Journal
PHYSICAL REVIEW LETTERS
Volume 120, Issue 14, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.120.146402
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Funding
- DOE Office of Basic Energy Sciences, Division of Materials Sciences and Engineering [DE-SC0010526]
- David and Lucile Packard Foundation
- MIT Alumni Fellowship Fund For Physics
- United States-Israel Binational Science Foundation (BSF) [2013508]
- Army Research Office through the Institute for Soldier Nanotechnologies [W911NF-13-D-0001]
- Air Force Office of Scientific Research [FA9550-18-1-0133]
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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.
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