High-Winding-Number Zero-Energy Edge States in Rhombohedral-Stacked Su-Schrieffer-Heeger Multilayers

TL;DR

This paper explores high-winding-number topological edge states in rhombohedral-stacked multilayer Su-Schrieffer-Heeger systems, revealing a linear relationship between layer number and topological invariant, and introduces Wigner entropy as a detection tool.

Contribution

It demonstrates that rhombohedral stacking enables systematic engineering of high-winding-number topological phases with a novel entropy-based detection method.

Findings

Zero-energy edge states scale with layer number

Winding number linearly increases with layers

Wigner entropy effectively detects topological states

Abstract

We study the topological properties of rhombohedral-stacked N-layer Su-Schrieffer-Heeger networks with interlayer coupling. We find that these systems exhibit $2N$-fold degenerate zero-energy edge states with winding number $W=N$, providing a direct route to high-winding-number topological phases where $W$ equals the layer number. Using effective Hamiltonian theory and Zak phase calculations, we demonstrate that the winding number scales linearly with $N$ through a layer-by-layer topological amplification mechanism. We introduce the Wigner entropy as a novel detection method for these edge states, showing that topological boundary states exhibit significantly enhanced Wigner entropy compared to bulk states. Our results establish rhombohedral stacking as a systematic approach for engineering high-winding-number topological insulators with potential applications in quantum information processing.