Breakdown of Non-Bloch Bulk-Boundary Correspondence and Emergent Topology in Floquet Non-Hermitian Systems

TL;DR

The paper addresses the breakdown of non-Bloch bulk–boundary correspondence in Floquet non-Hermitian systems due to finite-size quasienergy spectrum instability. It introduces a singular-value–based framework in momentum space, using $U(T)$ and its $\pm I$ sectors to define the invariants $\mathcal{V}_1$ and $\mathcal{V}_2$, which count zero- and $\pi/T$-mode edge states in the thermodynamic limit. It further develops a real-space counterpart with $\tilde{H}_{\pm}$ to count edge states via $\mathcal{V}'_1$ and $\mathcal{V}'_2$, validating bulk–boundary in the presence of disorder. The results yield phase diagrams with tunable edge states, including coexistence of 0- and $\pi/T$-mode topology, and point to experimental realizations in photonics and quantum walks, establishing an intrinsic bulk-boundary framework for Floquet non-Hermitian topology.

Abstract

Topological edge states in gaps of non-Hermitian systems are robust due to topological protection. Using the non-Hermitian Floquet Su-Schrieffer-Heeger model, we show that this robustness can break down: edge states may be suppressed by infinitesimal perturbations that preserve sublattice symmetry. We identify this fragility to the instability of the quasienergy spectrum in finite-size systems, leading to a breakdown of the non-Bloch bulk-boundary correspondence defined on the generalized Brillouin zone. To resolve this, we establish a correspondence between the number of stable zero-mode singular states and the topologically protected edge states in the thermodynamic limit. Our results formulate a bulk-boundary correspondence for Floquet non-Hermitian systems, where topology arises intrinsically from the driven non-Hermitian systems, even without symmetries. Our results provide a promising new avenue for exploring novel non-Hermitian topological phases.

Figures (4)

• Figure 1: Schematics of the Su-Schrieffer-Heeger model on a chain. The box indicates the unit cell.
• Figure 2: (a) Quasienergy spectra with the change of the driving amplitude under the open boundary conditions. The 0-mode (b) and (c) $\pi/T$-mode with the change of the disorder strength under the open boundary conditions. (d) disorder-averaged weighted inverse participation ratio. The results for green and crimson line are used $f=1$ and $f=1.5$, respectively. We use $w=1$, $\gamma=1.5$, $q=2$, $T_1=T_2=0.7$, and $N=25$. (b), (c), and (d) is obtained after 500 times average to the disorder.
• Figure 3: The singular spectra of $U(T)\pm I$ with the change of the driving amplitude under open boundary conditions in (a), (c) and corresponding winding number in (b), (d). We use $w=1$, $\gamma=1.5$, $q=2$, and $T_1=T_2=0.7$.
• Figure 4: Phase diagram characterized by $\mathcal{V}_1$ (a) and $\mathcal{V}_2$ (b). The white lines are the phase boundaries that can be obtained from the band touching points of ${H}_{eff}$. We use $\gamma=1.5$, $q=2$, and $T_1=T_2=0.7$.