Quantum Spin Hall Effect in Strip of Stripes Model

TL;DR

This paper explores quantum spin Hall effects in anisotropic stripe models, revealing helical modes with integer and fractional charges, and highlighting potential for studying electron correlations in topological insulators.

Contribution

Introduces two simple quasi-one-dimensional models demonstrating helical modes with integer and fractional charges, advancing understanding of electron correlations in topological insulators.

Findings

Helical modes exist in both models with opposite spin propagation.

Integer regime modes carry elementary electron charge.

Fractional regime modes carry fractional charges with anyonic statistics.

Abstract

We consider quantum spin Hall effect in an anisotropic strip of stripes and address both integer and fractional filling factors. The first model is based on a gradient of spin-orbit interaction in the direction perpendicular to the stripes. The second model is based on two weakly coupled strips with reversed dispersion relations. We demonstrate that these systems host helical modes, modes in which opposite spins propagate in opposite directions. In the integer regime, the modes carry an elementary electron charge whereas in the fractional regime they carry fractional charges, and their excitations possess anyonic braiding statistics. These simple quasi-one-dimensional models can serve as a platform for understanding effects arising due to electron-electron correlations in topological insulators.