Topology of time-reversal invariant energy bands with adiabatic structure

Omri Gat, J. M. Robbins

Research output: Contribution to journalArticlepeer-review


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 languageAmerican English
Article number375203
JournalJournal of Physics A: Mathematical and Theoretical
Issue number37
StatePublished - 18 Aug 2017


  • Adiabatic approximation
  • semiclassical approximation
  • space adiabatic
  • time reversal invariance
  • topological invariants

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • General Physics and Astronomy
  • Statistics and Probability
  • Mathematical Physics
  • Modelling and Simulation


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