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 language||American English|
|Journal||Journal of Physics A: Mathematical and Theoretical|
|State||Published - 18 Aug 2017|
Bibliographical noteFunding Information:
We benefited from discussions with Ronnie Kosloff, and Tahl Nowik. OG gratefully acknowledges support from the Leverhulme Trust Visiting Professorship program during his stay in Bristol.
© 2017 IOP Publishing Ltd.
- Adiabatic approximation
- semiclassical approximation
- space adiabatic
- time reversal invariance
- topological invariants