Energy spectra for quantum wires and 2DEGs in magnetic fields with Rashba and Dresselhaus spin-orbit interactions

We introduce an analytical approximation scheme to diagonalize parabolically confined two dimensional electron systems with both the Rashba and Dresselhaus spin-orbit interactions. The starting point of our perturbative expansion is a zeroth-order Hamiltonian for an electron confined in a quantum wire with an effective spin-orbit induced magnetic field along the wire, obtained by properly rotating the usual spin-orbit Hamiltonian. We find that the spin-orbit-related transverse coupling terms can be recast into two parts W and V, which couple crossing and non-crossing adjacent transverse modes, respectively. Interestingly, the zeroth-order Hamiltonian together with W can be solved exactly, as it maps onto the Jaynes-Cummings model of quantum optics. We treat the V coupling by performing a Schrieffer-Wolff transformation. This allows us to obtain an effective Hamiltonian to third order in the coupling strength k_Rl of V, which can be straightforwardly diagonalized via an additional unitary transformation. We also apply our approach to other types of effective parabolic confinement, e.g., 2D electrons in a perpendicular magnetic field. To demonstrate the usefulness of our approximate eigensolutions, we obtain analytical expressions for the n^th Landau-level g_n-factors in the presence of both Rashba and Dresselhaus couplings. For small values of the bulk g-factors, we find that spin-orbit effects cancel out entirely for particular values of the spin-orbit couplings. By solving simple transcendental equations we also obtain the band minima of a Rashba-coupled quantum wire as a function of an external magnetic field. These can be used to describe Shubnikov-de Haas oscillations. This procedure makes it easier to extract the strength of the spin-orbit interaction in these systems via proper fitting of the data.Comment: 13 pages, 11 figure

Gap formation in helical edge states with magnetic impurities

Helical edge states appear at the surface of two dimensional topological insulators and are characterized by spin up traveling in one direction and the spin down traveling in the opposite direction. Such states are protected by time reversal symmetry and no backscattering due to scalar impurities can occur. However, magnetic impurities break time reversal symmetry and lead to backscattering. Often their presence is unintentional, but in some cases they are introduced into the sample to open up gaps in the spectrum. We investigate the influence of random impurities on helical edge states, specifically how the gap behaves in the realistic case of impurities having both a magnetic and a scalar component. It turns out that for a fixed magnetic contribution the gap closes when either the scalar component, or Fermi velocity is increased. We compare diagrammatic techniques in the self-consistent Born approximation to numerical calculations which yields good agreement. For experimentally relevant parameters we find that even moderate scalar components can be quite detrimental for the gap formation.Comment: 6 pages, 6 figure

Temperature dependency of resonance fluorescence from InAs/GaAs quantum dots : dephasing mechanisms

We report a study on temperature-dependent resonant fluorescence from InAs/GaAs quantum dots. We combined spectral and temporal measurements in order to identify sources of dephasing. In the spectral domain, we observed temperature-dependent broadening of the zero-phonon line as 0.3 μeV/K, and a temperature-dependent phonon broadband. Time-resolved autocorrelation measurements revealed temperature-dependent spin pumping times between T1,s = 6 ns (4 K) and 0.5 ns (15 K). These results are compared against theoretical modeling with a master equation for a four-level system coupled to phonon and spin baths. We explained the results by phonon-mediated hole-spin scattering between two excited states, with the piezophonons as a dominant mechanism.Publisher PDFPeer reviewe

Snaking states on a cylindrical surface in a perpendicular magnetic field

We calculate electronic states on a closed cylindrical surface as a model of a core-shell nanowire. The length of the cylinder can be infinite or finite. We define cardinal points on the circumference of the cylinder and consider a spatially uniform magnetic field perpendicular to the cylinder axis,in the direction South-North. The orbital motion of the electrons depends on the radial component of the field which is not uniform around the circumference: it is equal to the total field at North and South, but vanishes at the West and East sides. For a strong field, when the magnetic length is comparable to the radius of the cylinder, the electronic states at North and South become localized cyclotron orbits, whereas at East and West the states become long and narrow snaking orbits propagating along the cylinder. The energy of the cyclotron states increases with the magnetic field whereas the energy of the snaking states is stable. Consequently, at high magnetic fields the electron density vanishes at North and South and concentrates at East and West. We include spin-orbit interaction with linear Rashba and Dresselhaus models. For a cylinder of finite length the Dresselhaus interaction produces an axial twist of the charge density relative to the center of the wire, which may be amplified in the presence of the Rashba interaction.Comment: 12 pages, 11 figure

Thermoelectric current in topological insulator nanowires with impurities

In this paper we consider charge current generated by maintaining a temperature difference over a nanowire at zero voltage bias. For topological insulator nanowires in a perpendicular magnetic field the current can change sign as the temperature of one end is increased. Here we study how this thermoelectric current sign reversal depends on magnetic field and how impurities affect the size of the thermoelectric current. We consider both scalar and magnetic impurities and show that their influence on the current are quite similar, although the magnetic impurities seem to be more effective in reducing the effect. For moderate impurity concentration the sign reversal persists.Comment: 8 pages, 3 figure

Reversal of thermoelectric current in tubular nanowires

We calculate the charge current generated by a temperature bias between the two ends of a tubular nanowire. We show that in the presence of a transversal magnetic field the current can change sign, i.e., electrons can either flow from the hot to the cold reservoir, or in the opposite direction, when the temperature bias increases. This behavior occurs when the magnetic field is sufficiently strong, such that Landau and snaking states are created, and the energy dispersion is non-monotonic with respect to the longitudinal wave vector. The sign reversal can survive in the presence of impurities. We predict this result for core/shell nanowires, for uniform nanowires with surface states due to the Fermi level pinning, and for topological insulator nanowires.Comment: Main text and Supplemental Material (8 pages, 7 figures