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.

5 pages, 2 figures

References in corpus (4)

• 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
• 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
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Cited by in corpus (3)

• Topological Defects and Gapless Modes in Insulators and Superconductors
• Spherical topological insulator
• Constructing vortex functions and basis states of Chern insulators: ideal condition, inequality from index theorem, and coherent-like states on von Neumann lattice