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