Exceptional non-Hermitian topological edge mode and its application to active matter

Abstract

Topological materials exhibit edge-localized scattering-free modes protected by their nontrivial bulk topology through the bulk-edge correspondence in Hermitian systems. While topological phenomena have recently been much investigated in non-Hermitian systems with dissipations and injections, the fundamental principle of their edge modes has not fully been established. Here, we reveal that, in non-Hermitian systems, robust gapless edge modes can ubiquitously appear owing to a mechanism that is distinct from bulk topology, thus indicating the breakdown of the bulk-edge correspondence. The robustness of these edge modes originates from yet another topological structure accompanying the branchpoint singularity around an exceptional point, at which eigenvectors coalesce and the Hamiltonian becomes nondiagonalizable. Their characteristic complex eigenenergy spectra are applicable to realize lasing wave packets that propagate along the edge of the sample. We numerically confirm the emergence and the robustness of the proposed edge modes in the prototypical lattice models. Furthermore, we show that these edge modes appear in a model of chiral active matter based on the hydrodynamic description, demonstrating that active matter can exhibit an inherently non-Hermitian topological feature. The proposed general mechanism would serve as an alternative designing principle to realize scattering-free edge current in non-Hermitian devices, going beyond the existing frameworks of non-Hermitian topological phases.

Non-Hermitian topology in rock–paper–scissors games

“…[69][70][71][72] discuss topology of interaction networks among strategies (i.e., interaction topology), it differs from the topology discussed in this paper. Thirdly, we note that EPs are also reported for active matters 73,74 . We would like to stress, however, that significance of this paper is to reveal the emergence of the EPs and how they affect the dynamics in systems of the evolutionary game theory which describes the population density of biological systems and human societies.…”

Topological phases protected by shifted sublattice symmetry in dissipative quantum systems

“…The topological phases are classified by the presence or absence of symmetries, and non-Hermicity of Hamiltonians enrichs their symmetry class [10][11][12]. Moreover, non-Hermitian systems exhibit unique topological phenomena that have no counterpart in closed systems, non-Hermitian skin effects, and breakdown of the bulk-edge correspondence [13][14][15][16][17]. Non-Hermitian Hamiltonians describe certain types of open systems, for example, classical optical systems with gain and/or loss [18,19], or postselected open quantum systems [20][21][22].…”

Exceptional mode topological surface laser

“…From a broad perspective, non-Hermitian topology influences a variety of fields in physics, including photonics [20][21][22], electrical circuits [23,24], quantum walks [25][26][27], and biological systems [28][29][30][31]. One of the promising applications of non-Hermitian topology is a topological laser [32][33][34][35][36] which amplifies the boundary modes. One can construct such topological laser by introducing judicious gain at the edge of the sample [33,34].…”

“…One can construct such topological laser by introducing judicious gain at the edge of the sample [33,34]. Another route to realize a topological laser is an exceptional edge mode [36], which is protected by nontrivial topology around EPs in the edge band structure.…”

“…Especially, topological lasers in three-dimensional systems are so far unexplored, while such extension is crucial to design a large-scale topological laser. Furthermore, topological lasers in two-dimensional systems have required judicious gains [33,34] or symmetries [11,35,36], which indicates their instability against noises that modify boundary configuration or break symme-tries. Thus, a three-dimensional topological laser without such restrictions will expand the potential of non-Hermitian devices.…”