Superior robustness of anomalous non-reciprocal topological edge states

Abstract

Robustness against disorder and defects is a pivotal advantage of topological systems1, manifested by the absence of electronic backscattering in the quantum-Hall2 and spin-Hall effects3, and by unidirectional waveguiding in their classical analogues4,5. Two-dimensional (2D) topological insulators4–13, in particular, provide unprecedented opportunities in a variety of fields owing to their compact planar geometries, which are compatible with the fabrication technologies used in modern electronics and photonics. Among all 2D topological phases, Chern insulators14–25 are currently the most reliable designs owing to the genuine backscattering immunity of their non-reciprocal edge modes, brought via time-reversal symmetry breaking. Yet such resistance to fabrication tolerances is limited to fluctuations of the same order of magnitude as their bandgap, limiting their resilience to small perturbations only. Here we investigate the robustness problem in a system where edge transmission can survive disorder levels with strengths arbitrarily larger than the bandgap—an anomalous non-reciprocal topological network. We explore the general conditions needed to obtain such an unusual effect in systems made of unitary three-port non-reciprocal scatterers connected by phase links, and establish the superior robustness of anomalous edge transmission modes over Chern ones to phase-link disorder of arbitrarily large values. We confirm experimentally the exceptional resilience of the anomalous phase, and demonstrate its operation in various arbitrarily shaped disordered multi-port prototypes. Our results pave the way to efficient, arbitrary planar energy transport on 2D substrates for wave devices with full protection against large fabrication flaws or imperfections.

Anomalous Floquet non-Hermitian skin effect in a ring resonator lattice

“…This type of complex spectrum is made possible by the fact that the present model is a Floquet system-i.e., it is governed by a (non-unitary) evolution operator Û rather than a (non-Hermitian) Hamiltonian, so that Re[φ] is an angle variable [45,47]. In other Floquet models, similar quasienergy wrappings have been shown to give rise to socalled anomalous Floquet insulators [47][48][49]54] and other anomalous Floquet phases [55,56]. Similarly, we call the present behavior the "anomalous Floquet NHSE".…”

“…By analyzing lattice modes as Floquet eigenstates [43][44][45], we found a new variant of the NHSE, the anomalous Floquet NHSE, in which skin modes exist at every quasienergy. This phenomenon arises from the special features of Floquet bandstructures, which had previously been exploited in anomalous Floquet insulators to produce broadband and extraordinarily robust topological states [54]. Similarly, the anomalous Floquet NHSE allows for broadband asymmetric transmission enabled by skin modes.…”

Topological properties of Floquet winding bands in a photonic lattice

“…They rather emerge from the generalised Floquet topological invariant related to the micromotion of the system during one driving period [4]. Such anomalous Floquet phases have been reported in 1D photonic lattices [20,[23][24][25] and in 2D systems [26][27][28][29], and they can also exist in a Floquet winding metal that features two non-touching bands.…”

Topological Photonic Crystals: Physics, Designs, and Applications

“…In the quantum Hall PCs under the external electric or magnetic fields, one‐way chiral edge modes can be achieved. [ 107–110,116,17,305 ] As shown in Figure a, these edge states are unidirectional and are robust against obstacles. Even when a metallic scatterer is placed in the interface, the left‐ward propagating edge modes do not suffer backscattering.…”