Non-Hermitian Disorder-induced Topological insulators

Abstract

Recent studies of disorder or non-Hermiticity induced topological insulators inject new ingredients for engineering topological matter. Here we consider the effect of purely non-Hermitian disorders, a combination of these two ingredients, in a 1D chiral symmetric lattice with disordered gain and loss. The increasing disorder strength can drive a transition from trivial to topological insulators, characterizing by the change of topological winding number defined by localized states in the gapless and complex bulk spectra. The non-Hermitian critical behaviors are characterized by the biorthogonal localization length of zero energy edge modes, which diverges at the critical transition point and establishes the bulk-edge correspondence. Furthermore, we show that the bulk topology may be experimentally accessed by measuring the biorthogonal chiral displacement C, which converges to the winding number through time-averaging and can be extracted from proper Ramsey-interference sequences. We propose a scheme to implement and probe such non-Hermitian disorder driven topological insulators using photons in coupled micro-cavities.

Topological Anderson insulators with different bulk states in quasiperiodic chains

“…As shown in Refs. [31,32,101], the real-space winding number ν can be generalized to non-Hermitian Hamiltonians under the biorthogonal basis. To this end, the matrix Q in Eq.…”

“…In recent years, the TAIs and their generalizations have been revealed in various systems [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30], even in some non-Hermitian systems [31][32][33][34][35][36][37] and in the presence of inter-particle interactions [38][39][40]. Some of them have been experimentally observed in engineered lattices, such as cold atomic gases [41], photonic and sonic crystals [42][43][44], electric circuits [45], and photonic quantum walks [36].…”

“…Moreover, exotic non-Hermitian TAIs induced by non-reciprocal hopping terms with random disorders in the generalized SSH model has been proposed and observed in Refs. [31][32][33][34][35][36]. It would be interesting to further study the disorder-induced TAIs in non-Hermitian quasiperiodic systems.…”

Bulk-Bulk Correspondence in Disordered Non-Hermitian Systems

“…Very recently, the study on disorder effect in non-Hermitian systems has also drawn extensive attentions [80][81][82][83][84][85][86][87][88][89][90][91][92][93]. Importantly, the NHSE could still exist in disordered samples [12][13][14][15][16][17] and leads to the breakdown of BBC for translational-symmetry-broken samples.…”

“…Although has achieved great successes in clean systems, the applicability of GBZ theory in disordered systems is still not fully understood because this theory is heavily based on the translational symmetry [52][53][54]. Therefore, the widely adopted GBZ theory may not be directly applicable [96] when disorder is presented [80][81][82][83][84][85][86][87][88][89][90][91][92][93][94][95]. The BBC mechanism as well as the quantitative description of the NHSE in disordered samples remain to be investigated.…”