507 research outputs found
The Interplay of Spin and Charge Channels in Zero Dimensional Systems
We present a full fledged quantum mechanical treatment of the interplay
between the charge and the spin zero-mode interactions in quantum dots. Quantum
fluctuations of the spin-mode suppress the Coulomb blockade and give rise to
non-monotonic behavior near this point. They also greatly enhance the dynamic
spin susceptibility. Transverse fluctuations become important as one approaches
the Stoner instability. The non-perturbative effects of zero-mode interaction
are described in terms of charge (U(1)) and spin (SU(2)) gauge bosons.Comment: 4.5 pages, 2 figure
Incoherent scatterer in a Luttinger liquid: a new paradigmatic limit
We address the problem of a Luttinger liquid with a scatterer that allows for
both coherent and incoherent scattering channels. The asymptotic behavior at
zero temperature is governed by a new stable fixed point: a Goldstone mode
dominates the low energy dynamics, leading to a universal behavior. This limit
is marked by equal probabilities for forward and backward scattering.
Notwithstanding this non-trivial scattering pattern, we find that the shot
noise as well as zero cross-current correlations vanish. We thus present a
paradigmatic picture of an impurity in the Luttinger model, alternative to the
Kane-Fisher picture.Comment: published version, 4 + epsilon pages, 1 figur
Non-equilibrium Luttinger liquid: Zero-bias anomaly and dephasing
A one-dimensional system of interacting electrons out of equilibrium is
studied in the framework of the Luttinger liquid model. We analyze several
setups and develop a theory of tunneling into such systems. A remarkable
property of the problem is the absence of relaxation in energy distribution
functions of left- and right-movers, yet the presence of the finite dephasing
rate due to electron-electron scattering, which smears zero-bias-anomaly
singularities in the tunneling density of states.Comment: 5 pages, 2 figure
Entanglement entropy and quantum phase transitions in quantum dots coupled to Luttinger liquid wires
We study a quantum phase transition which occurs in a system composed of two
impurities (or quantum dots) each coupled to a different interacting
(Luttinger-liquid) lead. While the impurities are coupled electrostatically,
there is no tunneling between them. Using a mapping of this system onto a Kondo
model, we show analytically that the system undergoes a
Berezinskii-Kosterlitz-Thouless quantum phase transition as function of the
Luttinger liquid parameter in the leads and the dot-lead interaction. The phase
with low values of the Luttinger-liquid parameter is characterized by an abrupt
switch of the population between the impurities as function of a common applied
gate voltage. However, this behavior is hard to verify numerically since one
would have to study extremely long systems. Interestingly though, at the
transition the entanglement entropy drops from a finite value of to
zero. The drop becomes sharp for infinite systems. One can employ finite size
scaling to extrapolate the transition point and the behavior in its vicinity
from the behavior of the entanglement entropy in moderate size samples. We
employ the density matrix renormalization group numerical procedure to
calculate the entanglement entropy of systems with lead lengths of up to 480
sites. Using finite size scaling we extract the transition value and show it to
be in good agreement with the analytical prediction.Comment: 12 pages, 9 figure
Measuring the transmission of a quantum dot using Aharonov-Bohm Interferometers
The conductance G through a closed Aharonov-Bohm mesoscopic solid-state
interferometer (which conserves the electron current), with a quantum dot (QD)
on one of the paths, depends only on cos(phi), where Phi= (hbar c phi)/e is the
magnetic flux through the ring. The absence of a phase shift in the
phi-dependence led to the conclusion that closed interferometers do not yield
the phase of the "intrinsic" transmission amplitude t_D=|t_D|e^{i alpha}
through the QD, and led to studies of open interferometers. Here we show that
(a) for single channel leads, alpha can be deduced from |t_D|, with no need for
interferometry; (b) the explicit dependence of G(phi) on cos(phi) (in the
closed case) allows a determination of both |t_D| and alpha; (c) in the open
case, results depend on the details of the opening, but optimization of these
details can yield the two-slit conditions which relate the measured phase shift
to alpha.Comment: Invited talk, Localization, Tokyo, August 200
Which phase is measured in the mesoscopic Aharonov-Bohm interferometer?
Mesoscopic solid state Aharonov-Bohm interferometers have been used to
measure the "intrinsic" phase, , of the resonant quantum
transmission amplitude through a quantum dot (QD). For a two-terminal "closed"
interferometer, which conserves the electron current, Onsager's relations
require that the measured phase shift only "jumps" between 0 and .
Additional terminals open the interferometer but then depends on the
details of the opening. Using a theoretical model, we present quantitative
criteria (which can be tested experimentally) for to be equal to the
desired : the "lossy" channels near the QD should have both a
small transmission and a small reflection
Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
The problem of electron--electron lifetime in a quantum dot is studied beyond
perturbation theory by mapping it onto the problem of localization in the Fock
space. We identify two regimes, localized and delocalized, corresponding to
quasiparticle spectral peaks of zero and finite width, respectively. In the
localized regime, quasiparticle states are very close to single particle
excitations. In the delocalized state, each eigenstate is a superposition of
states with very different quasiparticle content. A transition between the two
regimes occurs at the energy , where is
the one particle level spacing, and is the dimensionless conductance. Near
this energy there is a broad critical region in which the states are
multifractal, and are not described by the Golden Rule.Comment: 13 pages, LaTeX, one figur
Non-Equilibrium Magnetization in a Ballistic Quantum Dot
We show that Aharonov-Bohm (AB) oscillations in the magnetic moment of an
integrable ballistic quantum dot can be destroyed by a time dependent magnetic
flux. The effect is due to a nonequilibrium population of perfectly coherent
electronic states. For real ballistic systems the equilibrization process,
which involves a special type of inelastic electron backscattering, can be so
ineffective, that AB oscillations are suppressed when the flux varies with
frequency 10-10 s. The effect can be used to
measure relaxation times for inelastic backscattering.Comment: 11 pages LaTeX v3.14 with RevTeX v3.0, 3 post script figures
available on request, APR 93-X2
Effect of quantum entanglement on Aharonov-Bohm oscillations, spin-polarized transport and current magnification effect
We present a simple model of transmission across a metallic mesoscopic ring.
In one of its arm an electron interacts with a single magnetic impurity via an
exchange coupling. We show that entanglement between electron and spin impurity
states leads to reduction of Aharonov-Bohm oscillations in the transmission
coefficient. The spin-conductance is asymmetric in the flux reversal as opposed
to the two probe electrical conductance which is symmetric. In the same model
in contradiction to the naive expectation of a current magnification effect, we
observe enhancement as well as the suppression of this effect depending on the
system parameters. The limitations of this model to the general notion of
dephasing or decoherence in quantum systems are pointed out.Comment: Talk presented at the International Discussion Meeting on Mesoscopic
and Disordered systems, December, 2000, at IISc Bangalore 17 pages, 8figure
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