Topological Band Theory for Non-Hermitian Hamiltonians
Name
PhysRevLett.120.146402.pdf
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508.7 KB
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Author(s)
Shen, Huitao
Zhen, Bo
Fu, Liang
Date Issued
April 2018
Journal
Physical Review Letters
Publisher
American Physical Society
Citation
Shen, Huitao et al. "Topological Band Theory for Non-Hermitian Hamiltonians." Physical Review Letters 120, 14 (April 2018): 146402 © 2018 American Physical Society
Version
Final published version
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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevLett.120.146402
