Non-Hermitian extensions of higher-order topological phases and their biorthogonal bulk-boundary correspondence

Abstract

Non-Hermitian Hamiltonians, which describe a wide range of dissipative\nsystems, and higher-order topological phases, which exhibit novel boundary\nstates on corners and hinges, comprise two areas of intense current research.\nHere we investigate systems where these frontiers merge and formulate a\ngeneralized biorthogonal bulk-boundary correspondence, which dictates the\nappearance of boundary modes at parameter values that are, in general,\nradically different from those that mark phase transitions in periodic systems.\nBy analyzing the interplay between corner/hinge, edge/surface and bulk degrees\nof freedom we establish that the non-Hermitian extensions of higher-order\ntopological phases exhibit an even richer phenomenology than their Hermitian\ncounterparts and that this can be understood in a unifying way within our\nbiorthogonal framework. Saliently this works in the presence of the\nnon-Hermitian skin effect, and also naturally encompasses genuinely\nnon-Hermitian phenomena in the absence thereof.\n