Related papers: Half quantum spin Hall effect on the surface of we…
We study three dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where the QSH effect is distinguished by a single $Z_2$ topological invariant, in three dimensions there are 4 invariants…
A wide class of materials that were discovered to carry a topologically protected phase order has led to a highly active area of research called topological insulators. This phenomenon has radically changed our thinking because of their…
We develop a simple model of surface states for topological insulators, developing matching relations for states on surfaces of different orientations. The model allows one to write simple Dirac Hamiltonians for each surface, and to…
An intriguing property of three-dimensional (3D) topological insulator (TI) is the existence of surface states with spin-momentum locking, which offers a new frontier of exploration in spintronics. Here, we report the observation of a new…
The topological nature of topological insulators are related to the symmetries present in the material, for example, quantum spin Hall effect can be observed in topological insulators with time reversal symmetry, while broken time reversal…
A quantum spin Hall insulator hosts topological states at the one-dimensional edge, along which backscattering by nonmagnetic impurities is strictly prohibited and dissipationless current flows. Its 3D analogue, a weak topological insulator…
A three-dimensional weak topological insulator (WTI), being equivalent to stacked layers of two-dimensional quantum spin-Hall insulators, accommodates massless Dirac electrons on its side surface. A notable feature of WTIs is that surface…
We study the effects of spatially localized breakdown of time reversal symmetry on the surface of a topological insulator (TI) due to proximity to a helical spin density wave (HSDW). The HSDW acts like an externally applied one-dimensional…
A semimagnetic topological insulator -- a heterostructure combining a topological insulator with a ferromagnet -- exhibits a half-quantized Hall effect, characterized by a quantized Hall conductance of $\frac{1}{2}\frac{e^{2}}{h}$ (where…
Three-dimensional topological insulators (TIs) are a perfectly tuned quantum-mechanical machinery in which counter-propagating and oppositely spin-polarized conduction channels balance each other on the surface of the material. This…
We investigate the effects of magnetic and nonmagnetic impurities on the two-dimensional surface states of three-dimensional topological insulators (TIs). Modeling weak and strong TIs using a generic four-band Hamiltonian, which allows for…
We report the experimental realization of two-dimensional (2D) weak topological insulator (WTI) in spinless Su-Schrieffer-Heeger circuits with parity-time and chiral symmetries. Strong and weak $\mathbb{Z}_2$ topological indexes are adopted…
Fascinating phenomena have been known to arise from the Dirac theory of relativistic quantum mechanics, which describes high energy particles having linear dispersion relations. Electrons in solids usually have non-relativistic dispersion…
We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, 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…
Nontrivial band topology along with magnetism leads to different novel quantum phases. When time-reversal-symmetry is broken in three-dimensional topological insulators (TIs) by applying high enough magnetic field or proximity effect,…
We generalize the topological phase diagram of magnetic topological insulator (TI) thin films in an extended parameter space comprising out-of-plane (OP) and in-plane (IP) exchange fields in the presence of structural inversion asymmetry…
Two-dimensional (2D) topological insulators (TIs) hold promise for applications in spintronics based on the fact that the propagation direction of edge electrons of a 2D TI is robustly linked to their spin origination. Here, with the use of…
Topological insulators (TIs) are a new class of matter characterized by the unique electronic properties of an insulating bulk and metallic boundaries arising from non-trivial bulk band topology. While the surfaces of TIs have been well…
In ultra-thin film of topological insulator, the hybridization between the top and bottom surfaces opens an energy gap and forms two degenerate quantum anomalous Hall states, which give rise to a quantum spin Hall state. In this paper, we…