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Spin Hall effect (SHE) in two-dimensional (2D) materials is promising to effectively manipulate spin angular momentum and identify topological properties. In this work, we implemented an automated Wannierization with spin-orbit coupling on…
Quantum spin Hall (QSH) insulators are a topologically protected phase of matter in two dimensions that can support non-dissipative spin transport. A hallmark of the phase is a pair of helical edge states surrounding an insulating bulk. A…
Crystal symmetries in solids give rise to spin-momentum locking, which determines how an electron's spin orientation depends on its momentum. This relationship, often referred to as spin texture, influences both charge-to-spin conversion…
Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…
We develop a symmetry-based low-energy theory for monolayer $\mathrm{WTe}_2$ in its 1T$^{\prime}$ phase, which includes eight bands (four orbitals, two spins). This model reduces to the conventional four-band spin-degenerate Dirac model…
Generally, stacking two quantum spin Hall insulators gives rise to a trivial insulator. Here, based on first-principles electronic structure calculations, we confirm that monolayer TaIrTe$_{4}$ is a quantum spin Hall insulator and…
The search for new quantum spin Hall (QSH) phase and effective manipulations of their edge states are very important for both fundamental sciences and practical applications. Here, we use first-principles calculations to study the…
The Hall effect, the anomalous Hall effect and the spin Hall effect are fundamental transport processes in solids arising from the Lorentz force and the spin-orbit coupling respectively. The quantum versions of the Hall effect and the spin…
Transition metal dichalcogenide (TMD) materials are unique in the wide variety of structural and electronic phases they exhibit in the two-dimensional (2D) single-layer limit. Here we show how such polymorphic flexibility can be used to…
Quantum spin Hall (QSH) insulators are two-dimensional electronic materials that have a bulk band gap like an ordinary insulator but have topologically protected pairs of edge modes of opposite chiralities. To date, experimental studies…
Based on a combination of $k \cdot p$ theory, band topology analysis and electronic structure calculations, we predict the (111) thin films of the SnTe class of three-dimensional (3D) topological crystalline insulators realize the quantum…
Topological insulators present a bulk gap, but allow for dissipationless spin transport along the edges. These exotic states are characterized by the $Z_2$ topological invariant and are protected by time-reversal symmetry. The Kane-Mele…
The quantum anomalous Hall effect (QAHE) and magnetic Weyl semimetals (WSMs) are topological states induced by intrinsic magnetic moments and spin-orbit coupling. Their similarity suggests the possibility of achieving the QAHE by…
We investigate the interplay between topological effects and Mott physics in two dimensions on a graphene-like lattice, via a tight-binding model containing an anisotropic spin-orbit coupling on the next-nearest-neighbour links and the…
Electron correlation and topology are two central threads of modern condensed matter physics. Semiconductor moir\'e materials provide a highly tunable platform for studies of electron correlation. Correlation-driven phenomena, including the…
Topological magnetic insulators host chiral gapless edge modes. In the presence of strong interaction effects, the spin of these modes may fractionalize. Studying a 2D array of coupled insulating spin-1/2 chains, we show how spatially…
Two-dimensional transition metal dichalcogenides (TMDs) of Mo and W in their 1T' crystalline phase host the quantum spin Hall (QSH) insulator phase. We address the electronic properties of the QSH edge states by means of first-principles…
A two-dimensional kagome lattice is theoretically investigated within a simple tight-binding model, which includes the nearest neighbor hopping term and the intrinsic spin-orbit interaction between the next nearest neighbors. By using the…
As one of paradigmatic phenomena in condensed matter physics, the quantum anomalous Hall effect (QAHE) in stoichiometric Chern insulators has drawn great interest for years. By using model Hamiltonian analysis and first-principle…
We present the theory of a new type of topological quantum order which is driven by the spin-orbit density wave order parameter, and distinguished by $Z_2$ topological invariant. We show that when two oppositely polarized chiral bands…