Experimental observation of edge-dependent quantum pseudospin Hall effect

TL;DR

This study experimentally demonstrates an edge-dependent quantum pseudospin Hall effect in electric circuits, revealing how edge shape influences topological boundary states and helicity flipping.

Contribution

First experimental observation of edge-dependent quantum pseudospin Hall effect using electric circuits with different edge geometries, linking boundary shape to topological properties.

Findings

Helicity flipping of topological in-gap modes observed.

Edge shape determines the mirror winding number.

Boundary effects influence the QSH phase.

Abstract

It is a conventional wisdom that the helical edge states of quantum spin Hall (QSH) insulator are particularly stable due to the topological protection of time-reversal symmetry. Here, we report the first experimental observation of an edge-dependent quantum (pseudo-)spin Hall effect by employing two Kekule electric circuits with molecule-zigzag and partially-bearded edges, where the chirality of the circulating current in the unit cell mimics the electron spin. We observe a helicity flipping of the topological in-gap modes emerging in opposite parameter regions for the two edge geometries. Experimental findings are interpreted in terms of the mirror winding number defined in the unit cell, the choice of which exclusively depends on the edge shape. Our work offers a deeper understanding of the boundary effect on the QSH phase, and pave the way for studying the spin-dependent topological physics in electric circuits.