Non-Bloch topological invariants in a non-Hermitian domain wall system

Abstract

We study non-Bloch bulk-boundary correspondence in a non-Hermitian Su-Schieffer-Heeger model in a domain-wall configuration where the left and right bulks have different parameters. Focusing on the case where chiral symmetry is still conserved, we show that non-Hermitian skin effects of bulk states persist in the system, while the definition of the non-Bloch winding number of either bulk depends on parameters on both sides of the boundary. Under these redefined non-Bloch topological invariants, we confirm non-Bloch bulk-boundary correspondence under the domain-wall configuration, which exemplifies the impact of boundary conditions in non-Hermitian topological systems. II. MODEL AND BLOCH TOPOLOGICAL INVARIANTSAs illustrated in Fig. 1, we consider a non-Hermitian SSH model in a domain-wall configuration on a ring. The arXiv:1903.03811v3 [cond-mat.quant-gas]

Non-Hermitian bulk–boundary correspondence in quantum dynamics

“…Here we identify topological edge states by their quasienergies = 0, π and coin states |± = (|0 ± |1 )/ √ 2. It follows that the bulk-state wave functions can be written as [4,36]…”

Probing non-Hermitian skin effect and non-Bloch phase transitions

“…Among the most relevant features observed in non-Hermitian systems, one should mention the strong sensitivity of the energy spectra on boundary conditions [7,[15][16][17][18][19][20][21], the non-Hermitian skin effect (NHSE) [7,9,17,18,[20][21][22][23][24], i.e. the exponential localization of continuum-spectrum eigenstates to the edges, and the failure of the bulkboundary correspondence based on Bloch band topological invariants [4,17,18,[24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Recently, several attempts have been suggested to restore the bulk-boundary correspondence, such as those based on the biorthogonal bulk-boundary correspondence [17], the non-Bloch bulk topological invariants [18,[25][26][27][28][29]35], the singular value decomposition [30], and the Green functions [31,32].…”

“…the exponential localization of continuum-spectrum eigenstates to the edges, and the failure of the bulkboundary correspondence based on Bloch band topological invariants [4,17,18,[24][25][26][27][28][29][30][31][32][33][34][35][36][37]. Recently, several attempts have been suggested to restore the bulk-boundary correspondence, such as those based on the biorthogonal bulk-boundary correspondence [17], the non-Bloch bulk topological invariants [18,[25][26][27][28][29]35], the singular value decomposition [30], and the Green functions [31,32]. A major consequence of the NHSE is that the bulk bands of the OBC system are considerably different from those of the PBC system.…”

“…While the latter are defined by ordinary Bloch band theory, the former are non-Bloch bands that require the quasi-momentum to become complex and to vary on a generalized Brillouin zone [18,25,26]. The usefulness of non-Bloch band theory in non-Hermitian systems is demonstrated by restoration of (non-Bloch) bulkboundary correspondence [18,[25][26][27][28][29] and in the study of non-Hermitian wave scattering and domain walls [35,38]. Another major consequence of the NSHE is that distinct bulk symmetry breaking phase transitions are observed when considering Bloch and non-Bloch bands, i.e.…”

Inversion symmetric non-Hermitian Chern insulator

“…Notably, the bulk-boundary correspondence fails in some non-Hermitian topological systems [57,61,99,[129][130][131][132][133][134][135][136][137][138][139][140][141][142]. The spectrum under the periodical boundary condition (PBC) significantly differs from that under the open boundary condition (OBC), and the eigenstates under OBC are all localized at the system boundary (the non-Hermitian skin effect) [133].…”