302 research outputs found
The Anderson-Josephson quantum dot -- A theory perspective
Recent progress in nanoscale manufacturing allowed to experimentally
investigate quantum dots coupled to two superconducting leads in controlled and
tunable setups. The equilibrium Josephson current was measured in on-chip SQUID
devices and subgap states were investigated using weakly coupled metallic leads
for spectroscopy. This put back two "classic" problems also on the agenda of
theoretical condensed matter physics: the Josephson effect and quantum spins in
superconductors. We discuss the status of the theoretical understanding of the
Anderson-Josephson quantum dot in equilibrium mainly focusing on the Josephson
current. We introduce a minimal model consisting of a dot which can only host
one spin-up and one spin-down electron repelling each other by a local Coulomb
interaction. The dot is tunnel-coupled to two superconducting leads described
by the BCS Hamiltonian. This model was investigated using a variety of methods,
some capturing aspects of Kondo physics others failing in this respect. We
briefly review this. The model shows a first order level-crossing quantum phase
transition when varying any parameter provided the others are within
appropriate ranges. At vanishing temperature it leads to a jump of the
Josephson current. We show that a quantitative agreement between accurate
results obtained for the simple model and measurements of the current can be
reached. This confirms that the experiments reveal the finite temperature
signatures of the zero temperature transition. In addition, we consider two
examples of more complex dot geometries which might be experimentally realized
in the near future. The first is characterized by the interplay of the above
level-crossing physics and the Fano effect, the second by the interplay of
superconductivity and almost degenerate singlet and triplet two-body states.Comment: invited review for Journal of Physics: Condensed Matter, comments
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Spin-orbit coupling effects in one-dimensional ballistic quantum wires
We study the spin-dependent electronic transport through a one-dimensional
ballistic quantum wire in the presence of Rashba spin-orbit interaction. In
particular, we consider the effect of the spin-orbit interaction resulting from
the lateral confinement of the two-dimensional electron gas to the
one-dimensional wire geometry. We generalize a situation suggested earlier [P.
Streda and P. Seba, Phys. Rev. Lett. 90, 256601 (2003)] which allows for
spin-polarized electron transport. As a result of the lateral confinement, the
spin is rotated out of the plane of the two-dimensional system. We furthermore
investigate the spin-dependent transmission and the polarization of an electron
current at a potential barrier. Finally, we construct a lattice model which
shows similar low-energy physics. In the future, this lattice model will allow
us to study how the electron-electron interaction affects the transport
properties of the present setup.Comment: 7 pages, 6 figures, revised versio
Nonequilibrium functional renormalization group for interacting quantum systems
We propose a nonequilibrium version of functional renormalization within the
Keldysh formalism by introducing a complex valued flow parameter in the Fermi
or Bose functions of each reservoir. Our cutoff scheme provides a unified
approach to equilibrium and nonequilibrium situations. We apply it to
nonequilibrium transport through an interacting quantum wire coupled to two
reservoirs and show that the nonequilibrium occupation induces new power law
exponents for the conductance.Comment: 5 pages, 2 figures; published versio
The interacting resonant level model in nonequilibrium: finite temperature effects
We study the steady-state properties as well as the relaxation dynamics of
the nonequilibrium interacting resonant level model at finite temperatures. It
constitutes the prototype model of a correlated charge fluctuating quantum dot.
The two reservoirs are held at different chemical potentials---the difference
being the bias voltage---and different temperatures; we discuss the transport
through as well as the occupancy of the single level dot. First, we show
analytically that in the steady state the reservoir temperatures in competition
with the other energy scales act as infrared cutoffs. This is rather intuitive
but, depending on the parameter regime under consideration, leads to a
surprisingly rich variety of power laws in the current as a function of the
temperatures and the bias voltage with different interaction dependent
exponents. Next we clarify how finite reservoir temperatures affect the
dynamics. They allow to tune the interplay of the two frequencies
characterizing the oscillatory part of the time evolution of the model at zero
temperature. For the exponentially decaying part we disentangle the
contributions of the level-lead hybridization and the temperatures to the decay
rates. We identify a coherent-to-incoherent transition in the long time
dynamics as the temperature is raised. It occurs at an interaction dependent
critical temperature. Finally, taking different temperatures in the reservoirs
we discuss the relaxation dynamics of a temperature gradient driven current.Comment: 12 pages, 6 figures, 1 tabl
Finite-temperature linear conductance from the Matsubara Green function without analytic continuation to the real axis
We illustrate how to calculate the finite-temperature linear-response
conductance of quantum impurity models from the Matsubara Green function. A
continued fraction expansion of the Fermi distribution is employed which was
recently introduced by Ozaki [Phys. Rev. B 75, 035123 (2007)] and converges
much faster than the usual Matsubara representation. We give a simplified
derivation of Ozaki's idea using concepts from many-body condensed matter
theory and present results for the rate of convergence. In case that the Green
function of some model of interest is only known numerically, interpolating
between Matsubara frequencies is much more stable than carrying out an analytic
continuation to the real axis. We demonstrate this explicitly by considering an
infinite tight-binding chain with a single site impurity as an exactly-solvable
test system, showing that it is advantageous to calculate transport properties
directly on the imaginary axis. The formalism is applied to the single impurity
Anderson model, and the linear conductance at finite temperatures is calculated
reliably at small to intermediate Coulomb interactions by virtue of the
Matsubara functional renormalization group. Thus, this quantum many-body method
combined with the continued fraction expansion of the Fermi function
constitutes a promising tool to address more complex quantum dot geometries at
finite temperatures.Comment: version accepted by Phys. Rev.
Correlation induced resonances in transport through coupled quantum dots
We investigate the effect of local electron correlations on transport through
parallel quantum dots. The linear conductance as a function of gate voltage is
strongly affected by the interplay of the interaction U and quantum
interference. We find a pair of novel correlation induced resonances separated
by an energy scale that depends exponentially on U. The effect is robust
against a small detuning of the dot energy levels and occurs for arbitrary
generic tunnel couplings. It should be observable in experiments on the basis
of presently existing double-dot setups.Comment: 4+ pages, 5 figures included, version accepted for publication in PR
Kondo physics in transport through a quantum dot with Luttinger liquid leads
We study the gate voltage dependence of the linear conductance through a
quantum dot coupled to one-dimensional leads. For interacting dot electrons but
noninteracting leads Kondo physics implies broad plateau-like resonances. In
the opposite case Luttinger liquid behavior leads to sharp resonances. In the
presence of Kondo as well as Luttinger liquid physics and for experimentally
relevant parameters, we find a line shape that resembles the one of the Kondo
case.Comment: 4+ pages, 4 figures include
Efficiency and power of a thermoelectric quantum dot device
We study linear response and nonequilibrium steady-state thermoelectric
transport through a single-level quantum dot tunnel coupled to two reservoirs
held at different temperatures as well as chemical potentials. A fermion
occupying the dot interacts with those in the reservoirs by a short-ranged
two-particle interaction. For parameters for which particles flow against a
bias voltage from the hot to the cold reservoir this setup acts as an
energy-conversion device with which electrical energy is gained out of waste
heat. We investigate how correlations affect its efficiency and output power.
In linear response the changes in the thermoelectric properties can be traced
back to the interaction induced renormalization of the resonance line shape. In
particular, small to intermediate repulsive interactions reduce the maximum
efficiency. In nonequilibrium the situation is more complex and we identify a
parameter regime in which for a fixed lower bound of the output power the
efficiency increases.Comment: 6 pages, 6 figure
Dynamical regimes of dissipative quantum systems
We reveal several distinct regimes of the relaxation dynamics of a small
quantum system coupled to an environment within the plane of the dissipation
strength and the reservoir temperature. This is achieved by discriminating
between coherent dynamics with damped oscillatory behavior on all time scales,
partially coherent behavior being nonmonotonic at intermediate times but
monotonic at large ones, and purely monotonic incoherent decay. Surprisingly,
elevated temperature can render the system `more coherent' by inducing a
transition from the partially coherent to the coherent regime. This provides a
refined view on the relaxation dynamics of open quantum systems.Comment: 5 pages, 3 figure
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