22 research outputs found
Probability distribution of Majorana end-state energies in disordered wires
One-dimensional topological superconductors harbor Majorana bound states at
their ends. For superconducting wires of finite length L, these Majorana states
combine into fermionic excitations with an energy that is
exponentially small in L. Weak disorder leaves the energy splitting
exponentially small, but affects its typical value and causes large
sample-to-sample fluctuations. We show that the probability distribution of
is log normal in the limit of large L, whereas the distribution of
the lowest-lying bulk energy level has an algebraic tail at small
. Our findings have implications for the speed at which a
topological quantum computer can be operated.Comment: 4 pages, 2 figure
Spin Accumulation in Diffusive Conductors with Rashba and Dresselhaus Spin-Orbit Interaction
We calculate the electrically induced spin accumulation in diffusive systems
due to both Rashba (with strength and Dresselhaus (with strength
spin-orbit interaction. Using a diffusion equation approach we find
that magnetoelectric effects disappear and that there is thus no spin
accumulation when both interactions have the same strength, .
In thermodynamically large systems, the finite spin accumulation predicted by
Chaplik, Entin and Magarill, [Physica E {\bf 13}, 744 (2002)] and by Trushin
and Schliemann [Phys. Rev. B {\bf 75}, 155323 (2007)] is recovered an
infinitesimally small distance away from the singular point .
We show however that the singularity is broadened and that the suppression of
spin accumulation becomes physically relevant (i) in finite-sized systems of
size , (ii) in the presence of a cubic Dresselhaus interaction of strength
, or (iii) for finite frequency measurements. We obtain the parametric
range over which the magnetoelectric effect is suppressed in these three
instances as (i) , (ii), and (iii) |\alpha|-|\beta| \lesssiM
\sqrt{\omega/m p_{\rm F}\ell} with the elastic mean free path and
the Fermi momentum. We attribute the absence of spin accumulation
close to to the underlying U (1) symmetry. We illustrate and
confirm our predictions numerically
Measurement of Rashba and Dresselhaus spin-orbit magnetic fields
Spin-orbit coupling is a manifestation of special relativity. In the
reference frame of a moving electron, electric fields transform into magnetic
fields, which interact with the electron spin and lift the degeneracy of
spin-up and spin-down states. In solid-state systems, the resulting spin-orbit
fields are referred to as Dresselhaus or Rashba fields, depending on whether
the electric fields originate from bulk or structure inversion asymmetry,
respectively. Yet, it remains a challenge to determine the absolute value of
both contributions in a single sample. Here we show that both fields can be
measured by optically monitoring the angular dependence of the electrons' spin
precession on their direction of movement with respect to the crystal lattice.
Furthermore, we demonstrate spin resonance induced by the spin-orbit fields. We
apply our method to GaAs/InGaAs quantum-well electrons, but it can be used
universally to characterise spin-orbit interactions in semiconductors,
facilitating the design of spintronic devices
Spin-dephasing anisotropy for electrons in a diffusive quasi-1D GaAs wire
We present a numerical study of dephasing of electron spin ensembles in a
diffusive quasi-one-dimensional GaAs wire due to the D'yakonov-Perel'
spin-dephasing mechanism. For widths of the wire below the spin precession
length and for equal strength of Rashba and linear Dresselhaus spin-orbit
fields a strong suppression of spin-dephasing is found. This suppression of
spin-dephasing shows a strong dependence on the wire orientation with respect
to the crystal lattice. The relevance for realistic cases is evaluated by
studying how this effect degrades for deviating strength of Rashba and linear
Dresselhaus fields, and with the inclusion of the cubic Dresselhaus term
Side jump contribution to spin-orbit mediated Hall effects and Berry curvature
Anomalous Hall effect and spin Hall effect originate due to spin-orbit
coupling that in the Kohn-Luttinger formalism is
represented by anomalous terms in the coordinate and velocity operators.
Relation of these operators to the Berry curvature in the momentum space is
presented for electrons in GaAs type semiconductors. For centrosymmetric
semiconductors, transformational properties of Berry curvature are discussed.Comment: 4 pages. Accepted for a special issue of Fiz. Tech. Semicond.
(Semiconductors, StPetersburg) dedicated to Vladimir I. Pere
Spin-spin coupling in electrostatically coupled quantum dots
We study the spin-spin coupling between two single-electron quantum dots due to the Coulomb and spin-orbit interactions, in the absence of tunneling between the dots. We find an anisotropic XY spin-spin interaction that is proportional to the Zeeman splitting produced by the external magnetic field. This interaction is studied both in the limit of weak and strong Coulomb repulsion with respect to the level spacing of the dot. The interaction is found to be a nonmonotonic function of interdot distance a(0) and external magnetic field and, moreover, vanishes for some special values of a(0) and/or magnetic field orientation. This mechanism thus provides a new way to generate and tune spin interaction between quantum dots. We propose a scheme to measure this spin-spin interaction based on the spin-relaxation-measurement technique