Non-Hermitian Floquet topological phases: Exceptional points, coalescent edge modes, and the skin effect

Abstract

Periodically driven non-Hermitian systems can exhibit rich topological band structure and non-Hermitian skin effect, without analogs in their static or Hermitian counterparts. In this work we investigate the exceptional band-touching points in the Floquet quasi-energy bands, the topological characterization of such exceptions points and the Floquet non-Hermitian skin effect (FNHSE). Specifically, we exploit the simplicity of periodically quenched two-band systems in one dimension or two dimensions to analytically obtain the Floquet effective Hamiltonian as well as locations of the many exceptional points possessed by the Floquet bulk bands. Two different types of topological winding numbers are used to characterize the topological features. Bulk-edge correspondence (BBC) is naturally found to break down due to FNHSE, which can be drastically different among different bulk states. Remarkably, given the simple nature of our model systems, recovering the BBC is doable in practice only for certain parameter regime where a low-order truncation of the characteristic polynomial (which determines the Floquet band structure) becomes feasible. Furthermore, irrespective of which parameter regime we work with, we find a number of intriguing aspects of Floquet topological zero modes and π modes. For example, under the open boundary condition zero edge modes and π edge modes can individually coalesce and localize at two different boundaries. These anomalous edge states can also switch their accumulation boundaries when certain system parameter is tuned. These results indicate that non-Hermitian Floquet topological phases, though more challenging to understand than their Hermitian counterparts, can be extremely rich in the presence of FNHSE. arXiv:1909.10234v1 [cond-mat.mes-hall]

Dynamic transition from insulating state to eta-pairing state in a composite non-Hermitian system

“…In the above, we know that there are many degenerate eigenstates for H A + H B , which may become coalescing states when proper non-Hermitian term is added [9]. For non-Hermitian operators, when EP appears, there are eigenstates coalesce into one state, leading to an incomplete Hilbert space [10][11][12][13]. Mathematically, it relates to the Jordan block form in the matrix [14][15][16][17].…”

Untying links through anti-parity-time-symmetric coupling

“…If the non-Hermiticity is = (0, 0, γ ), the topological phase transition and the existence of the edge state are unaltered because of the pseudo-anti-Hermiticity protection [34]; the topological properties of the non-Hermitian system are inherited by the EPs (exceptional rings or exceptional surfaces in 2D or 3D) [60][61][62][63][64][65][66][67]. If the non-Hermiticity is = (0, γ , 0), the non-Hermitian skin effect occurs under open boundary condition [54][55][56][57][58][59][68][69][70][71][72][73][74][75][76][77][78], the non-Hermitian Aharonov-Bohm effect under periodical boundary condition invalidates the conventional bulk-boundary correspondence [54], and the non-Bloch band theory is developed for topological characterization [77][78][79][80][81][82]. Here, the dissipation induced anti-PT -symmetric coupling corresponds to the imaginary part = (γ , 0, 0).…”

Non-Hermitian Floquet Phases with Even-Integer Topological Invariants in a Periodically Quenched Two-Leg Ladder

“…Recently, the study of non-Hermitian physics has been extended to Floquet systems, in which the interplay between time-periodic driving fields and gains/losses or nonreciprocal effects could potentially yield topological phases that are unique to driven non-Hermitian systems [ 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 ]. In early studies, various non-Hermitian Floquet topological phases and phenomena have been discovered, including non-Hermitian Floquet topological insulators [ 49 , 50 , 53 , 54 , 55 ], superconductors [ 52 ], semimetals [ 63 ], and skin effects [ 56 , 57 ]. Meanwhile, the time-averaged spin texture and mean chiral displacement have been suggested as two dynamical tools to extract the topological invariants of non-Hermitian Floquet systems [ 49 , 50 , 51 , 53 ].…”