SPIN

Large-gap quantum spin Hall (QSH) insulators were previously predicted in stanene and its derivatives. Beyond stanene that is the thinnest $\alpha$-Sn(111) film, we propose to explore QSH insulators in $\alpha$-Sn films with different crystallographic orientations. Our first-principles calculations reveal that the thickness-dependent band gap of $\alpha$-Sn(100) and $\alpha$-Sn(110) films does not show a monotonic decrease as typically expected by quantum confinement, but displays an oscillating change behavior, an indicative of topological quantum phase transition. While these films are normal insulators in the ultrathin limit, the QSH phase emerges above a critical film thickness of around 10 layers. Remarkably, the QSH insulators are obtainable within a wide thickness range and their energy gaps are sizable (even $>$0.1eV), which facilitates experimental realization of the high-temperature QSH effect.

Pure spin currents carry information in quantum spintronics and could play an essential role in the next generation low-energy-consumption electronics. Here, we theoretically predict that the magnetic field can induce a quantum spin current without a concomitant charge current in metals without time reversal symmetry ${𝒯}$ and inversion symmetry ${𝒫}$ but respect the combined ${𝒫}{𝒯}$ symmetry. It is governed by the magnetic moment of the Bloch states on the Fermi surface, and can be regarded as a spinful generalization of the gyrotropic magnetic effect in ${𝒫}$-broken metals. The effect is explicitly studied for a minimal model of an antiferromagnetic Dirac semimetal, where the experimental signature is proposed. We further propose candidate materials, including topological antiferromagnetic Dirac semimetals, Weyl semimetals and tenary Heusler compounds.

Based on first-principles calculations, we predict that the monolayer AuTe₂Cl is a quantum spin Hall (QSH) insulator with a topological band gap about 10 meV. The three-dimensional (3D) AuTe₂Cl is a topological semimetal that can be viewed as the monolayer stacking along $b$ axis. By studying the energy-level distribution of $p$ orbitals of Te atoms for the bulk and the monolayer, we find that the confinement effect driven $p_y^{-}-p_z^{+}$ band inversion is responsible for the topological nontrivial nature of monolayer. Since 3D bulk AuTe₂Cl has already been experimentally synthesized, we expect that monolayer AuTe₂Cl can be exfoliated from a bulk sample and the predicted QSH effect can be observed.

Inversion asymmetric topological insulator promises great potential to realize many intriguing phenomena such as intrinsic topological $p$–$n$ junctions, pyroelectricity and novel topological magneto-electric effects that require inversion asymmetry. Recently, gapless helical surface Dirac fermions were observed in inversion-asymmetric BiTeCl crystal. However, heavy debate about whether BiTeCl is a topological insulator and controversial experimental results of the electronic structure of BiTeCl exist. In this work, through ab-initio calculations, we discovered that a BiTeCl-dominant BiTeCl/Bi₂Te₃ heterostructure can give rise to the observed band structures with a single surface Dirac fermion. Interestingly, we further suggest that such a BiTeCl/Bi₂Te₃ heterostructure could be naturally formed by annealing pure BiTeCl single crystals. Our results not only resolve the discrepancy between the previous experiments on heat treated samples and theoretical investigations, but also point out a pathway to design novel materials with sophisticated properties.

Elevating the temperature needed to realize the quantum anomalous Hall effect (QAHE) to above 77 K or higher is the key to practical applications of the effect as well as many others based on it. Here, we briefly review the recent progresses, especially the experimental ones, on searching for magnetic topological insulators that can exhibit the QAHE at higher temperature. Based on our understanding of these results, we will give the principles and roadmap for designing and constructing high-temperature quantum anomalous Hall systems.

As paradigmatic phenomena, Hall effects have inspired tremendous studies of symmetry and topology in condensed matter physics. Intriguingly, a second-order nonlinear Hall effect was recently proposed in noncentrosymmetric materials even in the presence of time-reversal symmetry. This effect originates from the Berry curvature dipole of electronic band structures and was predicted in Dirac and Weyl materials such as transition metal dichalcogenides and Weyl semimetals. Although it has been experimentally verified in some transition metal dichalcogenides, no obvious observation of such effects has been reported in Weyl semimetals. Taking advantage of the ideal Weyl phase with no coexisting trivial bands at the Fermi level, we use strained HgTe as a concrete example to show that the ideal Weyl semimetal is a promising platform for demonstrating the nonlinear Hall effect. Based on numerical calculations of the Berry curvature dipole, it was found that the magnitude of nonlinear Hall effect can be simply engineered by in-plane strain. Our work provides a versatile platform with high tunability, which could greatly facilitate the study of nonlinear Hall effect in three-dimensional topological materials.