Topology of time-reversal invariant energy bands with adiabatic structure

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We classify the topology of bands defined by the energy states of quantum systems with scale separation between slow and fast degrees of freedom, invariant under fermionic time reversal. Classical phase space transforms differently from momentum space under time reversal, and as a consequence the topology of adiabatic bands is different from that of Bloch bands. We show that bands defined over a two-dimensional phase space are classified by the Chern number, whose parity must be equal to the parity of the band rank. Even-rank bands are equivalently classified by the Kane–Mele index, an integer equal to one half the Chern number.
Original languageEnglish
Article number375203
JournalJournal of Physics A: Mathematical and General
Issue number37
Early online date18 Aug 2017
Publication statusPublished - 15 Sep 2017

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