  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.
