Topological classification of defects in non-Hermitian systems

Abstract

We classify topological defects in non-Hermitian systems with point gap, real line gap and imaginary line gap for all the Bernard-LeClair classes in all dimensions. The defect Hamiltonian H(k, r) is described by a non-Hermitian Hamiltonian with spatially modulated adiabatical parameter r surrounding the defect and belongs to any of 38 symmetry classes of general no-Hermitian systems. While the classification of defects in Hermitian systems has been explored in the context of standard ten-fold Altland-Zirnbauer symmetry classes, a complete understanding of the role of the general non-Hermitian symmetries on the topological defects and their associated classification are still lacking. By continuous transformation and homeomorphic mapping, these non-Hermitian defect systems can be mapped to topologically equivalent Hermitian systems with associated symmetries, and we get the topological classification by classifying the corresponding Hermitian Hamiltonians. We discuss some non-trivial classes with point gap according to our classification table, and give explicitly the topological invariants for these classes. By studying some lattice or continuous models, we find the correspondence between zero modes at the topological defect and the topological number in our studied models.

Impurity induced scale-free localization

“…It can trigger a wide variety of physical phenomena, such as the Anderson localization, topological edge states, and topological defect states. In non-Hermitian systems, intriguing physics from spatial inhomogeneity encompasses not just the non-Hermitian skin effect (NHSE) , but also impurity-induced or defect-induced topological bound states [30][31][32][33] , disorder-driven non-Hermitian topological phase transitions 34 , as well as non-Hermitian quasi-crystals and mobility edges with an incommensurate modulation [35][36][37][38] .…”

Symmetry and topological classification of Floquet non-Hermitian systems

“…For separable band structures without any symmetries, a purely homotopical classification [126][127][128] by taking into account the band braidings is carried out. Further refining the spectra to possess either a point-gap or line-gap results into the 38-fold BL classifications for the former and 54-fold generalized BL (GBL) classifications for the latter, respectively [14,[129][130][131][132][133]. The last quarter of the whole classification map for the Floquet non-Hermitian (FNH) system is not yet touched upon.…”

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

“…Non-Hermitian states of matter have attracted great attention in recent years due to their intriguing dynamical and topological properties (see [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 ] for reviews). Theoretically, a wide range of non-Hermitian topological phases and phenomena have been classified and characterized according to their symmetries [ 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ] and dynamical signatures [ 18 , 19 , 20 , 21 , 22 , 23 ]. Experimentally, non-Hermitian topological matter have also been realized in cold atom [ 24 , 25 ], photonic [ 26 , 27 , 28 , 29 ], acoustic [ 30 , 31 , 32 ], electrical circuit [ 33 , 34 , 35 ] systems, and nitrogen-vacancy-center in diamond [ 36 ], leading to potential applications such as topological lasers [ 37 , 38 , 39 ] and high-performance sensors [ 40 , 41 , 42 , 43 ].…”