLAO) substrates. Almost simultaneously, Zhou et al. [10] independently observed ambient-pressure SC with a T_c over 40 K in La_2.85Pr_0.15Ni₂O₇ thin films grown on the same substrates by gigantic-oxidative atomic-layer-by-layer epitaxy (GAE) [11, 12]. And many experiments have been conducted on the samples synthesized by GAE [13–15]. The microscopic structures of these thin films are shown in Fig. 1. Later, several groups reported ambient-pressure SC in related systems, including La₂PrNi₂O₇ [16–18], and La_3−xSr_xNi₂O₇ thin films [19–21]. And more and more La₃Ni₂O₇ thin-film samples are synthesized and various experimental explorations have been conducted on them until right now [22–25]. And among these findings, the effect of element doping on La₃Ni₂O₇ thin films has been investigated systematically. Partial substitution of La with Pr in La₃Ni₂O₇ has been reported to improve sample quality, enhancing phase purity and SC [10, 16]. The effect of carrier doping is studied through Sr²⁺ doping in La_3−xSr_xNi₂O₇, which serves as an equivalent approach for hole doping, giving a phase diagram where the highest T_c value of 42 K is achieved at x=0.21 [19]. These findings represent a significant advancement in the field of nickelate superconductors.

In this review, we begin by examining the role of epitaxial strain in enabling ambient-pressure SC in La₃Ni₂O₇ thin films. We then examine key experimental studies, especially ARPES measurements that reveal distinct Fermi surface (FS) topologies, and summarize methods for raising the superconducting transition temperature T_c. Finally, we review recent theoretical studies of the electronic structures and possible pairing symmetry in La₃Ni₂O₇ thin films.

2 Effects of epitaxial strain

To achieve ambient-pressure SC, one promising approach is to apply epitaxial strain to La₃Ni₂O₇ thin films. Before discussing the effects of epitaxial strain, it is necessary to analyze the pressure phase diagram of bulk La₃Ni₂O₇ [26], which can be divided into a low-pressure region (LP) and a high-pressure region (HP). The characteristic structure of La₃Ni₂O₇ is its bilayer NiO₂ planes, where each layer contains a NiO₆ octahedron [27, 28]. The two octahedra share an apical oxygen, forming a Ni-O-Ni bond. In the LP phase, the space group is Aman, characterized by a 168° bond angle. As the pressure approaches approximately 10 GPa, it transitions into the HP phase, characterized by two octahedra aligned with each other, leading to a bond angle tilting to 180° and the space group changing to Fmmm above 14 GPa and I4/mmm above 46.8 GPa.

Since SC only appears in the HP phase, the main challenge is to stabilize this HP phase in thin films at ambient pressure. Cui et al. [29] revealed that epitaxial misfit strain is the dominant factor controlling the phase formation in RP nickelates La_n+1Ni_nO_3n+1. Their report indicates that tensile strain stabilizes the perovskite LaNiO₃ (n = \mathrm{\infty }) phase, while compressive strain favors the formation of the La₃Ni₂O₇ (n = 2) phase. Therefore, substrates play an important role in the induction of SC in bilayer nickelate thin films. As shown in Fig. 2(a), the temperature-dependent resistivity \rho (T) of La₃Ni₂O₇ thin films grown on SLAO substrates begins to decrease at approximately 42 K and reaches zero resistance near 2 K. In contrast, \rho (T) for films grown on LaAlO₃ (LAO) and (LaAlO₃)_0.3(Sr₂TaAlO₆)_0.7 (LSAT) substrates shows an upturn below 40 K without reaching a zero-resistance state [9]. The main difference among these substrates comes from their in-plane lattice constants, with SLAO applying compressive strain, LAO exerting only a mild compressive strain, and LSAT introducing a slight tensile strain. These results demonstrate that compressive strain is crucial for inducing ambient-pressure SC in La₃Ni₂O₇ thin films. In addition, the results from Chen’s group showed that the transition to zero resistance exhibits signatures of a Berezinskii–Kosterlitz–Thouless (BKT) transition [10].

3 Characterization results

The absence of high-pressure requirements in these thin films enables direct experimental investigation of the superconducting phase. Consequently, various measurements have been performed on bilayer nickelate thin films to investigate the underlying mechanisms of SC. Scanning transmission electron microscopy (STEM) measurements show that the apical Ni–O–Ni bond angle approaches 180° [9], which is very similar to the HP phase of bulk La₃Ni₂O₇. It is also notable that ozone annealing plays an important role in ambient SC of La₃Ni₂O₇ thin films. After O₃ annealing, the as-grown La₃Ni₂O₇ thin films transition from an insulating state into a superconducting state [9]. And the X-ray absorption spectroscopy (XAS) measurements further indicate that the O₃-annealed thin films contain a combination of 50% Ni²⁺ and 50% Ni³⁺, whereas the as-grown thin films contain 55% Ni²⁺ and 45% Ni³⁺ [9]. Thus, the Ni ion in the O₃-annealed thin films exhibits a mixed valence state of 2.5. These facts show that ozone annealing can increase oxygen content, and maintain a Ni^2.5+ valence state in La₃Ni₂O₇ thin films. Angle-resolved photoemission spectroscopy (ARPES) studies [13, 17, 24] on bilayer nickelate thin films have been conducted to confirm the topology of FS. As shown in Fig. 2(b), ARPES measurements on La_2.85Pr_0.15Ni₂O₇ thin films [13] reveal a FS, where the \alpha, \beta and \gamma pockets are identified. Furthermore, direct measurement of the superconducting gap on the FS [24] reveals a significant gap opening on the \beta FS sheet with no signs of nodes along the Brillouin-zone diagonal, as shown in Fig. 2(d). Notably, this gap survives to a temperature above T_c and shows a particle–hole symmetric evolution, consistent with the presence of a pseudogap. However, ARPES measurements on La₂PrNi₂O₇ thin films [17] give a FS without the \gamma pocket, which is about 70 meV below the Fermi level, as shown in Fig. 2(c). ARPES measurements on Sr-doped La₃Ni₂O₇ thin films also reports a FS without the \gamma pocket [20]. The contrast results may arise from differences in the growth conditions and measurement environment of the thin films. It has been reported that Sr diffusion from substrates was observed, which may also result in the appearance of the \gamma pocket [13]. Whether \gamma pocket appears in the intrinsic La₃Ni₂O₇ thin films under 2% compressive strain is still under debate. Scanning tunneling microscopy (STM) measurements [18] reveal a two-gap structure on the FS, with fitting analyses indicating a preferred anisotropic s-wave pairing. Taken together, these observations support a predominant s\pm-wave pairing symmetry in the system. But whether the pairing symmetry is s^{\pm } wave is still under debate. Most recently, Nie et al. [14] reported ambient-pressure SC with onset T_c up to 50 K in both hybrid monolayer-bilayer (1212) and pure bilayer (2222) films, and onset T_c of 46 K in bilayer–trilayer (2323) thin films, while the hybrid monolayer-trilayer (1313) structure remained non-superconducting. The FS of these films measured by ARPES in Fig. 3 showed a clear difference: a hole-like \gamma band crosses the Fermi level in the superconducting films, but in the non-superconducting 1313 film, it is below the Fermi level. A recent theoretical work attributes the suppression of SC in 1313 La₃Ni₂O₇ to reduced pairing strength in the trilayer subsystem and weakened phase coherence between trilayer subsystems arising from S–N–S Josephson coupling [30].

4 Methods to increase T_c

Following the discovery of SC in bulk and thin-film La₃Ni₂O₇, methods to raise T_c have emerged as a major research focus. In thin film systems, methods to increase T_c mainly involve enhancing thin-film growth techniques and applying pressure. Zhou et al. [15] showed that their improved GAE technique, achieved by pushing the growth regime into an extreme non-equilibrium state, can stabilize an ambient-pressure superconducting phase with an onset temperature of up to 63 K. Osada et al. [23] showed that as the c/a ratio increases, the onset T_c under hydrostatic pressure rises from approximately 10 K under tensile strain to nearly 60 K under compressive strain. Applying hydrostatic pressure on compressively strained La₃Ni₂O₇ thin films, which raises the onset T_c to over 60 K, has also been reported recently [31]. And most recently, Zhao et al. [32] showed that hydrostatic pressure universally enhances SC in (La,Pr)₃Ni₂O₇ thin films, raising the onset T_c to 68.5 K at 2.0 GPa. They attribute the observed resistance dip above T_c to oxygen-vacancy-induced electron localization. The dip is suppressed by pressure, which directly correlates with the increase in T_c, establishing oxygen vacancies as a key tuning parameter for SC in bilayer nickelates. Overall, T_c in thin films is probably enhanced by pressure via increasing interlayer coupling, orbital hybridization, and spin fluctuations. Also, some theoretical works [33, 34] have explored methods to enhance T_c by applying an electric field to thin films, which require experimental verification. While in bulk systems, using element substitution to increase T_c [35] has advanced significantly. In bulk systems, Li et al. [36] reported bulk SC in La₂SmNi₂O₇ under high pressure, which exhibits a T_c up to 96 K, zero resistance temperature up to 73 K, and clear Meissner screening, confirming robust bulk high-T_c behavior. Qiu et al. [37] demonstrated that Nd substitution in bilayer La₃Ni₂O₇ compresses the lattice and enhances interlayer magnetic coupling, resulting in SC with an onset T_c of up to approximately 98 K. Chen et al. [38] systematically calculated the electronic structures of Nd-doping bulk La₃Ni₂O₇, revealing that increasing Nd doping leads to a larger interlayer d_{z^2} orbital hopping, which would result in a larger interlayer superexchange coupling and a higher T_c. In conclusion, rare-earth element substitutions can induce chemical pressure in bulk La₃Ni₂O₇ to raise T_c. It has been reported that applying pressure can increase T_c in thin films [31], suggesting that T_c might be enhanced by chemical pressure. The effectiveness of this approach needs further experimental verification.

5 Theory progress of bilayer nickelate thin films

Since the discovery of SC in bilayer nickelate thin films, significant focus has been directed toward their underlying electronic structures. Several research groups subsequently performed systematic calculations of the electronic band structures [16, 22, 39, 40, 43, 44], employing first-principles density functional theory (DFT) and model analyses to characterize the low-energy states, FS topology, and orbital composition [45]. Using the constrained random phase approximation (cRPA), Yue et al. [39] demonstrated intra-orbital Coulomb interaction U\approx 3.77 eV and Hund’s coupling J_{\mathrm{H}}\approx 0.56 eV. Combining DFT and dynamical mean-field theory (DMFT) with the U and J_{\mathrm{H}} obtained from cRPA and a particle filling of n=1.3, they reproduced FS comparable to ARPES results, as shown in Figs. 4(a) and (c). Using DFT, Hu et al. [40] systematically investigated the electronic structures and slab models across various thicknesses. They constructed the One-UC (unit cell) double-stack tight-binding model and the Half-UC slab model, which is used for comparison, and proposed a double-stack high-energy d–p model for the first time, laying the groundwork for future research. The energy bands and FS of the One-UC double-stack tight-binding model are shown in Figs. 4(b) and (d). Since the One-UC slab consists of two bilayers, there is some small hopping between the two bilayers, resulting in a small split of the \gamma pocket. It is notable that the interlayer d_{z^2} orbital hopping parameter for the One-UC slab is −0.550, while for the Half-UC slab it is −0.503. This suggests that the One-UC slab may have a larger interlayer d_{z^2} orbital superexchange coupling compared to the Half-UC case, according to J\sim 4t^2/U. Based on the double-stack model, the random phase approximation (RPA) spin susceptibility exhibits the strongest response reflecting nesting intra \gamma pocket. Building on a similar double-stack model, Li et al. [46] performed a DFT+U study of La₃Ni₂O₇/SrLaAlO₄ thin films, explicitly incorporating both substrate-induced compressive strain and interfacial Sr interdiffusion. Recently, using DQMC and DMFT, Zhong et al. [47] reported that, La₃Ni₂O₇ thin films exhibit a significantly enhanced charge-transfer capability together with interlayer and intralayer antiferromagnetic correlations of comparable magnitude.

Pairing symmetry is an important question in high-T_c superconductors. Weak-coupling methods, such as RPA [48, 49] and functional renormalization group (FRG) [50, 51], are typically used to find out the pairing symmetry. Yue et al. [39] used a modified RPA approach based on their model, resulting in an s^{\pm } wave pairing symmetry, as shown in Figs. 5(a) and (b). However, the RPA approach is very sensitive to the details of FS. Shao et al. [41] constructed a tight-binding model without \gamma pocket, giving rise to an s^{\pm } wave pairing symmetry, driven by nesting between the \alpha pocket and \beta pocket, as shown in Figs. 5(c) and (d). A work using the variational Monte Carlo method also reports a robust s^{\pm } symmetry against change in FS [52]. Combining first-principles and FRG calculations, Le et al. [43] found that scattering between FS sheets with opposite parity symmetry enhances interlayer s^{\pm } wave SC, while nesting between FS sheets with the same parity symmetry would break the pairing. Using FRG, Cao et al. [53] found that the pairing symmetry for both La₃Ni₂O₇ and La_2.85Pr_0.15Ni₂O₇ thin films is s^{\pm } wave and T_c could be enhanced under in-plane compression. Recently, Zhang et al. [54] used the RPA approach on a one-UC compressive La₃Ni₂O₇ thin film, revealing a leading d_{x^2-y^2} pairing state at moderate hole doping, and a d_{xy} pairing symmetry with higher doping level. However, there are also some works supporting d_{xy} wave or d+\mathrm{i}s symmetry [55, 56]. And a recent measurement of differential conductance (\mathrm{d}I/\mathrm{d}V) spectra on pressurized La₃Ni₂{\mathrm{O}}_{7-\delta } single crystal suggests a d-wave-like symmetry [57]. Another theoretical method for identifying the pairing symmetry is the renormalized mean-field theory (RMFT) [58, 59], which begins with the t-J model. Qiu et al. [42] used the t-J Hamiltonian, including superexchange couplings J_{\mathrm{\perp }}^z, J_{||}^x, J_{xz}, and J_{\mathrm{H}}, to investigate the pairing symmetry and superconducting gap structure on the FS in La₃Ni₂O₇ thin films. Using exact diagonalization, the authors estimated J_{\mathrm{\perp }}^z\approx 0.135 eV. The resulting superconducting gap projected on the FS is shown in Fig. 6(a), indicating a nodal s^{\pm } wave pairing symmetry. The angular dependences of the gap on different pockets are shown in Figs. 6(b)–(d). The gaps on the \beta and \gamma pockets are nodeless and have opposite signs, while a sign change occurs on the \alpha pocket. Whether there are nodes on the \alpha pocket still needs more experimental results to prove. On the \beta pocket, the gap shows a parabolic shape centered around 45°, and it slightly decreases as it nears the corner. Orbital-resolved superconducting gaps are displayed in Figs. 6(e)–(h). Qiu et al. [42] systematically studied the phase patterns and pointed out that they can be interpreted as maximizing the overall gap magnitude on FS. As a result, {\mathrm{\Delta }}_{||}^z tends to maximize the gap on the \gamma pocket, whereas {\mathrm{\Delta }}_{||}^x enhances the gap on the \alpha pocket, with only minor suppression on the \beta pocket. Moreover, as temperature rises, the energy gap of all pairing bonds decreases to zero at approximately 60 K in a mean-field manner. Recently, some researchers have paid attention to the prediction of the T_c in superconductors [60, 61]. They tried to explore intrinsic constraints on the T_c in unconventional superconductors [60] and give an empirical scaling relation connecting the maximum T_c^{\ast } to the effective on-site Coulomb interaction U in unconventional superconductors [61]. While the relation appears robust across some correlated superconductors, its microscopic origin remains an open question.

6 Summary

To date, some issues still need clarification. First, the role of the \gamma pocket in enabling SC in bilayer nickelate thin films remains to be fully clarified. Second, the relationship between the lattice ratio c/a and the superconducting transition temperature T_c in thin films differs from that in bulk La₃Ni₂O₇. These unresolved and seemingly contradictory results highlight the need for further experimental work to better understand SC in bilayer nickelate thin films.

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