We investigate the possibility of realizing quantum anomalous Hall effect in graphene. We show that a bulk energy gap can be opened in the presence of both Rashba spin-orbit coupling and an exchange field. We calculate the Berry curvature distribution and find a nonzero Chern number for the valence bands and demonstrate the existence of gapless edge states. Inspired by this finding, we also study, by first-principles method, a concrete example of graphene with Fe atoms adsorbed on top, obtaining the same result.

We derive the field correction to the Berry curvature of Bloch electrons, which can be traced back to a positional shift due to the interband mixing induced by external electromagnetic fields. The resulting semiclassical dynamics is accurate to second order in the fields, in the same form as before, provided that the wave packet energy is derived up to the same order. As applications, we discuss the orbital magnetoelectric polarizability and predict nonlinear anomalous Hall effects.

“Two-dimensional (2D) materials as electrodes” is believed to be the trend for future Li-ion and Na-ion battery technologies. Here, by using first-principles methods, we predict that the recently reported borophene (2D boron sheets) can serve as an ideal electrode material with high electrochemical performance for both Li-ion and Na-ion batteries. The calculations are performed on two experimentally stable borophene structures, namely β₁₂ and χ₃ structures. The optimized Li and Na adsorption sites are identified, and the host materials are found to maintain good electric conductivity before and after adsorption. Besides advantages including small diffusion barriers and low average open-circuit voltages, most remarkably, the storage capacity can be as high as 1984 mA h g⁻¹ in β₁₂ borophene and 1240 mA h g⁻¹ in χ₃ borophene for both Li and Na, which are several times higher than the commercial graphite electrode and are the highest among all the 2D materials discovered to date. Our results highly support that borophenes can be appealing anode materials for both Li-ion and Na-ion batteries with extremely high power density.

Recently, a type-II Weyl fermion was theoretically predicted to appear at the contact of electron and hole Fermi surface pockets. A distinguishing feature of the surfaces of type-II Weyl semimetals is the existence of topological surface states, so-called Fermi arcs. Although WTe₂ was the first material suggested as a type-II Weyl semimetal, the direct observation of its tilting Weyl cone and Fermi arc has not yet been successful. Here, we show strong evidence that WTe₂ is a type-II Weyl semimetal by observing two unique transport properties simultaneously in one WTe₂ nanoribbon. The negative magnetoresistance induced by a chiral anomaly is quite anisotropic in WTe₂ nanoribbons, which is present in b-axis ribbon, but is absent in a-axis ribbon. An extra-quantum oscillation, arising from a Weyl orbit formed by the Fermi arc and bulk Landau levels, displays a two dimensional feature and decays as the thickness increases in WTe₂ nanoribbon.

We study edge states in graphene systems where a bulk energy gap is opened by inversion symmetry breaking. We find that the edge bands dispersion can be controlled by potentials applied on the boundary with unit cell length scale. Under certain boundary potentials, gapless edge states with valley-dependent velocity are found, exactly analogous to the spin-dependent gapless chiral edge states in quantum spin Hall systems. The connection of the edge states to bulk topological properties is revealed.

A second-order topological insulator (SOTI) in $d$ spatial dimensions features topologically protected gapless states at its ($d-2$)-dimensional boundary at the intersection of two crystal faces, but is gapped otherwise. As a novel topological state, it has been attracting great interest, but it remains a challenge to identify a realistic SOTI material in two dimensions (2D). Here, based on combined first-principles calculations and theoretical analysis, we reveal the already experimentally synthesized 2D material graphdiyne as the first realistic example of a 2D SOTI, with topologically protected 0D corner states. The role of crystalline symmetry, the robustness against symmetry breaking, and the possible experimental characterization are discussed. Our results uncover a hidden topological character of graphdiyne and promote it as a concrete material platform for exploring the intriguing physics of higher-order topological phases.