Topological Insulators with Inversion Symmetry

Abstract

Topological insulators are materials with a bulk excitation gap generated by the spin orbit interaction, and which are different from conventional insulators. This distinction is characterized by Z_2 topological invariants, which characterize the groundstate. In two dimensions there is a single Z_2 invariant which distinguishes the ordinary insulator from the quantum spin Hall phase. In three dimensions there are four Z_2 invariants, which 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 2D quantum spin Hall phase and the 3D 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 wavefunctions at the time reversal invariant points in the Brillouin zone. Using this approach, we predict a number of specific materials 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.

16 pages, 7 figures; published version

References in corpus (7)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Dissipationless Quantum Spin Current at Room Temperature
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Quantum Spin Hall Effect and Enhanced Magnetic Response by Spin-Orbit Coupling
• SU(2) Non-Abelian Holonomy and Dissipationless Spin Current in Semiconductors

Cited by in corpus (29)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• First direct observation of Spin-textures in Topological Insulators : Spin-resolved ARPES as a probe of topological quantum spin Hall effect and Berry's phase
• Phase transition between the quantum spin Hall and insulator phases in 3D: emergence of a topological gapless phase
• Topological Surface States Protected From Backscattering by Chiral Spin Texture
• The Quantum Spin Hall Effect: Theory and Experiment
• Surface States of the Topological Insulator Bi_{1-x}Sb_x
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Quantum spin Hall effect in a transition metal oxide Na2IrO3
• Robustness of the Spin-Chern number
• Topological delocalization of two-dimensional massless Dirac fermions
• Topological spin-current in non-centrosymmetric superconductors
• Helical edge and surface states in HgTe quantum wells and bulk insulators
• Tuning phase transition between quantum spin Hall and ordinary insulating phases
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Electronic Structures and Surface States of Topological Insulator Bi${}_{1-x}$Sb${}_x$
• Z2 topological term, the global anomaly, and the two-dimensional symplectic symmetry class of Anderson localization
• Topological Insulators and Metals in Atomic Optical Lattices
• A $\Gamma$-matrix generalization of the Kitaev model
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• Three-dimensional topological phase on the diamond lattice
• Many-body generalization of the Z2 topological invariant for the quantum spin Hall effect
• Transport anomalies across the quantum limit in semimetallic Bi${}_{0.96}$Sb${}_{0.04}$
• Spin Hall effect in the kagome lattice with Rashba spin-orbit interaction
• Topological meaning of Z${}_2$ numbers in time reversal invariant systems
• A topological Dirac insulator in a quantum spin Hall phase (experimental realization of a 3D Topological Insulator)