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Dahlem Center for complex Quantum Systems
Dahlem Center for Complex Quantum SystemsContactMathias Duckheim


Publications Probability distribution of Majorana endstate energies in disordered wires Phys. Rev. Lett. 107, 196804 (2011) (pdf) ; arXiv:1104.1531v1 [condmat.meshall] (show/hide abstract)
Onedimensional 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 $\varepsilon_0$ that is exponentially small in $L$. Weak
disorder leaves the energy splitting exponentially small, but affects
its typical value and causes large sampletosample fluctuations. We
show that the probability distribution of $\varepsilon_0$ is log
normal in the limit of large $L$, whereas the distribution of the
lowestlying bulk energy level $\varepsilon_1$ has an algebraic tail
at small $\varepsilon_1$. Our findings have implications for the speed
at which a topological quantum computer can be operated.
Topological superconducting phases in disordered quantum wires with strong spinorbit coupling Phys. Rev. B 84, 144526 (2011) (pdf); arXiv:1103.2746v1 [condmat.meshall] (show/hide abstract)
Zeeman fields can drive semiconductor quantum wires with strong
spinorbit coupling and in proximity to swave superconductors into
a topological phase which supports end Majorana fermions and offers an
attractive platform for realizing topological quantum information
processing. Here, we investigate how potential disorder affects the
topological phase by a combination of analytical and numerical
approaches. Most prominently, we find that the robustness of the
topological phase against disorder depends sensitively and
nonmonotonously on the Zeeman field applied to the wire.
Andreev reflection from noncentrosymmetric superconductors and Majorana bound state generation in halfmetallic ferromagnets Highlighted as Editor's suggestion in Phys. Rev. B (show/hide abstract)
We study Andreev reflection at an interface between a half metal and a superconductor with spinorbit interaction. While the absence of minority carriers in the half metal makes singlet Andreev reflection impossible, the spinorbit interaction gives rise to triplet Andreev reflection, i.e., the reflection of a majority electron into a majority hole or vice versa. As an application of our calculation, we consider a thin half metal film or wire laterally attached to a superconducting contact. If the half metal is disorder free, an excitation gap is opened that is proportional to the spinorbit interaction strength in the superconductor. For electrons with energy below this gap a lateral halfmetalsuperconductor contact becomes a perfect triplet Andreev reflector. We show that the system supports localized Majorana end states in this limit.
Geometric Correlations and Breakdown of Mesoscopic Universality in Spin Transport Phys. Rev. Lett. 105, 246807 (2010) (pdf);arXiv:1008.4656v1 [condmat.meshall] (show/hide abstract)
We construct a unified semiclassical theory of charge and spin
transport in chaotic ballistic and disordered diffusive mesoscopic
systems with spinorbit interaction. Neglecting dynamic effects of
spinorbit interaction, we reproduce the random matrix theory results
that the spin conductance fluctuates universally around zero
average. Incorporating these effects in the theory, we show that
geometric correlations generate finite average spin conductances, but
that they do not affect the charge conductance to leading order. The
theory, which is confirmed by numerical transport calculations, allows
us to investigate the entire range from the weak to the previously
unexplored strong spinorbit regime, where the spin rotation time is
shorter than the momentum relaxation time.
Spin accumulation in diffusive conductors with Rashba and Dresselhaus spinorbit interaction Phys. Rev. B 81, 85303 (2010) (pdf);arXiv:0909.4253v1 [condmat.meshall] (show/hide abstract)
We calculate the electrically induced spin accumulation in diffusive
systems due to both Rashba (with strength $\alpha$) and Dresselhaus
(with strength $\beta$) spinorbit 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, $\alpha=\pm \beta$. In thermodynamically large
systems, the finite spin accumulation predicted by Chaplik, Entin and
Magarill, [Physica E 13, 744 (2002)] and by Trushin and
Schliemann
[Phys. Rev. B 75,
155323 (2007)] is recovered an infinitesimally small distance away
from the singular point $\alpha=\pm \beta$. We show however that the
singularity is broadened and that the suppression of spin accumulation
becomes physically relevant (i) in finitesized systems of size $L$,
(ii) in the presence of a cubic Dresselhaus interaction of strength
$\gamma$, or (iii) for finite frequency measurements. We obtain the
parametric range over which the magnetoelectric effect is suppressed
in these three instances as (i) $\alpha\beta \lesssim 1/mL$,
(ii)$\alpha\beta \lesssim \gamma p_{\rm F}^2$, and (iii)
$\alpha\beta \lesssiM \sqrt{\omega/m p_{\rm F}\ell}$ with
$\ell$ the elastic mean free path and $p_{\rm F}$ the Fermi
momentum. We attribute the absence of spin accumulation close to
$\alpha=\pm \beta$ to the underlying U (1) symmetry. We illustrate and
confirm our predictions numerically.
Dynamic spinHall effect and driven spin helix for linear spinorbit interactions Phys. Rev. B 80, 235327 (2009) (pdf); arXiv:0909.1892v1 [condmat.meshall] Highlighted as Editor's suggestion in Phys. Rev. B (show/hide abstract)
We derive boundary conditions for the electrically induced spin
accumulation in a finite 2D semiconductor channel. While for DC
electric fields these boundary conditions select spatially constant
spin profiles equivalent to a vanishing spinHall effect, we show that
an inplane ac electric field results in a nonzero ac spinHall
effect, i.e., it generates a spatially nonuniform outofplane
polarization even for linear intrinsic spinorbit
interactions. Analyzing different geometries in [001] and [110]grown
quantum wells, we find that although this outofplane polarization is
typically confined to within a few spinorbit lengths from the channel
edges, it is also possible to generate spatially oscillating spin
profiles which extend over the whole channel. The latter is due to the
excitation of a driven spinhelix mode in the transverse direction of
the channel. We show that while finite frequencies suppress this mode,
it can be amplified by a magnetic field tuned to resonance with the
frequency of the electric field. In this case, finite size effects at
equal strengths of Rashba and Dresselhaus SOI lead to an enhancement
of the magnitude of this helix mode. We comment on the relation
between spin currents and boundary conditions.
Semiconductor spintronics: Snapshots of spins separating Nature Physics 4, 836  837 (2008), News and Views (show/hide abstract)
Theories of the spin Hall effect suggest that spin currents generated
by electric fields accumulate spin polarization at the sample
edges. Now an experiment has observed this conversion in real time.
Mesoscopic fluctuations in the spinelectric susceptibility due to Rashba spinorbit interaction Phys. Rev. Lett. 101, 226602 (2008); arXiv:0805.4143v1 [condmat.meshall] (show/hide abstract)
We investigate mesoscopic fluctuations in the spin polarization
generated by a static electric field and by Rashba spinorbit
interaction in a disordered 2D electron gas. In a diagrammatic
approach we find that the outofplane polarization  while being
zero for selfaveraging systems  exhibits large sampletosample
fluctuations which are shown to be well within experimental reach. We
evaluate the disorderaveraged variance of the susceptibility and find
its dependence on magnetic field, spinorbit interaction, dephasing,
and chemical potential difference.
Resonant spin polarization and spin current in a twodimensional electron gas Phys. Rev. B 75, 201305(R) (2007); (show/hide abstract)
We study the spin polarization and its associated spinHall current
due to EDSR in disordered twodimensional electron systems. We show
that the disorder induced damping of the resonant spin polarization
can be strongly reduced by an optimal field configuration that
exploits the interference between Rashba and Dresselhaus spinorbit
interaction. This leads to a striking enhancement of the spin
susceptibility while the spinHall current vanishes at the same
time. We give an interpretation of the spin current in geometrical
terms which are associated with the trajectories the polarization
describes in spin space.
Electricdipoleinduced spin resonance in disordered semiconductors Nature Physics 2, 195199 (2006); Supplementary Information See also, 'Semiconductor physics: Electric fields drive spins', by Emmanuel I. Rashba, Nature Physics 2, 149150 (2006) News and Views. (show/hide abstract)
One of the hallmarks of spintronics is the control of magnetic moments
by electric fields enabled by strong spinorbit interaction (SOI) in
semiconductors. A powerful way of manipulating spins in such
structures is electricdipoleinduced spin resonance (EDSR), where the
radiofrequency fields driving the spins are electric, not magnetic as
in standard paramagnetic resonance. Here, we present a theoretical
study of EDSR for a twodimensional electron gas in the presence of
disorder, where random impurities not only determine the electric
resistance but also the spin dynamics through SOI. Considering a
specific geometry with the electric and magnetic fields parallel and
inplane, we show that the magnetization develops an outofplane
component at resonance that survives the presence of disorder. We also
discuss the spin Hall current generated by EDSR. These results are
derived in a diagrammatic approach, with the dominant effects coming
from the spin vertex correction, and the optimal parameter regime for
observation is identified.
Influence of lowfrequency noise on macroscopic quantum tunneling in superconducting circuits Phys. Rev. B 71, 134501 (2005); condmat/0411633. (show/hide abstract)
The influence of low to moderate frequency environments on Macroscopic
Quantum Tunneling (MQT) in superconducting circuits is studied within
the ImF approach to evaluate tunneling rates. Particular attention is
paid to two model environments, namely, a pure sluggish bath and a
sluggish bath with additional 1/fnoise. General findings are applied
to Zener flip tunneling, a MQT phenomenon recently predicted and
observed in a superconducting circuit implementing a quantum bit.
