Equivalent topological invariants of topological insulators

Details Equivalent topological invariants of topological insulators Equivalent topological invariants of topological insulators

2009-10-30

arxiv.org/abs/0910.5954v1

New J. Phys. 12, 065007 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

12 pages, 2 figures

Scientific paper

10.1088/1367-2630/12/6/065007

A time-reversal invariant topological insulator can be generally defined by the effective topological field theory with a quantized \theta coefficient, which can only take values of 0 or \pi. This theory is generally valid for an arbitrarily interacting system and the quantization of the \theta invariant can be directly measured experimentally. Reduced to the case of a non-interacting system, the \theta invariant can be expressed as an integral over the entire three dimensional Brillouin zone. Alternatively, non-interacting insulators can be classified by topological invariants defined over discrete time-reversal invariant momenta. In this paper, we show the complete equivalence between the integral and the discrete invariants of the topological insulator.

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