83 research outputs found
Role of coherence in resistance quantization
The quantization of resistances in the quantum Hall effect and ballistic
transport through quantum point contacts is compared with the quantization of
the charge relaxation resistance of a coherent mesoscopic capacitor. While the
former two require the existence of a perfectly transmitting channel, the
charge relaxation resistance remains quantized for arbitrary backscattering.
The quantum Hall effect and the quantum point contact require only local phase
coherence. In contrast quantization of the charge relaxation resistance
requires global phase coherence.Comment: 9 pages, 5 figure
Statistical theory of relaxation of high energy electrons in quantum Hall edge states
We investigate theoretically the energy exchange between electrons of two
co-propagating, out-of-equilibrium edge states with opposite spin polarization
in the integer quantum Hall regime. A quantum dot tunnel-coupled to one of the
edge states locally injects electrons at high energy. Thereby a narrow peak in
the energy distribution is created at high energy above the Fermi level. A
second downstream quantum dot performs an energy resolved measurement of the
electronic distribution function. By varying the distance between the two dots,
we are able to follow every step of the energy exchange and relaxation between
the edge states - even analytically under certain conditions. In the absence of
translational invariance along the edge, e.g. due to the presence of disorder,
energy can be exchanged by non-momentum conserving two-particle collisions. For
weakly broken translational invariance, we show that the relaxation is
described by coupled Fokker-Planck equations. From these we find that
relaxation of the injected electrons can be understood statistically as a
generalized drift-diffusion process in energy space for which we determine the
drift-velocity and the dynamical diffusion parameter. Finally, we provide a
physically appealing picture in terms of individual edge state heating as a
result of the relaxation of the injected electrons.Comment: 13 pages plus 6 appendices, 8 figures. Supplemental Material can be
found on http://quantumtheory.physik.unibas.ch/people/nigg/supp_mat.htm
Mesoscopic Charge Relaxation
We consider charge relaxation in the mesoscopic equivalent of an RC circuit.
For a single-channel, spin-polarized contact, self-consistent scattering theory
predicts a universal charge relaxation resistance equal to half a resistance
quantum independent of the transmission properties of the contact. This
prediction is in good agreement with recent experimental results. We use a
tunneling Hamiltonian formalism and show in Hartree-Fock approximation, that at
zero temperature the charge relaxation resistance is universal even in the
presence of Coulomb blockade effects. We explore departures from universality
as a function of temperature and magnetic field.Comment: 4 pages, 3 figure
Interaction induced edge channel equilibration
The electronic distribution functions of two Coulomb coupled chiral edge
states forming a quasi-1D system with broken translation invariance are found
using the equation of motion approach. We find that relaxation and thereby
energy exchange between the two edge states is determined by the shot noise of
the edge states generated at a quantum point contact (QPC). In close vicinity
to the QPC, we derive analytic expressions for the distribution functions. We
further give an iterative procedure with which we can compute numerically the
distribution functions arbitrarily far away from the QPC. Our results are
compared with recent experiments of Le Sueur et al..Comment: 10 pages, 7 figures, includes 5 pages of supplementary informatio
Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation
Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the
coherent splitting of Cooper pairs from a superconductor to two spatially
separated quantum dots has been predicted to generate nonlocal pairs of
entangled electrons. In order to test this hypothesis, we propose a scheme to
transfer the spin state of a split Cooper pair onto the polarization state of a
pair of optical photons. We show that the produced photon pairs can be used to
violate a Bell inequality, unambiguously demonstrating the entanglement of the
split Cooper pairs.Comment: 11 pages, 9 figures, v3 with added reference
Quantum to Classical Transition of the Charge Relaxation Resistance of a Mesoscopic Capacitor
We present an analysis of the effect of dephasing on the single channel
charge relaxation resistance of a mesoscopic capacitor in the linear low
frequency regime. The capacitor consists of a cavity which is via a quantum
point contact connected to an electron reservoir and Coulomb coupled to a gate.
The capacitor is in a perpendicular high magnetic field such that only one
(spin polarized) edge state is (partially) transmitted through the contact. In
the coherent limit the charge relaxation resistance for a single channel
contact is independent of the transmission probability of the contact and given
by half a resistance quantum. The loss of coherence in the conductor is modeled
by attaching to it a fictitious probe, which draws no net current. In the
incoherent limit one could expect a charge relaxation resistance that is
inversely proportional to the transmission probability of the quantum point
contact. However, such a two terminal result requires that scattering is
between two electron reservoirs which provide full inelastic relaxation. We
find that dephasing of a single edge state in the cavity is not sufficient to
generate an interface resistance. As a consequence the charge relaxation
resistance is given by the sum of one constant interface resistance and the
(original) Landauer resistance. The same result is obtained in the high
temperature regime due to energy averaging over many occupied states in the
cavity. Only for a large number of open dephasing channels, describing
spatially homogenous dephasing in the cavity, do we recover the two terminal
resistance, which is inversely proportional to the transmission probability of
the QPC. We compare different dephasing models and discuss the relation of our
results to a recent experiment.Comment: 10 pages, 8 figure
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