Inversion symmetric non-Hermitian Chern insulator

Abstract

We propose a two-dimensional non-Hermitian Chern insulator with inversion symmetry, which is anisotropic and has staggered gain and loss in both x and y directions. In this system, conventional bulk-boundary correspondence holds. The Chern number is a topological invariant that accurately predicts the topological phase transition and the existence of helical edge states in the topologically nontrivial phase. The band touching points are isolated and protected by the symmetry. The band touching affects the existence of helical edge states. Moreover, topologically protected helical edge states exist in the gapless phase for the system under open boundary condition in one direction. The detaching points between the edge states and the bulk states are predicted by the winding number associated with the vector field of average values of Pauli matrices. The non-Hermiticity also supports a topological phase with zero Chern number, where a pair of in-gap helical edge states exists. Our findings provide insights into the symmetry protected non-Hermitian topological insulators.

Tidal surface states as fingerprints of non-Hermitian nodal knot metals

“…If we consider V 1 as input and V 3 as output, we will have a positive term 1 R3 = −iω(i 1 ωR3 ), which is an imaginary positive term added to Eq. (19).…”

“…In those contexts, metallicity refers not to a Fermi surface intersection, but essentially embodies the antithesis of a band insulator, i.e. the absence of spectral gaps [6] Besides PT-symmetric systems with real eigenspectrum due to balanced gain and loss [7], non-Hermiticity, in combination with topology and surface terminations, has been recently shown to unfold a rich scope of experimentally robust phenomena far beyond mere dissipation [8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”

Non-Hermitian band topology with generalized inversion symmetry

“…Meanwhile, crystal symmetries give constraints on band structures. For instance, inversion symmetry prohibits a skin effect 3,21,78,79 . In Hermitian systems, symmetry constraints have been utilized to diagnose band topology from occupied states only at the highsymmetry points [80][81][82][83][84][85][86][87][88][89][90][91][92][93] .…”

Topological properties of non-Hermitian Creutz Ladders

“…Non-Hermitian extensions of the Creutz ladder have also been introduced in investigating anoma-lous edge localization of eigenmodes (i.e. the NHSE) [13,14] and non-Hermitian topological characterizations and BBC [37][38][39][40], and a potential application of controlling the NHSE via lattice shaking [41].…”