Emergence of two-fold non-Hermitian spectral topology through synthetic spin engineering

TL;DR

This paper introduces a spin-engineered non-Hermitian model that reveals a novel two-fold spectral topology, controllable skin effects, and flat bands, with potential experimental realization in topoelectric circuits.

Contribution

It presents a synthetic spin-engineered non-Hermitian model with multi-fold spectral topology and controllable skin effects, expanding the understanding of spectral topology in symmetry class AI.

Findings

Discovery of two-fold spectral topology in a synthetic spin model.

Control over skin effect directionality via spin parameters.

Emergence of non-dispersive flat bands within the model.

Abstract

The union of topology and non-Hermiticity has led to the unveiling of many intriguing phenomena. We introduce a synthetic spin-engineered model belonging to symmetry class AI, which is a rare occurrence, and demonstrate the emergence of a multi-fold spectral topology. As an example of our proposal, we engineer non-Hermiticity in the paradigmatic Su-Schrieffer-Heeger (SSH) model by introducing a generalized synthetic spin, leading to an emergent two-fold spectral topology that governs the decoupled behaviour of the corresponding non-Hermitian skin effect. As a consequence of the spin choice, our model exhibits a rich phase diagram consisting of distinct topological phases, which we characterize by introducing the notion of paired winding numbers, which, in turn, predict the direction of skin localization under open boundaries. We demonstrate that the choice of spin parameters enables control over the directionality of the skin effect, allowing for it to be unilateral or bilateral. Furthermore, we discover non-dispersive flat bands emerging within the inherent SSH model framework, arising from the spin-engineering approach. We also introduce a simplified toy model to capture the underlying physics of the emergent flat bands and direction-selective skin effect. As an illustration of experimental feasibility, we present a topoelectric circuit that faithfully emulates the underlying spin-engineered Hamiltonian, providing a viable platform for realizing our predicted effects. Our findings pave way for the exploration of unconventional spectral topology through spin-designed models.