arXiv subjects

Sigurdur I. Erlingsson

Publications and source records attributed to Sigurdur I. Erlingsson.

35 records · Page 2Linked to original sources

arXiv2018

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.

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arXiv2018

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.

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arXiv2015

Asymmetric Landau bands due to spin-orbit coupling

We show that the Landau bands obtained in a two-dimensional lateral semiconductor superlattice with spin-orbit coupling (SOC) of the Rashba/Dresselhaus type, linear in the electron momentum, placed in a tilted magnetic field, do not follow the symmetry of the spatial modulation. Moreover, this phenomenology is found to depend on the relative tilt of magnetic field and on the SOC type: a) when only Rashba SOC exists and the magnetic field is tilted in the direction of the superlattice b) Dresselhaus SOC exists and the magnetic field is tilted in the direction perpendicular to the superlattice. Consequently, measurable properties of the modulated system become anisotropic in a tilted magnetic field when the field is conically rotated around the $z$ axis, at a fixed polar angle, as we demonstrate by calculating the resistivity and the magnetization.

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arXiv2015

An all electron topological insulator in InAs double wells

We show that electrons in ordinary III-V semiconductor double wells with an in-plane modulating periodic potential and inter well spin-orbit interaction are tunable Topological Insulators (TIs). Here the essential TI ingredients, namely, band inversion and the opening of an overall bulk gap in the spectrum arise, respectively, from (i) the combined effect of the double well even-odd state splitting $Δ_{SAS}$ together with the superlattice potential and (ii) the interband Rashba spin-orbit coupling $η$. We corroborate our exact diagonalization results by an analytical nearly-free electron description that allows us to derive an effective Bernevig-Hughes-Zhang (BHZ) model. Interestingly, the gate-tunable $Δ_{SAS}$ drives a topological phase transition featuring a discontinuous Chern number at $Δ_{SAS}\sim 5.4$ meV. Finally, we explicitly verify the bulk-edge correspondence by considering a strip configuration and determining not only the bulk bands in the non-topological and topological phases but also the edge states and their Dirac-like spectrum in the topological phase. The edge electronic densities exhibit peculiar spatial oscillations as they decay away into the bulk. For concreteness, we present our results for InAs-based wells with realistic parameters.

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arXiv2013

Thermoelectric Current and Coulomb-Blockade Plateaus in a Quantum Dot

A Generalized Master Equation (GME) is used to study the thermoelectric currents through a quantum dot in both the transient and steady-state regime. The two semi-infinite leads are kept at the same chemical potential but at different temperatures to produce a thermoelectric current which has a varying sign depending on the chemical potential. The Coulomb interaction between the electrons in the sample is included via the exact diagonalization method. We observe a saw-teeth like profile of the current alternating with plateaus of almost zero current. Our calculations go beyond the linear response with respect to the temperature gradient, but are compatible with known results for the thermopower in the linear response regime.

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arXiv2011

Effects of scattering area shape on spin conductance in a four-terminal spin-Hall setup

We study spin conductance in a ballistic and quasi-ballistic two dimensional electron system with Rasbha spin-orbit coupling. The system has a four-terminal geometry with round corners at the connection to the leads. It is found that by going from sharp corners to more round corners in the ballistic system the energy depended spin conductance goes from being relatively flat to a curve showing a series of minima and maxima. It is also found that when changing the size of the terminal area by modifying the roundness of the terminal corners the maxima and minima in the transverse spin conductance are shifted in energy. This shift is due increased (decreased) energy for smaller (larger) terminal area. These results were also found to be reasonably stable in quasi-ballistic systems.

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arXiv2011

Rashba spin orbit interaction in a quantum wire superlattice

In this work we study the effects of a longitudinal periodic potential on a parabolic quantum wire defined in a two-dimensional electron gas with Rashba spin-orbit interaction. For an infinite wire superlattice we find, by direct diagonalization, that the energy gaps are shifted away from the usual Bragg planes due to the Rashba spin-orbit interaction. Interestingly, our results show that the location of the band gaps in energy can be controlled via the strength of the Rashba spin-orbit interaction. We have also calculated the charge conductance through a periodic potential of a finite length via the non-equilibrium Green's function method combined with the Landauer formalism. We find dips in the conductance that correspond well to the energy gaps of the infinite wire superlattice. From the infinite wire energy dispersion, we derive an equation relating the location of the conductance dips as a function of the (gate controllable) Fermi energy to the Rashba spin-orbit coupling strength. We propose that the strength of the Rashba spin-orbit interaction can be extracted via a charge conductance measurement.

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arXiv2010

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.

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arXiv2005

Determining the spin Hall conductance via charge transport

We propose a scheme where transport measurements of charge current and its noise can be used to determine the spin Hall conductance in a four-terminal setup. Starting from the scattering formalism we express the spin current and spin Hall conductance in terms of spin-dependent transmission coefficients. These coefficients are then expressed in terms of charge current and noise. We use the scheme to characterize the spin injection efficiency of a ferromagnetic/semiconductor interface.

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arXiv2005

Spin susceptibilities, spin densities and their connection to spin-currents

We calculate the frequency dependent spin susceptibilities for a two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit interaction. The resonances of the susceptibilities depends on the relative values of the Rashba and Dresselhaus spin-orbit constants, which could be manipulated by gate voltages. We derive exact continuity equations, with source terms, for the spin density and use those to connect the spin current to the spin density. In the free electron model the susceptibilities play a central role in the spin dynamics since both the spin density and the spin current are proportional to them.

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arXiv2004

Evolution of a localized electron spin in a nuclear spin environment

Motivated by recent interest in the role of the hyperfine interaction in quantum dots we study the dynamics of a localized electron spin coupled to many nuclei. An important feature of the model is that the coupling to an individual nuclear spin depends on its position in the quantum dot. We introduce a semi-classical description of the system valid in the limit of a large number of nuclei and analyze the resulting classical dynamics. Contrary to a natural assumption, the correlation functions of electron spin with an arbitrary initial condition show no decay in time. Rather, they exhibit complicated undamped oscillations. This may be attributed to the fact that the system has many integrals of motion and is close to an integrable one. The ensemble averaged correlation functions do exhibit a slow decay (1/ln(t)) for t -> \infty.

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arXiv2003

Coherent oscillations of current due to nuclear spins

We propose a mechanism for very slow coherent oscillations of current and nuclear spins in a quantum dot system, that may qualitatively explain some recent experimental observations. We concentrate on an experimentally relevant double dot setup where hyperfine interaction lifts the spin blockade. We study the dependence of the magnitude and period of the oscillations on magnetic field and anisotropy.

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arXiv2002

Hyperfine-mediated transitions between a Zeeman split doublet in GaAs quantum dots: The role of the internal field

We consider the hyperfine-mediated transition rate between Zeeman split spin states of the lowest orbital level in a GaAs quantum dot. We separate the hyperfine Hamiltonian into a part which is diagonal in the orbital states and another one which mixes different orbitals. The diagonal part gives rise to an effective (internal) magnetic field which, in addition to an external magnetic field, determines the Zeeman splitting. Spin-flip transitions in the dots are induced by the orbital mixing part accompanied by an emission of a phonon. We evaluate the rate for different regimes of applied magnetic field and temperature. The rates we find are bigger that the spin-orbit related rates provided the external magnetic field is sufficiently low.

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arXiv2001

Nucleus-mediated spin-flip transitions in GaAs quantum dots

Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the possibilities to manipulate spin states in the dots. We present here estimations of inelastic spin-flip rates mediated by hyperfine interaction with nuclei. Under general assumptions the nucleus mediated rate is proportional to the phonon relaxation rate for the corresponding non-spin-flip transitions. The rate can be accelerated in the vicinity of a singlet-triplet excited states crossing. The small proportionality coefficient depends inversely on the number of nuclei in the quantum dot. We compare our results with known mechanisms of spin-flip in $GaAs$ quantum dot.

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arXiv1999

Magnetization in short-period mesoscopic electron systems

We calculate the magnetization of the two-dimensional electron gas in a short-period lateral superlattice, with the Coulomb interaction included in Hartree and Hartree-Fock approximations. We compare the results for a finite, mesoscopic system modulated by a periodic potential, with the results for the infinite periodic system. In addition to the expected strong exchange effects, the size of the system, the type and the strength of the lateral modulation leave their fingerprints on the magnetization.

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arXiv1999

Finite size effects in the magnetization of periodic mesoscopic systems

We calculate the orbital magnetization of a confined 2DEG as a function of the number of electrons in the system. Size effects are investigated by systematically increasing the area of the confining region. The results for the finite system are compared to an infinite one, where the magnetization is calculated in the thermodynamic limit. In all calculations the electron-electron interaction is included in the Hartree approximation.

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arXiv1997

The far-infrared absorption of a periodic 2DEG in the transition regime between weak and strong modulation

We study the optical absorption of arrays of quantum dots and antidots in a perpendicular homogeneous magnetic field. The electronic system is described quantum mechanically using a Hartree approximation for the mutual Coulomb interaction of the electrons. The evolution of the absorption is traced from the homogeneous to the strongly modulated case identifying the ensuing collective modes, the magnetoplasmons, and their correlations with inherent length scales of the system.

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