The overall concept of employing topological quantum materials for energy storage applications is illustrated in Figure 1A. This schematic highlights their potential across two distinct applications: metal-ion battery anodes and Na-S hosts. The four monolayers V₂MoS₄, V₂MoSe₄, V₂WS₄, and V₂WSe₄ obey the molecular formula V₂AB₄ and the space group P-42m. Each unit cell consists of three layers: a central V₂A layer sandwiched between two chalcogen layers. Four chalcogen atoms coordinate each V and A atom to form tetrahedral units, as shown in Figure 1A. The optimized lattice constants for V₂MoS₄, V₂MoSe₄, V₂WS₄, and V₂WSe₄ are 5.72, 5.83, 5.74, and 5.82 Å, respectively, increasing from S to Se due to the larger atomic radius of Se. However, the W and Mo atoms contribute only a minor change due to their nearly identical atomic radii. In addition to structural characterization, the thermal and dynamical stability of V₂MoS₄, V₂MoSe₄, V₂WS₄, and V₂WSe₄ monolayers are investigated. Thermal stability was verified using AIMD simulations at 300 K and 500 K for 5 ps, as shown in Figure 1B and Supplementary Figures 1-3 of the Supplementary Materials. These simulations demonstrate that all monolayers maintain structural integrity with no bond breaking or phase transitions, confirming excellent thermal stability. Phonon dispersion calculations along the high-symmetry path reveal no imaginary frequencies across the entire Brillouin zone for all four materials, confirming their dynamical stability as depicted in Figure 1C. Overall, these materials possess dynamic, structural, and thermal stability, indicating potential for further electronic and battery applications.

In addition, the electronic band gaps are investigated by calculating spin-polarized band structures with spin-orbit coupling (SOC) along high-symmetry paths in the Brillouin zone to examine the SOC-induced evolution of the electronic states [Figure 1D]. For V₂MoS₄, V₂MoSe₄, V₂WS₄, and V₂WSe₄, the band structures without SOC exhibit several band crossings near the Fermi level, mainly associated with spin-polarized V_d states hybridized with A-site (A = Mo, W) d states, where no obvious band gap is observed (see Supplementary Figure 4 in Supplementary Materials). After the inclusion of SOC, these degeneracies are lifted and finite gaps open at the high-symmetry points in Figure 1D. This gap opening originates from the SOC-induced splitting of the spin-polarized quadratic band touching of the degenerate V d_xz/d_yz orbitals, together with the band inversion between these Vd states and the A-site d states, producing a topologically nontrivial insulating electronic structure. These band-structure features spin-polarized d-orbital band crossings, band inversion between the V d_xz/d_yz and A-site (Mo/W) d orbitals, and the SOC-driven gap opening are characteristic of the pristine V₂AB₄ monolayers, whose nontrivial topological nature has been established in a prior study^[35]. The high stability and favorable electronic structure position the V₂AB₄ vanadium chalcogenides as compelling candidates for ion-battery applications.

The suitability of V₂AB₄ surfaces as high-rate anodes was evaluated by systematically identifying three energetically favorable adsorption sites (a, b, and c) and examining their interactions with Na⁺ and K⁺ ions. The adsorption sites are defined as follows: site-a is located directly above the chalcogen B atom (S or Se), site-b is positioned above the A atom (Mo or W) coordinated by neighboring chalcogen atoms, and site-c is situated directly atop a V atom. Na⁺ and K⁺ atoms were initially placed approximately 2.5 Å above the monolayer plane, and the entire system was fully relaxed to determine equilibrium geometries and adsorption energies as depicted in Figure 2A. Adsorption energies for Na⁺ and K⁺ ions on all four V₂AB₄-type materials were calculated including van der Waals (vdW) corrections, with the corresponding values presented in Figure 2B. Site-a was identified as the most stable adsorption site for both Na⁺ and K⁺ ions, with adsorption energies ranging from -1.19 eV to -1.36 eV for Na⁺ and -1.36 eV to -1.83 eV for K⁺. Site-b was the second most stable site, exhibiting adsorption energies approximately 0.25-0.35 eV higher (less negative) than those of site-a, while site-c was the least favorable. The preference for site-a arises from its optimal coordination environment for the ions. At this site, both Na⁺ and K⁺ lie equidistant from six neighboring chalcogen atoms (three from the top layer and three from the bottom layer). This configuration provides the maximum possible electrostatic stabilization and charge transfer from the alkali metal to the substrate.

Improved ion cycling stability is aided by rapid ion flux, which helps limit structural degradation during charge and discharge. The diffusion kinetics of Na⁺ and K⁺ ions on the V₂AB₄ (A = Mo/W, B = S/Se) monolayers are systematically studied by the CI-NEB method. Figure 2A illustrates that the most favorable diffusion pathway involves in-plane migration between two neighboring sites a through the transition site. Figure 2C presents the corresponding CI-NEB energy profiles for Na⁺ and K⁺ diffusion across V₂MoS₄, V₂MoSe₄, V₂WS₄, and V₂WSe₄, respectively. For Na⁺ ions, the migration barrier is found to be 0.229, 0.216, 0.236, and 0.257 eV for V₂MoS₄, V₂MoSe₄, V₂WS₄, and V₂WSe₄, respectively. These values are benchmarked against reported Na⁺ ion diffusion barriers of representative 2D anode candidates such as BiC (0.217)^[54], Si₃C (0.34 eV)^[55], C₁₈ (0.46)^[56], Ti₃C₂ Mxene (0.09 eV)^[57] VS₂ (0.085 eV)^[58], h-BAs (0.248 eV)^[59], B-doped g-CN/BC₃N₃ (0.73 eV)^[60] CrSTe (0.32 eV)^[61], Ti₂PS₂ (0.1 eV)^[62], and TiS₂ (0.15 eV)^[63]. In contrast, the energy barriers for K ions are consistently lower, at 0.162, 0.1612, 0.164, and 0.20 eV, respectively. Sodium generally exhibits a higher diffusion barrier compared to potassium. This difference is primarily due to potassium’s larger atomic radius, which leads to weaker interactions with the host framework. Moreover, potassium ions are usually adsorbed farther from the host surface, reducing electrostatic adsorption and increasing ion mobility.

Charge transfer from the metal ion to the host is important because it stabilizes ion storage and improves anode performance. To elucidate the interaction mechanism between Na⁺/K⁺ ions and the host materials, the charge density difference (Δρ) was calculated using the Equation (2) as shown below^[64].

(2) $$ \Delta \rho=\rho_{{V}_{2} {AB}_{4}+N a / K}-\rho_{{V}_{2} {AB}_{4}}-\rho_{N a / K} $$

where $$ \rho_{{V}_{2} {AB}_{4}+{Na} / K} $$ is the charge density of the system with the adsorbed Na⁺ or K⁺ ion, $$ \rho_{{V}_{2} {AB}_{4}} $$ is the charge density of the pristine monolayer, and ρ_Na/K is the charge density of the isolated ion. The charge density difference for Na⁺ and K⁺ adsorption on V₂AB₄ is shown in Figure 2D and Supplementary Figure 5. The Δρ maps reveal a large redistribution of charge upon the adsorption of alkali ions. Electron density depletion (cyan regions) is observed around the alkali-metal ions, whereas electron accumulation (yellow regions) occurs in the interstitial space between the ions and the surrounding chalcogen atoms. The amount of charge transfer was further quantified using Bader charge analysis; the charge transferred from the Na⁺ and K⁺ ions to four anode materials is approximately 0.82-0.84 e, respectively. This pronounced charge transfer reflects the cationic nature of the adsorbed alkali atoms and is beneficial for reversible ion storage. All four V₂AB₄ materials exhibit qualitatively similar charge-density difference patterns. The result suggests that these materials can accommodate different alkali ions via a common physicochemical mechanism, highlighting their promise as versatile hosts for alkali-ion anodes. To assess the impact of Na⁺ and K⁺ ion adsorption on the electronic properties, the projected density of states (PDOS) of single Na⁺/K⁺ ion-adsorbed V₂AB₄ systems was calculated, as shown in Figure 2E and Supplementary Figure 6. This behavior results from electron donation to the host lattice, causing the Fermi level (E_F) to shift into a region characterized by a higher density of transition-metal d states. The PDOS analysis reveals that the states in the vicinity of E_F show a predominant contribution from V 3d orbitals, along with further contributions from A-site d orbitals (Mo 4d or W 5d) and a small contribution from B-site chalcogen p orbitals (S 3p or Se 4p).

The electrochemical behavior of V₂AB₄ monolayers is schematically depicted in Figure 3A. In the figure above, reversible ion insertion and extraction at the anode and cathode, along with ion transport across the separator, are shown during the charge/discharge process. This schematic illustration provides a basic overview of the working principle of rechargeable batteries and a conceptual basis for evaluating the electrochemical performance of the proposed materials. Based on this framework, the electrochemical performance of electrode materials is evaluated by measuring their ion-storage capacity and open-circuit voltage (OCV). The studied layered topological material exhibits a high ion-storage capacity for Na⁺ and K⁺ ions, underscoring its potential for anodic energy storage applications. The ion-storage capability of V₂AB₄ (A = Mo or W, B = S or Se) monolayers is systematically evaluated by progressively increasing the concentration of Na⁺ or K⁺ ions in the host materials. The binding energies of Na⁺ and K⁺ ions decrease with increasing ion concentration, primarily due to repulsive interactions between adjacent ions. As depicted in Figure 3B, all systems exhibit negative binding energies over the entire adsorption range; thus, Na⁺/K⁺ uptake is thermodynamically favorable at high concentrations. The theoretical specific capacity was calculated according to the following Equation^[65]:

(3) $$ C=\frac{n F}{3.6 M} $$

where n is the number of adsorbed Na⁺/K⁺ atoms, F is Faraday’s constant, and M is the molar mass of the pristine host material. Based on the maximum loading of Na⁺ atoms, the Na⁺ ion capacities are calculated to be 1,151 mAh g^-1 for V₈Mo₄S₁₆, 730 mAh g^-1 for V₈Mo₄Se₁₆, 907 mAh g^-1 for V₈W₄S₁₆, and 624 mAh g^-1 for V₈W₄Se₁₆. These values are substantially higher than that of hard carbon (~300 mAh g^-1)^[66] , the standard commercial sodium-ion anode, and are placed in comparison with computationally predicted 2D anodes evaluated under similar monolayer, full-surface-adsorption assumptions, including BiC (485 mAh g^-1)^[54], Si₃C (1,115 mAh g^-1)^[55], C₁₈ (991.32 mAh g^-1)^[56], Ti₃C₂ Mxene (351.8 mAh g^-1)^[57], VS₂ (232 mAh g^-1)^[58], h-BAs (522 mAh g^-1)^[59], B-doped g-CN/BC₃N₃ (603.30 mAh g^-1)^[60] (CrSSe/CrSTe/CrSeTe: 260/198/177 mAh g^-1)^[61], Ti₂PS₂ (842 mAh g^-1)^[62], and TiS₂ (479 mAh g^-1)^[63]. We note that these capacities represent ideal upper bounds derived from full monolayer coverage; the practically accessible capacity is expected to be lower owing to interlayer restacking, reduced electrochemically accessible surface area, irreversible adsorption at strong-binding sites, and electrode-level mass-loading constraints. The structural stability of fully sodiated and potassiated V₂AB₄ monolayers was further verified by AIMD simulations at maximum ion loading. The structures remained intact at high ion concentrations, without bond breaking or severe distortion, as shown in Supplementary Figure 7. Moreover, PDOS calculations for V₂AB₄ (A = Mo, W; B = S, Se) monolayers upon full Na⁺/K⁺ adsorption show a substantial increase in the density of states at the Fermi level, suggesting enhanced electrical conductivity [Supplementary Figure 8]. This is attributed to the strong charge transfer from Na⁺/K⁺ atoms to the substrate and the consequent contribution of alkali-metal states near the Fermi level, which increases the carrier density and promotes electronic conduction.

Another important parameter for battery operation is the OCV. The OCV during Na/K insertion is obtained using the following relation^[67]:

(4) $$ V=-\frac{E_{{Mx}_{2} {V}_{2} {AB}_{4}}-E_{{{{M}_{x1}}} {V}_{2} {AB}_{4}}-\left(x_{2}-x_{1}\right) E_{M}}{\left(x_{2}-x_{1}\right) e} $$

where $$ E_{{M}_{{x2}}} {V}_{2}{AB}_{4} $$, $$ E_{{M}_{{x1}}}{V}_{2}{AB}_{4} $$ and EM are the total energies of $$ {M}_{x2}{V}_{2}{AB}_{4} $$, $$ {M}_{x1}{V}_{2}{AB}_{4} $$ and E_M is the energy per metal atom in the bulk respectively. As shown in Figure 3C, all V₂AB₄ monolayers exhibit a step-like voltage profile with increasing Na/K ion concentration.

The OCV shows a similar decreasing trend as ion coverage increases, consistent with the variation observed in the binding energies. The Na⁺ ion systems operate at lower voltages than their K-ion counterparts, which is generally favorable for anode applications, as it can lead to higher full-cell voltage and energy density. Overall, the combination of low diffusion barriers [Figure 3D] and high theoretical capacities [Figure 3E], relative to representative 2D anode materials, highlights the V₂AB₄ monolayers as promising anodes for next-generation Na⁺ and K⁺ ion batteries.

To further clarify the interfacial behavior of the V₂AB₄ monolayers in the Na⁺/K⁺ ion-anode environment, we analyzed their interactions with representative electrolyte species using adsorption-energy calculations.

Figure 4A schematically summarizes the electrolyte species considered and their modeled adsorption on the V₂AB₄ surfaces. The adsorption strength between electrolyte solvents/salts and the electrode surface provides useful information about molecular-level interfacial interactions. Accordingly, we evaluated the adsorption behavior of carbonate solvents and common Na⁺/K⁺ salts on the V₂AB₄ monolayers in the Na⁺/K⁺ ion-anode environment. The calculated adsorption energies are shown in Figure 4B. The adsorption energy values indicate favorable adsorption interactions between the electrolyte species and the V₂AB₄ surfaces, indicating strong molecular-level affinity in the optimized configurations. Figure 4C and Supplementary Figures 9-12 illustrate the optimized structural configurations of typical carbonate solvents, including diethyl carbonate (DEC), ethylene carbonate (EC), and fluoroethylene carbonate (FEC), and electrolyte salts, including sodium bis(fluorosulfonyl)imide (NaFSI), sodium hexafluorophosphate (NaPF₆), potassium bis(fluorosulfonyl)imide (KFSI), and potassium hexafluorophosphate (KPF₆), respectively, on V₂AB₄ (A = Mo/W, B = S/Se) monolayers. These adsorption-energy results describe the molecular-level interfacial interactions between V₂AB₄ and representative electrolyte species in Na⁺/K⁺ ion anode applications.

In this section, we discuss electrochemical sodium-sulfur (Na-S) applications, particularly the reversible conversion of sulfur via sodium polysulfide species during charging and discharging. The reactions at the sulfur cathode are governed by ion transport, electron transfer, and phase conversion processes, which strongly influence reaction kinetics, cell-cycling stability, and sulfur utilization. In addition to anodic applications, the potential of V₂AB₄ monolayers as sulfur hosts is evaluated by examining the anchoring of sulfur and sodium polysulfide species, including elemental S₈, long-chain sodium polysulfides Na₂S₈, Na₂S₆, and Na₂S₄, and short-chain species Na₂S₂ and Na₂S. During discharge, these long-chain sodium polysulfides can dissolve in the liquid electrolyte, leading to the shuttle effect and capacity decay. A strong interaction between the host and polysulfides is necessary to immobilize these species and enable reversible reactions. For V₂AB₄ monolayers, adsorption energy data (see Figure 5A) indicate that all Na₂S_n species are strongly adsorbed on all four topological materials. Specifically, the adsorption energies of Na₂S₆ and Na₂S₈ exceed 1.5 eV, which is sufficient to prevent shuttling. The higher adsorption energies on S-based materials are attributed to the greater electronegativity of sulfur atoms, which results in stronger interactions with polysulfides. In contrast, Se-containing materials exhibit moderate adsorption energies that remain suitable for anchoring. However, excessively strong anchoring can cause a sluggish discharge process. Short-chain species demonstrate stronger chemical interactions, whereas long-chain species exhibit predominantly physical interactions. The adsorption configurations of Na₂S_n for all structures are shown in Supplementary Figures 13-16. The binding energies of these soluble species with common solvents, namely 1,2-dimethoxyethane (DME) and 1,3-dioxolane (DOL), were also calculated. The ether-based solvents (DME and DOL) considered here correspond specifically to the Na-S configuration, consistent with their standard use in Na-S chemistry. The interaction between soluble polysulfides and solvents is weaker than that with the V₂AB₄ monolayers. Collectively, the binding energies indicate strong binding and reversible conversion capability. The V₂AB₄ monolayers thus effectively immobilize sodium polysulfides, prevent their dissolution, and show significant promise as hosts for Na-S batteries.

The interaction mechanism between Na₂S_n clusters and V₂AB₄ monolayers was investigated using Bader charge analysis, as shown in Figure 5B. The results reveal a clear trend of increasing charge transfer with decreasing polysulfide chain length, ranging from approximately 0.15-0.33 e for long-chain Na₂S₈ and increasing to 0.84-0.91 e for the fully reduced Na₂S across the V₂AB₄ systems. This indicates progressively stronger chemical interactions between the V₂AB₄ substrates and short-chain species. To further elucidate this behavior, charge-density difference plots are presented in Figure 5C and Supplementary Figures 17-20. These plots demonstrate a distinct charge distribution at the interface after adsorption. Charge accumulation occurs primarily at the surface atoms of V₂AB₄, while charge depletion is concentrated within the Na₂S_n clusters, indicating electron transfer from the sodium polysulfides to the substrates. This charge redistribution is considerably more pronounced for short-chain species than for long-chain species. Overall, the charge-density difference and Bader charge analyses confirm that V₂AB₄ monolayers exhibit physicochemical interactions with sodium polysulfide intermediates, which are essential for suppressing the shuttle effect and improving the cycling stability of Na-S batteries. To further investigate the electronic properties of Na₂S_n species adsorbed on the V₂AB₄ substrates, the PDOS was calculated and analyzed, as presented in Supplementary Figures 21-24. The electronic states near the Fermi level are dominated by V-3d and Mo/W-d orbitals, with contributions from S/Se-p states, indicating interfacial coupling and charge redistribution upon adsorption. Across all configurations, the continuous states around the Fermi level confirm the metallic character of the adsorbed system. Overall, these results confirm effective electronic coupling between the host material and the Na₂S_n species, which facilitates redox reactions in Na-S batteries.

Next, the catalytic decomposition barrier of the discharge product Na₂S is calculated using the CI-NEB method^[52,68]. During charging of Na-S batteries, the final insoluble product, Na₂S, exhibits low electronic conductivity and a high decomposition energy barrier, thereby increasing overpotential and slowing the reaction rate. The electrochemical performance of the Na-S battery system is governed by the decomposition kinetics of sodium sulfide (Na₂S), which involve cleavage of Na-S bonds and migration of Na⁺ ions across the surface. The decomposition reaction, *Na₂S → *NaS + Na⁺ + e^-, proceeds through cleavage of a Na-S bond at the adsorption site, followed by migration of the released Na⁺ ion to a neighboring site. The decomposition energy barriers for Na₂S adsorbed on the V₂AB₄ monolayers are shown in Figure 5D. The calculated decomposition energy barriers are 0.382, 0.901, 0.361, and 0.915 eV for V₂MoS₄, V₂MoSe₄, V₂WS₄, and V₂WSe₄, respectively. These values are significantly lower than the decomposition barrier for isolated Na₂S in the gas phase and are comparable to, or lower than, those of many previously reported Na-S host materials, including Cr@NG (1.54 eV)^[69], Fe@NG (1.16 eV)^[69], COP (0.68 eV)^[70] Co@NG (1.17 eV)^[69], V@WSe₂ (0.99 eV)^[71], Fe@MoS₂ (1.08 eV)^[72], Ni@MoS₂ (1.34 eV)^[71], HfTiTe₄ (0.917)^[16], ZrTiTe₄ (0.89)^[16], HfZrTe₄ (0.83)^[16], Mo₂TiC₂S₂ (1.59 eV)^[73], Mo₂TiC₂O₂ (1.67 eV)^[73], MnN₄/C (1.52 eV), and YN₄/C (1.52 eV)^[74]. The lowered energy barriers suggest that the V₂AB₄-type surfaces can activate the oxidative decomposition of Na₂S during charging. Figure 5E schematically illustrates that V₂AB₄ monolayers serve as effective hosts for Na-S cathodes by strongly anchoring sodium polysulfides and promoting their catalytic redox conversion. During cycling, these monolayers suppress the polysulfide shuttle effect through robust adsorption and surface catalysis. In addition, enhanced electron transfer and rapid Na⁺ diffusion kinetics improve reaction efficiency, sulfur utilization, and the overall electrochemical performance of Na-S batteries. Finally, the conversion of sulfur on V₂MoSe₄, V₂MoS₄, V₂WS₄, and V₂WSe₄ monolayers involves multiple reaction steps, starting from sulfur crown (S₈) and ultimately reducing to the short-chain sulfide Na₂S. The overall sulfur reduction reaction during the discharge process of Na-S batteries can be described as a 16-electron conversion^[53]:

(5) $$ S_{8}+16 \mathrm{Na}^{+}+16 e^{-} \rightarrow 8 \mathrm{Na}_{2} \mathrm{S} $$

The SRR with elementary steps is given below (* denotes the adsorbed species):

(6) $$ S_{8}+16 \mathrm{Na}^{+}+16 e^{-} \rightarrow 8 \mathrm{Na}_{2} \mathrm{S} $$

(7) $$ ^{*}\mathrm{Na}_{2} \mathrm{S}_{8} \rightarrow \mathrm{^{*}Na}_{2} \mathrm{S}_{6}+1 / 4 \mathrm{S}_{8} $$

(8) $$ ^{*}\mathrm{Na}_{2} \mathrm{S}_{6} \rightarrow \mathrm{^{*}Na}_{2} \mathrm{S}_{4}+1 / 4 \mathrm{S}_{8} $$

(9) $$ ^{*}\mathrm{Na}_{2} \mathrm{S}_{4} \rightarrow \mathrm{^{*}Na}_{2} \mathrm{S}_{2} +1 / 4 \mathrm{S}_{8} $$

(10) $$ ^{*}\mathrm{Na}_{2} \mathrm{S}_{2} \rightarrow \mathrm{^{*}Na}_{2} \mathrm{S} +1 / 8 \mathrm{S}_{8} $$

The Gibbs free-energy change of each elementary step was calculated using Equation (1), and the resulting profiles are presented in Figure 5F. Initially, the discharge process converts S₈ into a series of soluble sodium polysulfides, including Na₂S₈, Na₂S₆, and Na₂S₄, which are subsequently reduced to short-chain molecules (Na₂S₂) and ultimately to the insoluble product Na₂S. The Gibbs free-energy profile for the conversion of S₈ to Na₂S on V₂AB₄ monolayers provides insight into the reaction mechanism and catalytic properties. The reduction of S₈ to Na₂S₈ is highly exergonic for all materials, indicating that adsorption and activation of sulfur species occur spontaneously. The reaction step with the largest positive Gibbs free-energy change (ΔG) is considered the rate-limiting step of the sulfur reduction reaction. The calculated maximum Gibbs free-energy changes (ΔG) for V₂MoSe₄, V₂MoS₄, V₂WS₄, and V₂WSe₄ are 0.401, 0.55, 0.450, and 0.672 eV, respectively. These findings show that all V₂AB₄ monolayers possess comparable thermodynamic favorability for sulfur reduction. The catalytic performance is further evaluated by comparing it with a wide range of previously reported Na-S electrocatalysts. The rate-limiting step for sulfur reduction on V₂MoSe₄ (0.401 eV) is substantially lower than those of Co-V@N-C (1.11 eV)^[75], Cr-V@N-C (2.09 eV)^[75], AP-C^[76] (0.88), ZP-C (0.80)^[76], AZP-C (0.75)^[76], Cr-Cr@N-C (2.09 eV)^[75], and V-V@N-C (2.14 eV)^[75], and is also lower than Fe-Co/NC (0.65 eV)^[77], Co/NC (0.70 eV)^[77], and Fe/NC (0.73 eV)^[77]. Additionally, it outperforms transition-metal carbide systems such as Mo₂TiC₂S₂ (0.85 eV)^[73], Mo₂TiC₂O₂ (1.24 eV)^[73], and Mo₂C (0.92 eV)^[78]. These findings demonstrate that V₂AB₄ monolayers possess highly competitive catalytic activity for both sulfur reduction and Na₂S decomposition, positioning them among the most efficient Na-S electrocatalysts.