Topological insulators with inversion symmetry

Abstract

Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by Z 2 topological invariants, which characterize the ground state. In two dimensions, there is a single Z 2 invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four Z 2 invariants that distinguish the ordinary insulator from "weak" and "strong" topological insulators. These phases are characterized by the presence of gapless surface (or edge) states. In the two-dimensional quantum spin-Hall phase and the threedimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z 2 invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy Bi 1−x Sb x as well as α-Sn and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments. Topological insulators are materials with a bulk excitation gap generated by the spin-orbit interaction that are different from conventional insulators. This distinction is characterized by Z 2 topological invariants, which characterize the ground state. In two dimensions, there is a single Z 2 invariant that distinguishes the ordinary insulator from the quantum spin-Hall phase. In three dimensions, there are four Z 2 invariants that distinguish the ordinary insulator from "weak" and "strong" topological insulators. These phases are characterized by the presence of gapless surface ͑or edge͒ states. In the two-dimensional quantum spin-Hall phase and the threedimensional strong topological insulator, these states are robust and are insensitive to weak disorder and interactions. In this paper, we show that the presence of inversion symmetry greatly simplifies the problem of evaluating the Z 2 invariants. We show that the invariants can be determined from the knowledge of the parity of the occupied Bloch wave functions at the time-reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials that are strong topological insulators, including the semiconducting alloy Bi 1−x Sb x as well as ␣-Sn and HgTe under uniaxial strain. This paper also includes an expanded discussion of our formulation of the topological insulators in both two and three dimensions, as well as implications for experiments.

New Family of Quantum Spin Hall Insulators in Two-dimensional Transition-Metal Halide with Large Nontrivial Band Gaps

“…38 The central quantity here is the parity product (When the crystal structure has inversion symmetry, δ i is the product of parity eigenvalues of the valence bands at Γ i .) …”

On the Quantum Spin Hall Gap of Monolayer 1T′‐WTe2

“…The theoretical proposal and experimental discovery of topological insulators [1][2][3] have provided an invigorating momentum to condensed matter and materials physics. In two dimensions, a topological insulator displays the QSH effect [4][5][6][7][8] , in which the symmetryprotected helical edge modes are gapless and can propagate unscattered [9,10] .…”

“…Van der Waals interactions between the adjacent layers were taken into account by using PBE with optB86 [25,26] While the many-body effect opens a quasi-particle gap in monolayer 1T'-WTe 2 , its topological character remains intact. As monolayer 1T'-WTe 2 processes inversion symmetry, the topology of the occupied bands can be straightforwardly evaluated through the parity of valence bands at the four time-reversal invariant points, (0, 0), (0, π), (π, 0) and (π, π) [2] . We the direct projection formalism [27] .…”

Electrical Detection of Spin-Polarized Surface States Conduction in (Bi0.53Sb0.47)2Te3 Topological Insulator

“…Overall, the spin signal amplitude decreases as the temperature increases, 30 suggesting that the effective spin polarization of the total current decreases. This could be attributed to the fact that with the temperature increasing: (1) the bulk conduction increases due to thermally activated bulk dopants, so that the relative contribution from the spin-polarized surface states conduction decreases; 48 (2) inelastic scatterings such as phonon scatterings increase so that the spin polarization of surface states conduction also decreases. To explain the temperature dependence of the surface states conduction more clearly, standard magneto-transport measurements were performed on the Hall bar structure patterned on the same (Bi 0.53 Sb 0.47 ) 2 Te 3 film (see Figure 1d for the device structure and dimension).…”