Abstract
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.
Keywords
Hermitian matrixPhysicsTopology (electrical circuits)Theoretical physicsQuantum mechanicsMathematical physicsMathematicsCombinatorics
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Publication Info
- Year
- 2018
- Type
- article
- Volume
- 120
- Issue
- 14
- Pages
- 146402-146402
- Citations
- 1123
- Access
- Closed
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Cite This
Huitao Shen,
Bo Zhen,
Liang Fu
(2018).
Topological Band Theory for Non-Hermitian Hamiltonians.
Physical Review Letters
, 120
(14)
, 146402-146402.
https://doi.org/10.1103/physrevlett.120.146402
Identifiers
- DOI
- 10.1103/physrevlett.120.146402