Surface oxygen termination-dependent topological states in two-dimensional Ru₂Si₂O_x (x = 1, 2): From topological insulator to type-II Weyl semimetal

Abstract

Surface termination engineering serves as a crucial technique for tuning the electronic and topological properties of two-dimensional (2D) materials. In this work, we present a combined experimental and theoretical study on the structure and electronic properties of a novel etchable 2D material, Ru₂Si₂T_x (T = O, F). Experimentally, Ru₂Si₂T_x with an “accordion-like” layered structure was successfully synthesized via selective etching of the YRu₂Si₂ precursor. Theoretically, different termination configurations by O/F on the 2D Ru₂Si₂ are systematically investigated through first-principles calculations on five representative structures. We find that the resulting topological quantum states depend strongly on oxygen termination. The fully O-terminated Ru₂Si₂O₂ is identified as a strong topological insulator with a band gap of 0.18 eV, hosting topologically protected edge states. The Ru₂Si₂O monolayer with O termination on only one side hosts six pairs of mirror-symmetry-protected type-II Weyl points. Our work not only predicts and establishes a termination-driven pathway from the topological insulator to the type-II Weyl semimetal in a 2D silicide system, but also highlights Ru₂Si₂T_x as a tunable 2D material platform for topological phase control via surface chemistry, providing a new material basis for future research in topological spintronics.

Graphical abstract

Keywords

Ru₂Si₂T_x / etchable 2D material / topological insulator / type-II Weyl semimetal

1 Introduction

The isolation of graphene in 2004 marked a seminal advance in materials science [1, 2], heralding the era of two-dimensional (2D) materials with unique electronic, optical, and mechanical properties [1–3]. This breakthrough spurred the discovery of other 2D systems, notably MXenes-transition metal carbides/nitrides first synthesized in 2011 via selective etching of MAX-phase precursors [3]. Similar etching strategies were later extended to MAB-phase borides [4], yielding 2D transition metal borides (MBenes) with tunable surface terminations [5–7]. These materials exhibit versatile chemistry and hold promise for energy, biomedical, and quantum applications [8–16].

Despite progress, the search for novel etchable 2D materials continues. Recently, YRu₂Si₂ was identified as a promising precursor, from which yttrium layers can be removed to produce a new 2D silicide, {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x (\mathrm{T} = O, F) [17]. Unlike conventional MXenes/MBenes, {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x represents the first etched 2D material based on a silicide and a platinum-group metal (Ru). A key distinction lies in the surface composition: in {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x, the silicon atoms are situated at the material surface, rather than being embedded within a metallic layer. Moreover, its crystal symmetry evolves from tetragonal in the pristine layer to a rare monoclinic phase (P{2}_1/m) upon functionalization − a structure exceptionally uncommon among 2D materials that induces strong in-plane anisotropy and is expected to yield novel electronic and optical behaviors.

Ruthenium (Ru), as the core element, is mainly based on its unique material endowment and the key blank in the current 2D material system. As a platinum group metal, ruthenium is not only renowned for its excellent chemical stability and outstanding catalytic activity, but also its strong spin-orbit coupling is conducive to inducing novel quantum states in low-dimensional systems [18–21]. Zhang et al. [22] theoretically demonstrated the realization of the quantum anomalous valley Hall effect (QAVHE) in single-layer RuClBr, where electron correlation drives a series of valley-dependent quantum phase transitions, forming a Chern insulator with chiral spin-valley locking. However, such high-performance elements are still scarce in chemically etchable 2D materials. Therefore, the preparation of {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x by etching the YRu₂Si₂ precursor provides us with a strategic opportunity: this not only introduces high-performance ruthenium into a solution-processable 2D form, but also, due to its unique silicon-based surface termination and potential low-symmetry structure, is expected to create a new material platform with both excellent physical properties and novel anisotropy, thereby substantially expanding the composition and functional boundaries of 2D materials.

Yet, the fundamental properties of {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x especially its termination-dependent electronic and topological behaviors-are still largely unknown. To address this gap, we combine experimental synthesis with first-principles calculations. We successfully etched YRu₂Si₂ with HF to obtain few- to multilayer {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x and characterized its morphology, structure, surface chemistry, and magnetism using FE-SEM, TEM, XPS, and VSM. In parallel, we performed density functional theory (DFT) calculations to systematically investigate five termination configurations: termination-free, fully O-terminated, fully F-terminated, Janus O-terminated, and asymmetric O/F-terminated systems.

Our study reveals two notable quantum states in oxygen-terminated structures: Ru₂Si₂O₂ is identified as a strong topological insulator with a band gap of 0.18 eV, whereas Ru₂Si₂O hosts type-II Weyl points protected by mirror symmetry. These findings establish {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_x as a chemically tunable platform for topological phase transitions and provide the first theoretical framework for designing functional quantum devices based on 2D ruthenium silicides.

2 Method

2.1 Preparation of YRu₂Si₂ precursor powder

High-purity yttrium (Y), ruthenium (Ru), and silicon (Si) powders (purity 99.9%) were blended in a stoichiometric ratio of 1:2:2 and homogenized using ball milling for two hours. The mixture was subsequently compressed into disc-shaped pellets under a uniaxial pressure of 10 MPa. The pellets were then melted into an ingot under a vacuum of less than {10}^{-3}\mathrm{P}\mathrm{a}. Melting was conducted using a current of 300 A, with a magnetic stirring current of 10 A, maintained for five minutes per cycle. This melting process was repeated five times to ensure compositional uniformity. The resultant ingot was annealed at 900 °C for 15 hours under an argon atmosphere to alleviate residual stresses, followed by grinding and sieving through a 400-mesh (38 μm) screen.

2.2 Synthesis of Ru₂Si₂T_x powder

Approximately 0.5 g of YRu₂Si₂ powder was gradually added to 20 mL of hydrofluoric acid (HF, 49%) with continuous stirring in a PTFE container. The reaction was carried out at 60 °C for 48 hours. The product was extensively washed with deionized water to achieve a neutral pH (approximately 7), employing multiple centrifugation steps. The sediment was resuspended in deionized water and subjected to ultrasonication (40 kHz, 300 W) for 20 minutes to facilitate layer exfoliation. After 24 hours of gravitational settling, the supernatant (containing few-layer dispersion) and the sediment (multilayer paste) were separately collected using vacuum filtration through polypropylene membranes. The samples were then dried at 60 °C under dynamic vacuum for 12 hours.

2.3 Materials characterization of Ru₂Si₂T_x powder

The morphology and structure were investigated using field-emission scanning electron microscopy (FE-SEM, Zeiss Sigma 500) and high-resolution transmission electron microscopy (HRTEM, JEOL JEM-2100F) operated at 200 kV. The surface chemistry was analyzed using X-ray photoelectron spectroscopy (XPS, Thermo Scientific K-\alpha) with Al K-\alpha radiation (1486.6 eV), calibrated to C 1s (284.8 eV).

2.4 First-principle calculations

First-principles calculations were conducted employing the Vienna Ab Initio Simulation Package (VASP) [23–25]. The exchange-correlation potential was addressed within the Generalized Gradient Approximation (GGA), utilizing the Perdew−Burke−Ernzerhof (PBE) functional [24]. A plane-wave basis with a cutoff energy of 520 eV and a \mathrm{\Gamma }-centered k-mesh with a spacing not exceeding 0.03 Å{}^{-1} were used. The structures were fully relaxed until the residual forces on all atoms were less than 0.01 eV/Å, incorporating a 15 Å vacuum layer to mitigate interlayer interactions. The influence of different vacuum layer thicknesses on the calculations is discussed in the Supporting Information (Figs. S3 and S4), and the rationale for setting a vacuum layer thickness of 15 Å is explained. Phonon dispersion spectra were computed employing the PHONOPY package [26, 27] through the Density Functional Perturbation Theory (DFPT) method. Maximally localized Wannier functions (MLWFs) were derived from ab initio bands near the Fermi level using the WANNIER90 package [28, 29]. Topological invariants such as Z_2 indices, Chern numbers, Wilson loops, and edge states were calculated from MLWFs using the WannierTools package. Among them, the edge states are calculated using the recursive Green’s function method [30, 31]. For the topological analysis of Ru₂Si₂O₂, to compensate for the underestimation of the band gap by the GGA method, we calculated the band structure of Ru₂Si₂O₂ using the HSE hybrid functional method [32]. The symmetry analysis of the band was performed using the IRVSP program [33].

3 Result and discussion

3.1 Material characterizations

Figure 1(a) illustrates the preparation principle of {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x: the yttrium (Y) layer in the sandwich-like structure of YRu₂Si₂ exhibits strong reactivity and is capable of reacting with HF as shown in the reaction equation: YRu₂Si₂ + 3HF = Ru₂Si₂ + YF₃ + 3/2H₂. The silicon (Si) and ruthenium (Ru) atomic layers remain stable in an HF solution. Consequently, by etching YRu₂Si₂ with HF, 2D materials of Ru₂Si₂ can be obtained. The specific experimental steps are detailed in the Methods section. To verify the successful synthesis of the precursor YRu₂Si₂, X-ray diffraction (XRD) characterization was performed on the precursor powder as mentioned in the Methods section. The results, displayed in Fig. 1(b), show diffraction peaks that are largely consistent with other work [34], confirming that the primary phase of the sample is YRu₂Si₂. Additionally, a few impurity peaks were observed, attributable to a Ru−Y alloy. This alloy formation is due to partial volatilization of Si during the melting process, resulting in a final ingot where the atomic ratios of Y, Ru, and Si deviate from the stoichiometric 1:2:2. Excess Y and Ru form the Ru−Y alloy which is present as an impurity in the sample. The low intensity of these impurity peaks suggests that the proportion of Ru−Y alloy impurities is significantly lower compared to that of YRu₂Si₂, thereby indicating the successful synthesis of the YRu₂Si₂ precursor.

The XRD pattern of the etched sample is shown in Fig. 1(c). Within the 2\theta range of 5^{\circ }-{15}^{\circ }, diffraction peaks are observed at {5.7}^{\circ } and {11.4}^{\circ }, corresponding to the (002) and (004) planes of the 2D material, respectively. Based on Bragg’s law (\lambda = 2dsin\theta), the interlayer spacing d is calculated to be approximately 1.55 nm. Figure 1(d) presents a scanning electron microscopy (SEM) image of the material, revealing a distinct layered morphology. The etched product exhibits a multilayer stacked structure, resembling the characteristic “accordion-like” morphology commonly observed in typical MXenes [35, 36]. This structure arises from the selective removal of the highly reactive Y layers during chemical etching, which induces interlayer expansion, while individual or few layers are not completely exfoliated and subsequently restack into this unique accordion-like form. Although YRu₂Si₂ is not strictly a MAX phase, its layered structure and etchability are analogous to those of MAX phases [3]. Therefore, this morphology can still be regarded as strong evidence for the successful preparation of a 2D material via chemical etching. Figure 1(e) shows a transmission electron microscopy (TEM) image of a thin flake, indicating that the material consists of 3−4 stacked layers, which confirms its few-layer 2D structure. Figure 1(f) displays a high-resolution TEM (HRTEM) image of the edge of a multilayer particle, where the layered boundaries are clearly visible. The measured total thickness of three layers is about 3.10 nm, corresponding to an average interlayer distance of approximately 1.55 nm between adjacent layers, consistent with the XRD results. Figure 1(g) presents the selected-area electron diffraction (SAED) pattern of the few-layer material. The square arrangement of the diffraction spots confirms a tetragonal crystal structure, which is in agreement with the structure predicted by density functional theory (DFT) calculations [Fig. 2(a)].

{\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x was synthesized through the selective etching of Y atomic layers from the bulk YRu₂Si₂ using HF etching as illustrated in Fig. 1(a). To explore possible configurations of {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x, we commenced by removing Y atoms from the YRu₂Si₂ bulk structure, which yielded Ru₂Si₂ monolayer as shown in Figs. 2(a) and (b). This derivation is consistent with the actual chemical reaction pathways. This termination-free structure is experimentally predominant and might serve as a precursor for subsequent surface terminations. To enable comparison with experimental results, we constructed a 1.55 nm vacuum layer based on the measured data and performed first-principles calculations (DFT) to fully relax the structure, obtaining the intrinsic Ru₂Si₂ without surface terminations, as shown in Figs. 2(a) and (b), and compared it with Fig. 1(g). The intrinsic termination-free monolayer Ru₂Si₂ exhibits a sandwich-like configuration with a Ru layer enclosed between two Si layers. The optimized structure crystallizes in the tetragonal system (space group P4/mmm) with lattice constant a = 4.36 Å. The red arrows in Fig. 1(g) and Fig. 2(a) indicate the Miller indices of the diffraction spots and the corresponding crystal planes, respectively. Table 1 compares the measured interplanar spacings (d-spacing) with the theoretical values obtained from DFT calculations. It can be seen that the measured values are in good agreement with the theoretical ones, demonstrating that the DFT results are consistent with the experimental observations. The phonon spectrum as shown in Fig. 2(c) shows no imaginary frequencies, confirming the dynamic stability of monolayer Ru₂Si₂. This indicates that, the experimentally observed phase corresponds to the intrinsic termination-free monolayer Ru₂Si₂, and despite partial O/F terminations on some surface regions, the underlying lattice largely retains the termination-free crystal structure. Qualitative EDS mapping, shown in Fig. 1(h), reveals the distribution of four elements: F, O, Ru, and Si. Each element is distributed relatively uniformly across the surface, suggesting a homogeneous coverage of F and O surface terminations on the Ru₂Si₂ surface. Generally, the distribution of Ru coincided with that of the other three elements in most regions. However, in the areas indicated by red arrows in Fig. 1(h), concentrations of F, O, and Si were observed while Ru was notably scarce. These findings suggest that these regions might be composed of F-doped {\mathrm{S}\mathrm{i}\mathrm{O}}_x{\mathrm{F}}_y, likely formed as impurities due to the detachment of Si atomic layers in an HF solution. Further details of the chemical bond analysis are provided in the Supporting Information [Figs. S2(a)−(d)], these experimental results demonstrate the successful preparation of the 2D material {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x (\mathrm{T} = O, F) with a tetragonal crystal system via chemical etching.

3.2 Crystal structure of monolayer and bilayer Ru₂Si₂

To explore the electronic structure of monolayer Ru₂Si₂, the band structures without and with SOC are calculated by DFT and shown in Fig. 2(d). It turns out that monolayer Ru₂Si₂ is metallic and non-magnetic. In experiment, the magnetization M of {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x with temperature as shown in Fig. S1 decreases exponentially to zero as the temperature increases, with the heating and cooling curves nearly overlapping. It indicates non-magnetic phase transition within the temperature range of 2−300 K and {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x nanosheets exhibit paramagnetism.

Experimentally, the obtained material is few-layered as shown in Fig. 1(e). To examine layer-dependent properties, we compared two bilayer stacking configurations AA{}^{\mathrm{\prime }} and AA as shown in Figs. 3(a) and (d). The AA stacking has a total free energy of −59.03 eV, lower than AA{}^{\mathrm{\prime }} stacking (−56.80 eV), indicating higher stability. Band calculations as shown in Figs. 3(b) and (e) confirm that both bilayer Ru₂Si₂ remain metallic, similar to the monolayer.

Since the etching is performed in HF solution, O and F terminations are experimentally observed on the surface. To understand their influence, we systematically computed structures with various terminations. Figures S5−S9 summarize the optimized geometries, phonon spectra, and band structures for these configurations. Furthermore, Fig. S11 and Table S1 discuss the binding energies of various possible configurations and the ground state energy, and present the thermodynamically most stable configuration.

To establish a quantitative thermodynamic basis for comparing the relative stability of different surface termination configurations, we computed the binding energies of the terminal O and F atoms, as well as the average total energy per atom, using first-principles total-energy calculations within the DFT framework. Our calculations show that among the fully oxygen-terminated structures, the Ru₂Si₂O₂(2) configuration [Fig. S11(b)] exhibits a significantly lower binding energy, indicating that the structure shown in Fig. S11(b) is thermodynamically more favorable. Among the Janus structures with oxygen termination on one side, Ru₂Si₂O(2) [Fig. S11(e)] is thermodynamically more stable. Among all configurations, the fully terminated Ru₂Si₂F₂ possesses the most negative binding energy, consistent with the high electronegativity of fluorine; however, its average total energy per atom is higher than that of the oxygen-terminated structures, suggesting that under typical synthesis conditions, the oxygen-terminated structures are overall more thermodynamically favorable. Detailed computational results are provided in Section 6 of the Supporting Information, along with Fig. S11 and Table S1. In the following sections, we focus on two representative cases: the fully O-terminated Ru₂Si₂O₂ and Ru₂Si₂O with O termination on only one side.

3.3 Topological insulator in monolayer Ru₂Si₂O₂

The fully optimized crystal structures of monolayer Ru₂Si₂O₂ with saturated oxygen terminations on both sides are shown in Figs. 4(a)−(c). It exhibits a zigzag layer arrangement with lattice constants a = 4.64 Å, b = 3.42 Å and belongs to the monoclinic space group (P{2}_1/m). The oxygen atoms are coordinated to Si and Ru with bond lengths of Si−O = 1.62 Å and Ru−O = 2.07 Å, respectively. Experimentally, the XPS analysis as shown in Fig. S2 confirms the coexistence of Ru−O and Si−O bonds, supporting the feasibility of this structure in actual samples. The phonon spectrum of the Ru₂Si₂O₂ monolayer as presented in Fig. 4(d) exhibits no imaginary frequencies, confirming its dynamic stability.

The calculated band structure of Ru₂Si₂O₂ without spin−orbit coupling (SOC) is shown in Fig. 4(e). The Dirac point due to the band inversion between conduction and valence bands is along the high-symmetry \mathrm{\Gamma }−X path at the Fermi level. When SOC is included, a bandgap of approximately 0.18 eV opens at the Dirac point as shown in Fig. 4(f). This value is comparable to that reported for HgTe/CdTe quantum wells (0.04 eV) and R-Bi bilayer (0.12 eV) [37, 38], consistent with the behavior of a topological insulator. Since the band inversion is a critical feature of topological insulators [39]. To confirm its occurrence, we calculated the orbital-projected band structure [Figs. S10(c) and (d)]. In the presence of SOC, a clear d−p band inversion between conduction and valence bands is observed at the Dirac point, further confirming the topological insulator nature of monolayer Ru₂Si₂O₂. In addition, the band structures obtained by the HSE method and the DFT+U method (with U taking values of 2, 3, and 4 respectively) are compared in Figs. S10(a) and (b). The band inversion [shown in Figs. S10(c) and (d)] and gap opening at the Dirac point are preserved in these cases, confirming the robustness of the topological phase.

To confirm the topological nature of monolayer Ru₂Si₂O₂, we examine its edge states and bulk topological invariant. The calculated spin-resolved edge spectrum by recursive Green’s function method [31] is shown in Fig. 4(g). It exhibits gapless states inside the bulk gap, connecting the valence and conduction bands. These states are spin-polarized: the red and blue colors denote spin-up (S_z = +\hslash/2) and spin-down (S_z = -\hslash/2) components, respectively. Notably, the two counterpropagating edge states possess opposite spin polarizations. Specifically, as the crystal momentum varies from the \mathrm{\Gamma } point toward +\mathrm{X}, the edge states exhibit predominantly spin-down character; conversely, when moving toward -\mathrm{X}, the spin polarization flips to spin-up. This behavior is a direct manifestation of spin-momentum locking − a hallmark of the quantum spin Hall effect − where the direction of electron motion is intimately coupled to the spin orientation, rendering the edge channels immune to backscattering from nonmagnetic impurities. We also note that at the +\mathrm{X} and -\mathrm{X} points, some impurity states appear near the Fermi level. These impurity states, visible in the edge spectrum [Fig. 4(g)], are attributed to unsaturated dangling bonds at the nanoribbon edges. Such states are localized at the edge terminations and are not protected by any bulk topological invariant. Importantly, they do not traverse the entire bulk band gap; instead, they remain confined to discrete energy windows near the Fermi level and do not connect the valence and conduction bands across the gap. Consequently, these impurity states do not form gapless conducting channels and are susceptible to localization or backscattering in the presence of edge disorder or surface passivation. In contrast, the topologically protected helical edge states-characterized by spin-momentum locking-span the full bulk gap and connect the valence and conduction bands, forming robust, dissipationless conduction pathways immune to weak disorder. To unambiguously determine its topological classification, we compute the Z_2 invariant via Wilson-loop method [40–42]. The evolution of the Wannier center \theta(k_x) along the high-symmetry cut is shown in Fig. 4(h). It exhibits a smooth \pi-phase shift, indicating that the Wannier center traverses the Brillouin zone, forming a non-contractible loop. This result unambiguously classifies the system as a strong topological insulator. This winding behavior corresponds to a nontrivial Berry phase accumulation and yields a Z_2 index of 1. The parities of the occupied states at the high-symmetry points are provided in Table S2. According to Fu−Kane criterion [43], the Z_2 invariant \nu is given by

(-1{)}^{\nu }={\displaystyle \prod _{i=1}^N{\displaystyle \prod _{n=1}^{N_{\mathrm{o}\mathrm{o}\mathrm{c}}}{\xi }_{2n}({\mathrm{\Gamma }}_i),}}

where {\xi }_{2n}({\mathrm{\Gamma }}_i)=\pm 1 denotes the parity eigenvalue of the 2n-th occupied band at the TRIM point {\mathrm{\Gamma }}_i. For Ru₂Si₂O₂, the computed product yields (-1{)}^{\nu } = −1, corresponding to \nu = 1. Together, the presence of gapless helical edge states and the quantized Wilson-loop winding establish monolayer Ru₂Si₂O₂ as a 2D topological insulator hosting quantum spin Hall effect.

3.4 Type-II Weyl semimetal in monolayer Ru₂Si₂O

We now turn to the monolayer Ru₂Si₂O, which features O termination on only one side. Its fully relaxed crystal structure is shown in Figs. 5(a)−(c) adopts an orthorhombic lattice with space group Pmm2 and constants a = 2.89 Å and b = 5.45 Å. The phonon spectrum in Fig. 5(d) confirms its dynamic stability. The structure preserves mirror symmetries in the x and y directions, denoted as M_y: (x, y, z) \to (x, −y, z) and M_x: (x, y, z) \to (−x, y, z). These symmetries, together with TRS, enforce a total Chern number of zero and constrain the emergent topological nodes. While strict Weyl points require dispersion along k_z, 2D systems with similar symmetry protection can host robust, paired Dirac points that evolve into paired Weyl points under SOC [44, 45].

As shown in Fig. 5(e), the band structure without SOC exhibits two massless Dirac points near the Fermi level, labeled DP1 and DP2. To elucidate the physical origin of DP1 and DP2 in monolayer Ru₂Si₂O, we performed a symmetry analysis of the electronic bands near these points using the IRVSP program, which determines the irreducible representations (irreps) of the eigenstates at high-symmetry points and along high-symmetry lines. The bands at DP1 and DP2 are protected by the M_x Mirror symmetry. Under this operation, the Bloch states transform with eigenvalues \pmi due to the combination of mirror reflection and spin−orbit coupling. The matrix representation of M_x in the spinor basis is given by -\mathrm{i}\left(\begin{array}{cc}0& 1\\ 1& 0\end{array}\right). where the prefactor −i ensures the proper fermionic transformation. The eigenvalues of M_x for bands in the vicinity of DP1 and DP2 are shown in Fig. 5(e). Critically, the two bands that cross at each Dirac point carry distinct M_x eigenvalues-one with eigenvalue +i and the other with −i. Because states with different mirror eigenvalues cannot hybridize, the crossing is symmetry-protected against gap opening, provided that M_x remains unbroken. This protection mechanism is analogous to that of Dirac points in other 2D materials with mirror symmetry. Thus, DP1 and DP2 are identified as mirror-symmetry-protected Dirac points. When SOC is included, these Dirac points gap into type-II Weyl points WP1 and WP2 as shown in Fig. 5(f), characterized by strongly tilted paired band crossings. The 3D band structure around WP1 is plotted in Fig. 6(a). Constant-energy surfaces at E = −0.041 eV and 0.039 eV intersect the bands along open contours as shown in Fig. 6(b), confirming the type-II classification. Four symmetry-related pairs of Weyl points appear in the Brillouin zone at (\pm0.05, \pm0.788) Å{}^{-1} and (\pm0.063, \pm0.831) Å{}^{-1}, generated by mirror operations M_x and M_y. Wilson-loop calculations yield Chern numbers of \pm1 for these nodes as shown in Fig. 6(b), verifying their nontrivial topology and opposite chirality.

Similarly, WP2 is analyzed via its 3D band dispersion as shown in Fig. 6(c). Located near E = −0.110 eV, it lies close to the Fermi level and emerges from a Dirac point protected by the k_x = 0 mirror plane. Under SOC, it splits into two pairs of Weyl points symmetric about k_y = 0, positioned at (\pm0.021, \pm0.274) Å{}^{-1}. The open contours in the constant-energy surface as shown in Fig. 6(d) and the calculated Chern numbers of \pm1 confirm that WP2 also belongs to the type-II class. Taken together, the symmetry analysis, the emergence of tilted band crossings, and the quantized Chern numbers establish monolayer Ru₂Si₂O as a 2D material hosting mirror-protected type-II Weyl points.

To investigate the microscopic origin of the topological phase transition, we adopted a comparative approach to decouple the effects of structural distortion from those of chemical modification. Specifically, we removed the terminal oxygen atoms from the fully relaxed topological insulator (Ru₂Si₂O₂) and type-II Weyl semimetal (Ru₂Si₂O) configurations, while retaining the underlying Ru₂Si₂ lattice geometry as modified by the presence of these terminal atoms. We then recalculated the electronic band structures of these “termination-removed” systems, both without and with SOC, and compared them with the original structures containing the terminal atoms. The results for the topological insulator and Weyl semimetal cases are presented in Figs. S12 and S13, respectively.

We find that the topological phase transition originates from the structural distortion induced by the introduction of oxygen atoms-namely, the transition from a tetragonal lattice to a lower-symmetry lattice-rather than from the chemical presence of oxygen atoms per se. Specifically, for the topological insulator Ru₂Si₂O₂, the structure transforms from a tetragonal lattice (space group P4/mmm) to a monoclinic lattice (space group P{2}_1/m); for the type-II Weyl semimetal Ru₂Si₂O, it transforms to an orthorhombic lattice (space group Pmm2). Minor differences in the band dispersion near the Fermi level, particularly in the energetic positions of the bands, are attributable to charge transfer between the oxygen terminations and the underlying Ru₂Si₂ substrate (see Fig. S14). A more detailed discussion is provided in Section 7 of the Supporting Information.

4 Conclusion

In summary, we have systematically investigated the structural, electronic, and topological properties of the novel 2D material {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_x (x = 1, 2) through a synergistic combination of chemical synthesis, experimental characterization, and first-principles calculations. The material was successfully synthesized via selective HF etching of the YRu₂Si₂ precursor, yielding few- to multilayer sheets with an accordion-like morphology and confirming the presence of O/F surface terminations. Our comprehensive theoretical study of five representative termination configurations reveals that surface oxygen coverage acts as a powerful knob for engineering distinct topological phases. Specifically, fully oxygen-terminated Ru₂Si₂O₂ is identified as a strong topological insulator (Z_2 = 1) with a SOC-induced band gap of 0.18 eV and protected helical edge states. The monolayer Ru₂Si₂O with oxygen termination on only one side hosts multiple pairs of mirror-symmetry-protected type-II Weyl points near the Fermi level, characterized by open Fermi pockets and quantized Chern numbers.

These results establish {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{O}}_x as a rare example of a 2D material platform in which topological states-from topological insulator to Weyl semimetal-can be selectively accessed via surface chemistry. The compatibility of this material with solution-based etching, along with its ambient stability, further enhances its potential for scalable device integration. Although a metal-to-insulator transition in {\mathrm{R}\mathrm{u}}_2{\mathrm{S}\mathrm{i}}_2{\mathrm{T}}_x is theoretically predicted, its experimental verification remains challenging at present. This difficulty arises from two main factors. First, synthesis challenges: the material is prepared via aqueous reactions, which hinders precise control over the types and distribution of surface terminations. Consequently, obtaining high-purity single-phase samples suitable for reliable transport measurements remains a significant challenge. Second, instrumental limitations: the current experimental setup in our laboratory does not yet support the necessary transport and spectroscopic measurements. Addressing these challenges represents a key goal for future research.

Overall, this work not only expands the family of etchable 2D materials into silicide-based systems but also provides a chemically tunable platform for exploring topological phase transitions and developing future topological electronic and spintronic devices.

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