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Title: Topological Band Theory for Non-Hermitian Hamiltonians

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. Lastly, we also systematically classify all types of band degeneracies.

Authors:
 [1];  [2];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Physics; Univ. of Pennsylvania, Philadelphia, PA (United States). Dept. of Physics and Astronomy
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22); United States–Israel Binational Science Foundation (BSF); Army Research Office (ARO)
OSTI Identifier:
1505749
Alternate Identifier(s):
OSTI ID: 1432099
Grant/Contract Number:  
SC0010526; 2013508; W911NF-13-D-0001; FA9550-18-1-0133
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 120; Journal Issue: 14; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Shen, Huitao, Zhen, Bo, and Fu, Liang. Topological Band Theory for Non-Hermitian Hamiltonians. United States: N. p., 2018. Web. doi:10.1103/physrevlett.120.146402.
Shen, Huitao, Zhen, Bo, & Fu, Liang. Topological Band Theory for Non-Hermitian Hamiltonians. United States. doi:10.1103/physrevlett.120.146402.
Shen, Huitao, Zhen, Bo, and Fu, Liang. Fri . "Topological Band Theory for Non-Hermitian Hamiltonians". United States. doi:10.1103/physrevlett.120.146402. https://www.osti.gov/servlets/purl/1505749.
@article{osti_1505749,
title = {Topological Band Theory for Non-Hermitian Hamiltonians},
author = {Shen, Huitao and Zhen, Bo and Fu, Liang},
abstractNote = {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. Lastly, we also systematically classify all types of band degeneracies.},
doi = {10.1103/physrevlett.120.146402},
journal = {Physical Review Letters},
number = 14,
volume = 120,
place = {United States},
year = {2018},
month = {4}
}

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Works referenced in this record:

Z2 Topological Order and the Quantum Spin Hall Effect
journal, September 2005


Topological Insulators in Three Dimensions
journal, March 2007


Topological invariants of time-reversal-invariant band structures
journal, March 2007