Non-Hermitian robust edge states in one dimension: Anomalous localization and eigenspace condensation at exceptional points

By V. M. Alvarez, J. Vargas, Luis E. F. Foa Torres. 2017

612 citations recorded by the source corpus.

Capital to topological insulators, the bulk-boundary correspondence ties a topological invariant computed from the bulk (extended) states with those at the boundary, which are hence robust to disorder. Here we put forward a different ordering unique to non-Hermitian lattices whereby a pristine system becomes devoid of extended states, a property which turns out to be robust to disorder. This is enabled by a peculiar type of non-Hermitian degeneracy where a macroscopic fraction of the states coalesce at a single point with a geometrical multiplicity of 1.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/e52b1dd16d5d515fc598d54d7562373f9f0eef54

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

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-”
Symmetry and Topology in Non-Hermitian Physics (2018, methodology): “Importantly, nonHermiticity alters the nature of the bulk-boundary correspondence [108, 116, 119, 121, 124, 130, 132–134, 136, 137, 139, 143, 144].”
A review on non-Hermitian skin effect (2022, background): “It should be pointed out that even though their emergence has topological origin as discussed, the skin modes are not topological [34,36,96].”
Perspective on topological states of non-Hermitian lattices (2019, background): “Finally, we comment on an extreme case of defectiveness found in non-Hermitian lattices: A pristine (without disorder) finite system may become devoid of extended states having all eigenstates localized close to a boundary [45, 46], the same systems typically show an”
Non-Hermitian Chern Bands. (2018, positive): “The dissimilarity between open-boundary and Bloch spectra has also been found in a 1D model [46,53,54,56], whose spectra can be readily obtained via a similarity transformation to a Hermitian Hamiltonian [56].”
Higher-order non-Hermitian skin effect (2020, neutral): “[44] V.”
Probing non-Hermitian skin effect and non-Bloch phase transitions (2019, methodology): “Among the most relevant features observed in non-Hermitian systems, one should mention the strong sensitivity of the energy spectra on boundary conditions [7, 15–21], the non-Hermitian skin effect (NHSE) [7, 9, 17, 18, 20–24], i.”
Biorthogonal Bulk-Boundary Correspondence in Non-Hermitian Systems. (2018, background): “The paramount issue is the so-called non-Hermitian skin effect, meaning that a macroscopic number of left and right eigenmodes can pile up exponentially close to the boundary [13, 15, 23].”
Reciprocal skin effect and its realization in a topolectrical circuit (2019, background): “[13] V.”