$q$th-root non-Hermitian Floquet topological insulators

Abstract

Floquet phases of matter have attracted great attention due to their dynamical and topological nature that are unique to nonequilibrium settings. In this work, we introduce a generic way of taking any integer qqth-root of the evolution operator UU that describes Floquet topological matter. We further apply our qqth-rooting procedure to obtain 2^n2nth- and 3^n3nth-root first- and second-order non-Hermitian Floquet topological insulators~(FTIs). There, we explicitly demonstrate the presence of multiple edge and corner modes at fractional quasienergies \pm(0,1,...2^{n})\pi/2^{n}±(0,1,...2n)π/2n and \pm(0,1,...,3^{n})\pi/3^{n}±(0,1,...,3n)π/3n, whose numbers are highly controllable and capturable by the topological invariants of their parent systems. Notably, we observe non-Hermiticity induced fractional-quasienergy corner modes and the coexistence of non-Hermitian skin effect with fractional-quasienergy edge states. Our findings thus establish a framework of constructing an intriguing class of topological matter in Floquet open systems.

Generalized bulk-boundary correspondence in periodically driven non-Hermitian systems

“…Another important type of periodically driven systems are the periodically quenched systems [103,137,140,149,160,161]. For these systems, the topological invariants can be defined in real space (dubbed as open-bulk topological invariants) for the periodically driven non-Hermitian systems.…”

Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence

“…They have attracted great attention over the past decade [1][2][3][4][5][6]. The coupling of periodic driving fields to a system could not only deform its band structures and open topological gaps [7][8][9][10][11][12], but also generate new symmetry classifications [13][14][15][16] and anomalous Floquet phases with no static counterparts [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. The realization of Floquet topological matter in solid state and artificial systems [34][35][36][37][38][39][40][41][42][43][44][45] further promotes their applications in ultrafast electronics [3] and quantum computation [46][47]…”

Floquet topological superconductors with many Majorana edge modes: topological invariants, entanglement spectrum and bulk-edge correspondence

“…They have attracted great attention over the past decade [1][2][3][4][5]. The coupling of periodic driving fields to a system could not only deform its band structures and open topological gaps [6][7][8][9][10][11], but also generate new symmetry classifications [12][13][14][15] and anomalous Floquet phases with no static counterparts [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. The realization of Floquet topological matter in solid state and artificial systems [33][34][35][36][37][38][39][40][41][42][43][44] further promote their applications in ultrafast electronics [3] and quantum computation [45][46]…”