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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., Comment: 14 pages, 13 figures

The fractional-dimensional space approach is extended to study exciton and shallow-donor states in symmetric-coupled ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}\ensuremath{-}\mathrm{G}\mathrm{a}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ multiple quantum wells. In this scheme, the real anisotropic ``exciton (or shallow donor) plus multiple quantum well'' semiconductor system is mapped, for each exciton (or donor) state, into an effective fractional-dimensional isotropic environment, and the fractional dimension is essentially related to the anisotropy of the actual semiconductor system. Moreover, the fractional-dimensional space approach was extended to include magnetic-field effects in the study of shallow-impurity states in ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}\ensuremath{-}\mathrm{G}\mathrm{a}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ quantum wells and superlattices. In our study, the magnetic field was applied along the growth direction of the semiconductor heterostructure, and introduces an additional degree of confinement and anisotropy besides the one imposed by the heterostructure barrier potential. The fractional dimension is then related to the anisotropy introduced both by the heterostructure barrier potential and magnetic field. Calculations within the fractional-dimensional space scheme were performed for the binding energies of $1s$-like heavy-hole direct exciton and shallow-donor states in symmetric-coupled semiconductor quantum wells, and for shallow-impurity states in semiconductor quantum wells and superlattices under growth-direction applied magnetic fields. Fractional-dimensional theoretical results are shown to be in good agreement with previous variational theoretical calculations and available experimental measurements.

The fractional-dimensional approach, in which the real semiconductor heterostructure system is substituted by an effective isotropic environment with a fractional dimension, was used in the study of ground and excited excitonic states in GaAs-(Ga,Al)As quantum wells. The fractional-dimensional formalism was extended to include the possibility of dealing with excited states and varying effective masses across the heterostructure interfaces, with the fractional dimension chosen in a systematic way. Theoretical fractional-dimensional results for ground-state $1s$-like exciton states in GaAs-(Ga,Al)As quantum wells were shown to be in good agreement with previous detailed calculations and recent experimental measurements. Moreover, theoretical results within the fractional-dimensional scheme were found in excellent agreement with the recent experimental high-resolution spectroscopic studies on excited-exciton states of shallow ${\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}\ensuremath{-}\mathrm{G}\mathrm{a}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ quantum wells with Al concentration in the range of 1--4.5 %.

The charge density relaxation propagator of a two dimensional electron system, which is the slope of the imaginary part of the polarization function, exhibits singularities for bosonic momenta having the order of the spin-orbit momentum and depending on the momentum orientation. We have provided an intuitive understanding for this non-analytic behavior in terms of the inter chirality subband electronic transitions, induced by the combined action of Bychkov-Rashba (BR) and Dresselhaus (D) spin-orbit coupling. It is shown that the regular behavior of the relaxation propagator is recovered in the presence of only one BR or D spin-orbit field or for spin-orbit interaction with equal BR and D coupling strengths. This creates a new possibility to influence carrier relaxation properties by means of an applied electric field., 4 figures

Using analytical formulas as well as a finite-difference scheme, we investigate the magnetic field dependence of the energy spectra and magnetic edge states of HgTe/CdTe-based quantum wells in the presence of perpendicular magnetic fields and hard walls, for the band-structure parameters corresponding to the normal and inverted regimes. Whereas one cannot find counterpropagating, spin-polarized states in the normal regime, below the crossover point between the uppermost (electron-like) valence and lowest (hole-like) conduction Landau levels, one can still observe such states at finite magnetic fields in the inverted regime, although these states are no longer protected by time-reversal symmetry. Furthermore, the bulk magnetization and susceptibility in HgTe quantum wells are studied, in particular their dependence on the magnetic field, chemical potential, and carrier densities. We find that for fixed chemical potentials as well as for fixed carrier densities, the magnetization and magnetic susceptibility in both the normal and the inverted regimes exhibit de Haas-van Alphen oscillations, whose amplitude decreases with increasing temperature. Moreover, if the band structure is inverted, the ground-state magnetization (and consequently also the ground-state susceptibility) is discontinuous at the crossover point between the uppermost valence and lowest conduction Landau levels. At finite temperatures and/or doping, this discontinuity is canceled by the contribution from the electrons and holes and the total magnetization and susceptibility are continuous. In the normal regime, this discontinuity of the ground-state magnetization does not arise and the magnetization is continuous for zero as well as finite temperatures., Comment: 19 pages, 26 figures

By exploiting our recently derived exact formula for the Lindhard polarization function in the presence of Bychkov-Rashba (BR) and Dresselhaus (D) spin-orbit interaction (SOI), we show that the interplay of different SOI mechanisms induces highly anisotropic modifications of the static dielectric function. We find that under certain circumstances the polarization function exhibits doubly-singular behavior, which leads to an intriguing novel phenomenon, beating of Friedel oscillations. This effect is a general feature of systems with BR+D SOI and should be observed in structures with a sufficiently strong SOI., Comment: 3 figures

By considering a linear in momentum but otherwise arbitrary spin-orbit coupling (SOC), we derive a simple analytical expression for the current-driven spin torque in a single ferromagnetic layer. Explicit forms of the spin torque are given for structures with different SOC fields, in dependence of strain effects, growth direction, and/or symmetry under spatial inversion. The Landau-Lifshitz-Gilbert equation including the effects of the SOC mediated spin torque on the magnetization dynamics is briefly discussed.

Using a microscopic theory based on the density matrix formalism we investigate quantum revivals and collapses of the charge polarization and charge current dynamics in mesoscopic rings driven by short asymmetric electromagnetic pulses. The collapsed state is utilized for sub-picosecond switching of the current and associated magnetization, enabling thus the generation of pulsed magnetic fields with a tunable time structure and shape asymmetry which provides a new tool to study ultrafast spin-dynamics and ratchet-based effects., 4 pages, 2 figures

A presently realizable picosecond half-cycle electromagnetic pulse (HCP) consists of a short (

The binding energy and the effective mass of a polaron confined in a $\mathrm{GaAs}\ensuremath{-}{\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}\mathrm{As}$ quantum well are calculated within the framework of the fractional-dimensional space approach. In this scheme, the real confined ``polaron plus quantum well'' system is mapped onto an effective fractional-dimensional bulk in which the polaron behaves unconfined, and the fractional dimension is essentially related to the degree of confinement of the actual system. Analytical expressions allowing a very simple estimation of the corresponding polaron corrections are found. The fractional-dimensional theoretical results are shown to be in good agreement with previous more detailed calculations.