Topological Band Theory for Non-Hermitian Hamiltonians.

By Huitao Shen, B. Zhen, Liang Fu. Physical Review Letters, 2017

942 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4859287735a18e34b9ce86c0a15fef03a0932087

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Citations in the corpus

Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices (2019, background): “[46] Huitao Shen, Bo Zhen, and Liang Fu.”
Probing non-Hermitian skin effect and non-Bloch phase transitions (2019, methodology): “[6] H.”
Experimental realization of a Weyl exceptional ring (2018, background): “[54] Huitao Shen, Bo Zhen, and Liang Fu, “Topological Band Theory for Non-Hermitian Hamiltonians,” Phys.”
Symmetry-protected nodal phases in non-Hermitian systems (2018, background): “Very recently, intense theoretical [7–37] and experimental [38–45] efforts have been made to extend the concept of topological band structures to non-Hermitian (NH) systems which play an important role in the effective description of dissipation effects in various physi-”
Non-Hermitian Chern Bands. (2018, positive): “One can obtain that the HðkÞ-based Chern number (Bloch Chern number) [44,45] is 0 for m > mþ, 1 for m < m−, and becomes nondefinable in the gapless region m ∈ 1⁄2m−; mþ .”
Topological active matter (2020, background): “[209] Shen, H.”
Symmetry and Topology in Non-Hermitian Physics (2018, background): “(43) [104, 117, 121, 124].”
A review on non-Hermitian skin effect (2022, background): “That is, by phase-winding the eigenenergy, not the wave functions, of a non-Hermitian Hamiltonian over the BZ, a nontrivial winding number emerges, which constitutes a topological object unique to the non-Hermitian systems [143].”