Probing topological transitions in HgTe/CdTe quantum wells by magneto-optical measurements

TL;DR

This paper theoretically explores magneto-optical signatures of topological phase transitions in HgTe/CdTe quantum wells, identifying a distinctive low-energy absorption peak linked to edge states that signals the transition from quantum spin Hall to quantum Hall regimes.

Contribution

It introduces a method to distinguish QSH and QH regimes via magneto-optical measurements, highlighting the role of edge states and their signatures in the absorption spectrum.

Findings

Additional low-energy absorption peak in QSH regime due to edge states

Peak vanishes in QH regime when Fermi level is in the bulk gap

Edge state signature persists across various Fermi levels

Abstract

In two-dimensional topological insulators, such as inverted HgTe/CdTe quantum wells, helical quantum spin Hall (QSH) states persist even at finite magnetic fields below a critical magnetic field $B_\mathrm{c}$, above which only quantum Hall (QH) states can be found. Using linear-response theory, we theoretically investigate the magneto-optical properties of inverted HgTe/CdTe quantum wells, both for infinite two-dimensional and finite-strip geometries, and possible signatures of the transition between the QSH and QH regimes. In the absorption spectrum, several peaks arise due to non-equidistant Landau levels in both regimes. However, in the QSH regime, we find an additional absorption peak at low energies in the finite-strip geometry. This peak arises due to the presence of edge states in this geometry and persists for any Fermi level in the QSH regime, while in the QH regime the peak vanishes if the Fermi level is situated in the bulk gap. Thus, by sweeping the gate voltage, it is possible to experimentally distinguish between the QSH and QH regimes due to this signature. Moreover, we investigate the effect of spin-orbit coupling and finite temperature on this measurement scheme.