We present first-principles results on monolayer (ML) and bulk titanium carbide (TiC) exhibiting dual topological characteristics: a quantum spin Hall insulator state in two-dimensional ML and a type-II Dirac semimetal state in its three-dimensional bulk form. The nontrivial nature of ML TiC is confirmed through the calculation of a Z2 invariant, spin Hall conductivity, and edge states. The edge band structure of ML TiC displays a single pair of gapless edge states at the 𝑀 point. The insulating topological phase in ML TiC is driven by a band inversion around the 𝑀 point involving Ti-𝑑 orbitals, with a nontrivial band gap of 0.47 eV. Our findings also indicate that ML TiC possesses excellent dynamical and thermal stability. Moreover, the bulk, ML hollow sphere arrays, and a 4-nm-thick film of TiC have already been synthesized, suggesting the high feasibility of the experimental synthesizing of ML TiC. On the other hand, we demonstrate that the bulk TiC hosts both a type-II Dirac cone and a topological nodal surface without spin-orbit coupling, protected by a combined symmetry of inversion and time reversal. The presence of spin-orbit coupling removes the nodal surface while preserving the type-II Dirac cone. Surface states connecting bulk Dirac nodes in bulk TiC can be readily observed, making the surface characteristics easily detectable in experiments.

We present first-principles insights into the electrical and electrochemical properties of Cu2N, a newly synthesized two-dimensional material that features a planar, checkerboard lattice structure [Hu et al., Nano Lett. 2023, 23 (12), 5610–5616]. We evaluate the suitability of monolayer Cu2N as an anode material for Li and Na-ion batteries by examining its storage capacity, diffusion barrier, open-circuit voltage (OCV), volume expansion, and the impact of defects on its electrochemical performance. The monolayer Cu2N demonstrates a storage capacity of 379.88 mAh.g−1 for both Li and Na, comparable to that of commercial graphite for Li (372 mAh.g−1) and significantly higher for Na (less than 35 mAh.g−1). The migration barriers for Li and Na are found to be 0.1 eV and 0.01 eV, respectively, substantially lower than those theoretically reported for commercial anodes TiO2 (0.4–1.0 eV) and graphite (∼0.4 eV), which imply that monolayer Cu2N demonstrates excellent charge/discharge capabilities. Moreover, the volume growth of monolayer Cu2N is 4.14 % with maximal Li adsorption, which is 2.4 times less than graphite. The analysis of vacancy defects reveals a significant enhancement in the binding energies of Li and Na atoms, accompanied by minimal changes in diffusion barriers. Since monolayer Cu2N has already been successfully synthesized, these findings would pave the way for large-scale experimental fabrication of monolayer Cu2N as a battery anode.

Two-dimensional Dirac materials have stimulated substantial research interest as binder-free anodes in metal-ion batteries, owing to their ultrahigh electronic conductivity, large specific area, and higher energy density. Here, using first-principles density functional theory calculations, we have investigated the feasibility of monolayer TiC as a potential anode material for Li/Na-ion batteries. The results indicate that monolayer TiC exhibits excellent dynamical and thermal stability. The electronic structure of monolayer TiC shows semimetallic characteristics with a Dirac cone at the M high symmetry point and the formation of Ti or C vacancies transforms the Dirac cone into a nodal loop or a nodal surface, respectively. Thus, monolayer TiC possesses superior electrical conductivity, which can be further enhanced by the formation of Ti or C vacancies in the material. Furthermore, the calculated adsorption energy values of -0.85 and -0.46 eV for Li-ion and Na-ion, respectively, indicate that Li/Na atom adsorption over monolayer TiC is a favorable process. The density of states plots show that after the adsorption of a single Li/Na atom, monolayer TiC maintains its metallic state, which is advantageous for the diffusion of stored electrons. Most remarkably, monolayer TiC exhibits energy densities of 2684 and 2015 mWh/g for Li and Na, respectively, which are significantly higher than commercial graphite and most other 2D anode materials. The fully loaded TiC anode exhibits excellent cycle stability with volume expansions as low as 0.13 and 0.11%, for Li and Na, respectively. Furthermore, an ultrafast diffusivity with low energy barriers of 0.02 and 0.10 eV is found in monolayer TiC for Li-ion and Na-ion, respectively, which suggests that it has an excellent charge/discharge capability. These exceptional properties make monolayer TiC an excellent candidate as an anode material for Li-ion and Na-ion batteries. Finally, SiC(111) has been proposed as a candidate substrate for monolayer TiC due to its minimal lattice mismatch.

We have used density functional theory simulations to explore the topological characteristics of a new MXene-like material, V4C3, and its oxide counterpart, assessing their potential as anode materials for Mg-ion batteries. Our research reveals that V4C3 monolayer is a topological type-II nodal line semimetal, protected by time reversal and spatial inversion symmetries. This type-II nodal line is marked by unique drumhead-like edge states that appear either inside or outside the loop circle, contingent upon the edge ending. Intriguingly, even with an increase in metallicity due to oxygen functionalization, the topological features of V4C3 remain intact. Consequently, the monolayer V4C3 has a topologically enhanced electrical conductivity that amplifies further upon oxygen functionalization. During the charging phase, a remarkable storage concentration led to a peak specific capacity of 894.73 mAh g−1 for V4C3, which only decreases to 789.33 mAh g−1 for V4C3O2. When compared to V2C, V4C3 displays a significantly lower specific capacity loss due to functionalization, demonstrating its superior electrochemical properties. Additionally, V4C3 and V4C3O2 exhibit moderate average open-circuit voltages (0.54 V for V4C3 and 0.58 V for V4C3O2) and energy barriers for intercalation migration (ranging between 0.29–0.63 eV), which are desirable for anode materials. Thus, our simulation results support V4C3 potential as an efficient anode material for Mg-ion batteries.

The coexistence of non-trivial topology and superconductivity in a material may induce a novel physical phenomenon known as topological superconductivity. Topological superconductors have been the subject of intense research, yet there are severe limitations in their application due to a lack of suitable materials. Topological nodal surface semimetals with nearly flat nodal surfaces near the Fermi level can be promising materials to achieve topological superconductivity. Here, we use first-principles calculations to examine the topological electronic characteristics of two new superconductors, ScH3 and LuH3, at both ambient and high pressures. Our studies show that both ScH3 and LuH3 have van Hove singularities, which confirms their superconductivity. Interestingly, both materials host topological nodal surface states under the protection of time reversal and spatial inversion symmetries in the absence of spin–orbit coupling (SOC). These nodal surfaces are distinguished by a pair of unique drum-head-like surface states not previously observed in nodal surface semimetals. Moreover, the nodal surfaces transform into essential spin–orbit quadratic Dirac points when SOC is included. Our findings demonstrate that ScH3 and LuH3 are good candidates to investigate the exotic properties of both nodal surface semimetals (NSSMs) and quadratic Dirac semimetal states and also provide a platform to explore the coexistence of topology and superconductivity in NSSMs with promising applications in high-speed electronics and topological quantum computing.