Non-Hermitian anomalous skin effect

Abstract

A non-Hermitian topological insulator is fundamentally different from conventional topological insulators. The non-Hermitian skin effect arises in a nonreciprocal tight binding lattice with open edges. In this case, not only topological states but also bulk states are localized around the edges of the nonreciprocal system. We discuss that controllable switching from topological edge states into topological extended states in a chiral symmetric non-Hermitian system is possible. We show that the skin depth decreases with non-reciprocity for bulk states but increases with it for topological zero energy states.

Compatibility of transport effects in non-Hermitian nonreciprocal systems

“…Over the last few years, these endeavours have received substantial impetus by the realization that non-Hermitian physics can equip existing topological states with unique physical features, and also function as a source of topological effects in themselves [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. A particularly prominent manifestation is the non-Hermitian skin effect, in which the bulk states become localized at an edge of a finite system, resulting in a behaviour that is drastically different from its periodic counterpart [20][21][22][23][24][25][26][27][28][29][30][31][32][33]. While traditional non-Hermitian physics is mostly captured in imaginary scalar potentials that describe local gain and loss, the non-Hermitian skin effect relies on imaginary vector potentials [34], making the system nonreciprocal.…”

Probing phase transitions in non-Hermitian systems with Multiple Quantum Coherences

“…Among them, physical systems which can be described by non-hermitian Hamiltonians are particularly important. Indeed, non-Hermitian systems are becoming a central focus of research in optics [7][8][9][10][11][12][13][14][15][16], photonics [17][18][19][20], quantum many-body systems [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40], quantum metrology [41][42][43][44][45], and systems with topological order [46][47][48][49][50][51][52][53][54][55][56]…”

Nonlinear non-Hermitian skin effect

“…It has recently been predicted [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] and experimentally realized [19][20][21][22][23] that the transition from periodic boundary conditions (PBC) to open boundary conditions (OBC) in sufficiently long non-reciprocal lattices can become substantially non-perturbative even though the corresponding non-Hermitian Hamiltonians are perturbatively different from each other. More specifically, the spectra and corresponding eigenstates with or without boundaries can be significantly different in non-Hermitian systems.…”