A Z${}_2$ index of Dirac operator with time reversal symmetry

Abstract

With time reversal symmetry a Dirac operator has vanishing index and Chern number. We show that we can nevertheless define a nontrivial Z${}_2$ index as well as a corresponding topological invariant given by gauge field, which implies that such a Dirac operator is topologically nontrivial.

arXiv comment5 pages, 2 figures

References in corpus (9)

• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Quantum Spin Hall Effect
• 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
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Quantum spin Hall effect in three dimensional materials: Lattice computation of Z${}_2$ topological invariants and its application to Bi and Sb
• Abelian chiral gauge theories on the lattice with exact gauge invariance

Cited by in corpus (7)

• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Spherical topological insulator
• The Noncommutative Index Theorem and the Periodic Table for Disordered Topological Insulators and Superconductors
• The $Z_2$ Index of Disordered Topological Insulators with Time Reversal Symmetry
• Notes on topological insulators
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice