Geometric Response and Disclination-Induced Skin Effects in Non-Hermitian Systems

Abstract

We study the geometric response of three-dimensional non-Hermitian crystalline systems with non-trivial point gap topology. For systems with four-fold rotation symmetry, we show that in presence of disclination lines with a total Frank angle which is an integer multiple of 2π, there can be non-trivial, one-dimensional point gap topology along the direction of disclination lines. This results in disclination-induced non-Hermitian skin effects. We extend the recently proposed non-Hermitian field theory approach to describe this phenomenon as a Euclidean Wen-Zee term. Furthermore, by doubling a non-Hermitian Hamiltonian to a Hermitian 3D chiral topological insulator, we show that the disclination-induced skin modes are zero modes of the surface Dirac fermion(s) in the presence of a pseudo-magnetic flux induced by disclinations.

Eigenvalue topology of non-Hermitian band structures in two and three dimensions

“…In one spatial dimension, it was recently shown that eigenvalue topology is classified by the braid group [25]. The nature of eigenvalue topology in two and three dimensions has not yet been established, although simpler point-gap winding number invariants have been explored [32][33][34][35]. Certain features are known which suggest and e2 = σ1.…”

Discriminant indicator with generalized rotational symmetry

“…Consider an N × N -Hamiltonian H(k) for twodimensional systems with generalized C n symmetry under the periodic boundary condition [51,61,70,72,[97][98][99][100][101]. In this case, the Hamiltonian satisfies…”

“…In parallel with this progress, recent extensive studies have opened up a new arena of topological physics: non-Hermitian systems [30][31][32][33][34][35][36][37]. In these systems, the eigenvalues of the Hamiltonian may become complex, which induces exotic phenomena [38][39][40][41][42][43][44][45][46][47][48][49][50][51] such as the emergence of exceptional points [52][53][54][55][56][57][58][59][60][61] and skin effects [62][63][64][65][66][67][68][69][70][71][72]. On the exceptional points, non-Hermitian topological properties protect band touching for both of the real and the imaginary part of the eigenvalues which are further enriched by symmetry [73][74][75][76]…”

Observation of Dislocation-Induced Topological Modes in a Three-Dimensional Acoustic Topological Insulator

“…Moreover, although we have focused on screw dislocations, there are other types of lattice defects that may host topological modes with different characteristics, which could be similarly studied using acoustic structures. Finally, it would be interesting to study non-Hermitian band topological effects [52][53][54][55][56][57][58][59][60][61][62], which can have interesting interactions with topological lattice defects [63][64][65][66], by using passive [57,58] or active [59] methods to introduce non-Hermiticity into acoustic structures.…”