Topological meaning of Z$_2$ numbers in time reversal invariant systems

Details Topological meaning of Z$_2$ numbers in time reversal invariant systems Topological meaning of Z$_2$ numbers in time reversal invariant systems

2008-09-26

arxiv.org/abs/0809.4532v2

J. Phys. Soc. Jpn. 77 (2008) 123705

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, typos corrected

Scientific paper

10.1143/JPSJ.77.123705

We show that the Z$_2$ invariant, which classifies the topological properties
of time reversal invariant insulators, has deep relationship with the global
anomaly. Although the second Chern number is the basic topological invariant
characterizing time reversal systems, we show that the relative phase between
the Kramers doublet reduces the topological quantum number Z to Z$_2$.

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