Non-Hermitian skin effect as an impurity problem

Abstract

A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if the spectrum under periodic boundary conditions is point gapped, by opening the lattice the non-Hermitian skin effect will necessarily occur. Finding the exact skin eigenstates may be demanding in general, and many methods in the literature are based on ansatzes and on recurrence equations for the eigenstates' components. Here we devise a general procedure based on the Green's function method to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions. We apply it to the Hatano-Nelson and non-Hermitian SSH models and finally we contrast the edge states localization with that of bulk states.

Reservoir-assisted symmetry breaking and coalesced zero-energy modes in an open PT-symmetric Su-Schrieffer-Heeger model

“…It is also notable that all of the EP2s and EP4s associated with the gap closing discussed above correspond to a degenerate eigenvalue z = 0 that resides directly in the middle between the two SSH bands. This recalls the same property of the edge states in the finite, Hermitian SSH model 58 that also appear in at least some non-Hermitian extensions of the original model 69,70 (note such states are also sometimes referred to as mid-gap states, although this references the band gap, not the PT gap introduced in this paper). It should be emphasized that the while the edge states in those models arise due to a bulk-boundary correspondence, in our model the exceptional points instead occur due to the presence of the PT -symmetric central potential.…”

“…Recently, non-Hermitian extensions of the SSH model have been actively investigated by many authors who mainly focused on the topological properties of the systems. [60][61][62][63][64][65][66][67][68][69][70] In our model, the semi-infinite SSH chains form the reservoir. We mainly focus on the parameter region corresponding to the topologically non-trivial phase of the bare SSH chains, 58 in which edge states can form that are topologically protected.…”

Unconventional node voltage accumulation in generalized topolectrical circuits with multiple asymmetric couplings

“…Nonhermicity has brought about a plethora of interesting new phenomena [1][2][3][4][5][6][7][8][9][10][11][12][13][14], of which the non-Hermitian skin-effect (NHSE) [15][16][17][18][19][20][21][22][23][24][25][26] (i.e, extreme localization of the eigenstates to a boundary) has galvanized various reformulations of the conventional concepts of the Brillouin zone (BZ) and bulk-boundary correspondence (BBC) [27,28]. While the BBC can already be broken with a single asymmetric non-Hermitian coupling, the more interesting interplay between multiple asymmetric non-Hermitian couplings has not been thoroughly explored.…”