Topological Band Theory for Non-Hermitian Hamiltonians

Huitao Shen; Bo Zhen; Liang Fu

doi:10.1103/physrevlett.120.146402

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

Affiliated Institutions

Related Publications

Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems

Flore K. Kunst , Elisabet Edvardsson , Jan Carl Budich +1 more

Non-Hermitian systems exhibit striking exceptions from the paradigmatic bulk-boundary correspondence, including the failure of bulk Bloch band invariants in predicting boundary ...

2018 Physical Review Letters 1265 citations

Exceptional topology of non-Hermitian systems

Emil J. Bergholtz , Jan Carl Budich , Flore K. Kunst

The current understanding of the role of topology in non-Hermitian (NH) systems and its far-reaching physical consequences observable in a range of dissipative settings are revi...

2021 Reviews of Modern Physics 1475 citations

Edge States and Topological Invariants of Non-Hermitian Systems

Shunyu Yao , Zhong Wang

The bulk-boundary correspondence is among the central issues of non-Hermitian topological states. We show that a previously overlooked "non-Hermitian skin effect" necessitates r...

2018 Physical Review Letters 1993 citations

Topological Phases of Non-Hermitian Systems

Zongping Gong , Yuto Ashida , Kohei Kawabata +3 more

Recent experimental advances in controlling dissipation have brought about\nunprecedented flexibility in engineering non-Hermitian Hamiltonians in open\nclassical and quantum sy...

2018 Physical Review X 1319 citations

<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>Z</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math>Topological Order and the Quantum Spin Hall Effect

C. L. Kane , E. J. Melé

The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge st...

2005 Physical Review Letters 6059 citations

Publication Info

Year: 2018
Type: article
Volume: 120
Issue: 14
Pages: 146402-146402
Citations: 1123
Access: Closed

External Links

View on DOI.org

Social Impact

Altmetric

Topological Band Theory for Non-Hermitian Hamiltonians

PlumX Metrics

Social media, news, blog, policy document mentions

Citation Metrics

1123

OpenAlex

Cite This

APA Style

                            
                                    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