Finite size effects of helical edge states in HgTe/CdTe quantum wells

TL;DR

This paper investigates how finite size influences the energy spectrum of helical edge states in HgTe/CdTe quantum wells, revealing size-dependent gaps and magnetic field effects relevant to quantum spin Hall systems.

Contribution

It provides an analytical solution for finite size effects on helical edge states, including the exponential decay of the energy gap with sample width.

Findings

Edge states exhibit a finite energy gap due to coupling in finite samples.

The energy gap decays exponentially with increasing sample width.

Magnetic field dependence distinguishes these edge states from quantum Hall states.

Abstract

The solutions for the helical edge states for an effective continuum model for the quantum spin Hall effect in HgTe/CdTe quantum wells are presented. For a sample of a large size, the solution gives the linear dispersion for the edge states. However, in a finite strip geometry, the edge states at two sides will couple with each other, which leads to a finite energy gap in the spectra. The gap decays in an exponential law of the width of sample. The magnetic field dependence of the edge states illustrates the difference of the edge states from those of a conventional quantum Hall strip of two-dimensional electron gas.