Non-Hermitian Chern Bands.

By Shunyu Yao, Fei Song, Zhong Wang. Physical Review Letters, 2018

652 citations recorded by the source corpus.

The relation between chiral edge modes and bulk Chern numbers of quantum Hall insulators is a paradigmatic example of bulk-boundary correspondence. We show that the chiral edge modes are not strictly tied to the Chern numbers defined by a non-Hermitian Bloch Hamiltonian. This breakdown of conventional bulk-boundary correspondence stems from the non-Bloch-wave behavior of eigenstates (non-Hermitian skin effect), which generates pronounced deviations of phase diagrams from the Bloch theory. We introduce non-Bloch Chern numbers that faithfully predict the numbers of chiral edge modes. The theory is backed up by the open-boundary energy spectra, dynamics, and phase diagram of representative lattice models. Our results highlight a unique feature of non-Hermitian bands and suggest a non-Bloch framework to characterize their topology.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/d16bd2eda13ff46fdb59241467e9ad052b41441c

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Symmetry and Topology in Non-Hermitian Physics (2018, methodology): “Our discussion can also be applied to the generalized non-Bloch wave functions [121, 137, 143], as long as the corresponding symmetry is respected with complex wavenumbers (see Sec.”
Interplay of non-Hermitian skin effects and Anderson localization in nonreciprocal quasiperiodic lattices (2019, background): “[54] Shunyu Yao, Fei Song, and Zhong Wang.”
Exceptional topology of non-Hermitian systems (2019, neutral): “…(2018) took a direct cue from the properties of systems with OBCs and examined the (de) localization transitions of the biorthogonal wave functions, Yao, Song, and Wang (2018) and Yao and Wang (2018) instead augmented the Bloch Hamiltonian with information from the OBCs leading to a generalized…”
Non-Hermitian systems and topology: A transfer-matrix perspective (2018, methodology): “Various topological invariants have been defined using a generalization of the conventional Berry connection by replacing the standard inner product with a biorthogonal one [52–56], but they often fail to predict the existence of robust boundary modes [50, 56–58].”
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-”