Harper-Hofstadter problem for 2D electron gas with k{\bf k}-linear Rashba spin-orbit coupling

The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum, spinor wave functions as well as the spin density and average spin polarization are calculated for actual parameters of semiconductor structure. Our calculations show that in two-dimensional electron gas subject to periodic potential and uniform magnetic field the effects of energy spectrum splitting caused by large spin-orbit Rashba coupling can be observed experimentally.Comment: 8 pages, 6 figures. submitted to Europhys. Letter

Evidence for magnetoplasmon character of the cyclotron resonance response of a two-dimensional electron gas

Experimental results on the absolute magneto-transmission of a series of high density, high mobility GaAs quantum wells are compared with the predictions of a recent magnetoplasmon theory for values of the filling factor above 2. We show that the magnetoplasmon picture can explain the non-linear features observed in the magnetic field evolution of the cyclotron resonance energies and of the absorption oscillator strength. This provides experimental evidence that inter Landau level excitations probed by infrared spectroscopy need to be considered as many body excitations in terms of magnetoplasmons: this is especially true when interpreting the oscillator strengths of the cyclotron transitions

Double-exciton component of the cyclotron spin-flip mode in a quantum Hall ferromagnet

We report on the calculation of the cyclotron spin-flip excitation (CSFE) in a spin-polarized quantum Hall system at unit filling. This mode has a double-exciton component which contributes to the CSFE correlation energy but can not be found by means of a mean field approach. The result is compared with available experimental data.Comment: 9 pages, 2 figure

Interacting fermions in two dimensions: beyond the perturbation theory

We consider a system of 2D fermions with short-range interaction. A straightforward perturbation theory is shown to be ill-defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By re-summing the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a non-analytic, $T^{2}$-part of the specific heat.Comment: 5 pages, 4 figure

Spin relaxation and anticrossing in quantum dots: Rashba versus Dresselhaus spin-orbit coupling

The spin-orbit splitting of the electron levels in a two-dimensional quantum dot in a perpendicular magnetic field is studied. It is shown that at the point of an accidental degeneracy of the two lowest levels above the ground state the Rashba spin-orbit coupling leads to a level anticrossing and to mixing of spin-up and spin-down states, whereas there is no mixing of these levels due to the Dresselhaus term. We calculate the relaxation and decoherence times of the three lowest levels due to phonons. We find that the spin relaxation rate as a function of a magnetic field exhibits a cusp-like structure for Rashba but not for Dresselhaus spin-orbit interaction.Comment: 6 pages, 1 figur

Observation of exchange Coulomb interactions in the quantum Hall state at nu=3

Coulomb exchange interactions of electrons in the nu=3 quantum Hall state are determined from two inter-Landau level spin-flip excitations measured by resonant inelastic light scattering. The two coupled collective excitations are linked to inter-Landau level spin-flip transitions arising from the N=0 and N=1 Landau levels. The strong repulsion between the two spin-flip modes in the long-wave limit is clearly manifested in spectra displaying Coulomb exchange contributions that are comparable to the exchange energy for the quantum Hall state at nu=1. Theoretical calculations within the Hartree-Fock approximation are in a good agreement with measured energies of spin-flip collective excitations.Comment: 5 pages, 3 figures, to appear in PRB Rapid Communication

De Haas-van Alphen effect in two- and quasi two-dimensional metals and superconductors

An analytical form of the quantum magnetization oscillations (de Haas-van Alphen effect) is derived for two- and quasi two-dimensional metals in normal and superconducting mixed states. The theory is developed under condition that the chemical potential is much greater than the cyclotron frequency, which is proved to be valid for using grand canonical ensemble in the systems of low dimensionality. Effects of impurity, temperature, spin-splitting and vortex lattice - in the case of superconductors of type II -, are taken into account. Contrary to the three dimensional case, the oscillations in sufficiently pure systems of low dimensionality and at sufficiently low temperatures are characterized by a saw-tooth wave form, which smoothened with temperature and concentration of impurities growth. In the normal quasi two-dimensional systems, the expression for the magnetization oscillations includes an extra factor expressed through the transfer integral between the layers. The additional damping effect due to the vortex lattice is found. The criterion of proximity to the upper critical field for the observation of de Haas-van Alphen effect in the superconducting mixed state is established.Comment: 18 pages, Latex, revised versio

Electron spin-orbit splitting in InGaAs/InP quantum well studied by means of the weak antilocalization and spin-zero effects in tilted magnetic fields

The coupling between Zeeman spin splitting and Rashba spin-orbit terms has been studied experimentally in a gated InGaAs/InP quantum well structure by means of simultaneous measurements of the weak antilocalization (WAL) effect and beating in the SdH oscillations. The strength of the Zeeman splitting was regulated by tilting the magnetic field with the spin-zeros in the SdH oscillations, which are not always present, being enhanced by the tilt. In tilted fields the spin-orbit and Zeeman splittings are not additive, and a simple expression is given for the energy levels. The Rashba parameter and the electron g-factor were extracted from the position of the spin zeros in tilted fields. A good agreement is obtained for the spin-orbit coupling strength from the spin-zeros and weak antilocalization measurements.Comment: Accepted for publication in Semiconductors Science and Technolog

Quasi-ballistic transport in HgTe quantum-well nanostructures

The transport properties of micrometer scale structures fabricated from high-mobility HgTe quantum-wells have been investigated. A special photoresist and Ti masks were used, which allow for the fabrication of devices with characteristic dimensions down to 0.45 $\mu$m. Evidence that the transport properties are dominated by ballistic effects in these structures is presented. Monte Carlo simulations of semi-classical electron trajectories show good agreement with the experiment.Comment: 3 pages, 3 figures; minor revisions: replaced "inelastic mean free path" with "transport mean free path"; corrected typing errors; restructered most paragraphs for easier reading; accepted for publication in AP

Anomalous Hall effect in a two-dimensional electron gas with spin-orbit interaction

We discuss the mechanism of anomalous Hall effect related to the contribution of electron states below the Fermi surface (induced by the Berry phase in momentum space). Our main calculations are made within a model of two-dimensional electron gas with spin-orbit interaction of the Rashba type, taking into account the scattering from impurities. We demonstrate that such an "intrinsic" mechanism can dominate but there is a competition with the impurity-scattering mechanism, related to the contribution of states in the vicinity of Fermi surface. We also show that the contribution to the Hall conductivity from electron states close to the Fermi surface has the intrinsic properties as well.Comment: 9 pages, 6 figure