101 research outputs found
Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations
Finite-temperature transport properties of one-dimensional systems can be
studied using the time dependent density matrix renormalization group via the
introduction of auxiliary degrees of freedom which purify the thermal
statistical operator. We demonstrate how the numerical effort of such
calculations is reduced when the physical time evolution is augmented by an
additional time evolution within the auxiliary Hilbert space. Specifically, we
explore a variety of integrable and non-integrable, gapless and gapped models
at temperatures ranging from T=infty down to T/bandwidth=0.05 and study both
(i) linear response where (heat and charge) transport coefficients are
determined by the current-current correlation function and (ii) non-equilibrium
driven by arbitrary large temperature gradients. The modified DMRG algorithm
removes an 'artificial' build-up of entanglement between the auxiliary and
physical degrees of freedom. Thus, longer time scales can be reached
Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains
We propose an easily implemented approach to study time-dependent correlation
functions of one dimensional systems at finite temperature T using the density
matrix renormalization group. The entanglement growth inherent to any
time-dependent calculation is significantly reduced if the auxiliary degrees of
freedom which purify the statistical operator are time evolved with the
physical Hamiltonian but reversed time. We exploit this to investigate the long
time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg
chain. This allows a direct extraction of the Drude weight D at intermediate to
large T. We find that D is nonzero -- and thus transport is dissipationless --
everywhere in the gapless phase. At low temperatures we establish an upper
bound to D by comparing with bosonization
Mesoscopic Spin Hall Effect
We investigate the spin Hall effect in ballistic chaotic quantum dots with
spin-orbit coupling. We show that a longitudinal charge current can generate a
pure transverse spin current. While this transverse spin current is generically
nonzero for a fixed sample, we show that when the spin-orbit coupling time is
large compared to the mean dwell time inside the dot, it fluctuates universally
from sample to sample or upon variation of the chemical potential with a
vanishing average. For a fixed sample configuration, the transverse spin
current has a finite typical value ~e^2 V/h, proportional to the longitudinal
bias V on the sample, and corresponding to about one excess open channel for
one of the two spin species. Our analytical results are in agreement with
numerical results in a diffusive system [W. Ren et al., Phys. Rev. Lett. 97,
066603 (2006)] and are further confirmed by numerical simulation in a chaotic
cavity.Comment: 4 pages, 2 figure
Electrostatic confinement of electrons in an integrable graphene quantum dot
We compare the conductance of an undoped graphene sheet with a small region
subject to an electrostatic gate potential for the cases that the dynamics in
the gated region is regular (disc-shaped region) and classically chaotic
(stadium). For the disc, we find sharp resonances that narrow upon reducing the
area fraction of the gated region. We relate this observation to the existence
of confined electronic states. For the stadium, the conductance looses its
dependence on the gate voltage upon reducing the area fraction of the gated
region, which signals the lack of confinement of Dirac quasiparticles in a
gated region with chaotic classical electron dynamics.Comment: 4 pages, 4 figures; [v2] Added discussion of large aspect ratio
A proof of the Kramers degeneracy of transmission eigenvalues from antisymmetry of the scattering matrix
In time reversal symmetric systems with half integral spins (or more
concretely, systems with an antiunitary symmetry that squares to -1 and
commutes with the Hamiltonian) the transmission eigenvalues of the scattering
matrix come in pairs. We present a proof of this fact that is valid both for
even and odd number of modes and relies solely on the antisymmetry of the
scattering matrix imposed by time reversal symmetry.Comment: 2 page
Signatures of Klein tunneling in disordered graphene p-n-p junctions
We present a method for obtaining quantum transport properties in graphene
that uniquely combines three crucial features: microscopic treatment of charge
disorder, fully quantum mechanical analysis of transport, and the ability to
model experimentally relevant system sizes. As a pertinent application we study
the disorder dependence of Klein tunneling dominated transport in p-n-p
junctions. Both the resistance and the Fano factor show broad resonance peaks
due to the presence of quasi bound states. This feature is washed out by the
disorder when the mean free path becomes of the order of the distance between
the two p-n interfaces.Comment: 4 pages, 4 figure
How spin-orbit interaction can cause electronic shot noise
The shot noise in the electrical current through a ballistic chaotic quantum
dot with N-channel point contacts is suppressed for N --> infinity, because of
the transition from stochastic scattering of quantum wave packets to
deterministic dynamics of classical trajectories. The dynamics of the electron
spin remains quantum mechanical in this transition, and can affect the
electrical current via spin-orbit interaction. We explain how the role of the
channel number N in determining the shot noise is taken over by the ratio
l_{so}/lambda_F of spin precession length l_{so} and Fermi wave length
lambda_F, and present computer simulations in a two-dimensional billiard
geometry (Lyapunov exponent alpha, mean dwell time tau_{dwell}, point contact
width W) to demonstrate the scaling (lambda_F/l_{so})^{1/alpha tau_{dwell}} of
the shot noise in the regime lambda_F << l_{so} << W.Comment: 4 pages, 3 figure
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