1,229 research outputs found
Infrared catastrophe and tunneling into strongly correlated electron systems: Exact solution of the x-ray edge limit for the 1D electron gas and 2D Hall fluid
In previous work we have proposed that the non-Fermi-liquid spectral
properties in a variety of low-dimensional and strongly correlated electron
systems are caused by the infrared catastrophe, and we used an exact functional
integral representation for the interacting Green's function to map the
tunneling problem onto the x-ray edge problem, plus corrections. The
corrections are caused by the recoil of the tunneling particle, and, in systems
where the method is applicable, are not expected to change the qualitative form
of the tunneling density of states (DOS). Qualitatively correct results were
obtained for the DOS of the 1D electron gas and 2D Hall fluid when the
corrections to the x-ray edge limit were neglected and when the corresponding
Nozieres-De Dominicis integral equations were solved by resummation of a
divergent perturbation series. Here we reexamine the x-ray edge limit for these
two models by solving these integral equations exactly, finding the expected
modifications of the DOS exponent in the 1D case but finding no changes in the
DOS of the 2D Hall fluid with short-range interaction. We also provide, for the
first time, an exact solution of the Nozieres-De Dominicis equation for the 2D
electron gas in the lowest Landau level.Comment: 6 pages, Revte
Effects of two dimensional plasmons on the tunneling density of states
We show that gapless plasmons lead to a universal
correction to the tunneling
density of states of a clean two dimensional Coulomb interacting electron gas.
We also discuss a counterpart of this effect in the "composite fermion metal"
which forms in the presence of a quantizing perpendicular magnetic field
corresponding to the half-filled Landau level. We argue that the latter
phenomenon might be relevant for deviations from a simple scaling observed by
A.Chang et al in the tunneling characteristics of Quantum Hall liquids.Comment: 12 pages, Latex, NORDITA repor
Full counting statistics for noninteracting fermions: Exact finite temperature results and generalized long time approximation
Exact numerical results for the full counting statistics (FCS) of a
one-dimensional tight-binding model of noninteracting electrons are presented
at finite temperatures using an identity recently presented by Abanov and
Ivanov. A similar idea is used to derive a new expression for the cumulant
generating function for a system consisting of two quasi-one-dimensional leads
connected by a quantum dot in the long time limit. This provides a
generalization of the Levitov-Lesovik formula for such systems.Comment: 17 pages, 6 figures, extended introduction, additional comment
Full counting statistics of a chaotic cavity with asymmetric leads
We study the statistics of charge transport in a chaotic cavity attached to
external reservoirs by two openings of different size which transmit non-equal
number of quantum channels. An exact formula for the cumulant generating
function has been derived by means of the Keldysh-Green function technique
within the circuit theory of mesoscopic transport. The derived formula
determines the full counting statistics of charge transport, i.e., the
probability distribution and all-order cumulants of current noise. It is found
that, for asymmetric cavities, in contrast to other mesoscopic systems, the
third-order cumulant changes the sign at high biases. This effect is attributed
to the skewness of the distribution of transmission eigenvalues with respect to
forward/backward scattering. For a symmetric cavity we find that the third
cumulant approaches a voltage-independent constant proportional to the
temperature and the number of quantum channels in the leads.Comment: new section on probability distribution and new references adde
Full counting statistics of Luttinger liquid conductor
Non-equilibrium bosonization technique is used to study current fluctuations
of interacting electrons in a single-channel quantum wire representing a
Luttinger liquid (LL) conductor. An exact expression for the full counting
statistics of the transmitted charge is derived. It is given by Fredholm
determinant of the counting operator with a time dependent scattering phase.
The result has a form of counting statistics of non-interacting particles with
fractional charges, induced by scattering off the boundaries between the LL
wire and the non-interacting leads.Comment: 5 pages, 2 figure
Full counting statistics of chiral Luttinger liquids with impurities
We study the statistics of charge transfer through an impurity in a chiral
Luttinger liquid (realized experimentally as a quantum point contact in a
fractional quantum Hall edge state device). Taking advantage of the
integrability we present a procedure for obtaining the cumulant generating
function of the probability distribution to transfer a fixed amount of charge
through the constriction. Using this approach we analyze in detail the
behaviour of the third cumulant C_3 as a function of applied voltage,
temperature and barrier height. We predict that C_3 can be used to measure the
fractional charge at temperatures, which are several orders of magnitude higher
than those needed to extract the fractional charge from the measurement of the
second cumulant. Moreover, we identify the component of C_3, which carries the
information about the fractional charge.Comment: 5 pages, 2 figures (EPS files
Reentrant behavior in the superconducting phase-dependent resistance of a disordered 2-dimensional electron gas
We have investigated the bias-voltage dependence of the phase-dependent
differential resistance of a disordered T-shaped 2-dimensional electron gas
coupled to two superconducting terminals. The resistance oscillations first
increase upon lowering the energy. For bias voltages below the Thouless energy,
the resistance oscillations are suppressed and disappear almost completely at
zero bias voltage. We find a qualitative agreement with the calculated
reentrant behavior of the resistance and discuss quantitative deviations.Comment: 4 pages, 5 figures, to be published in Phys. Rev.
Full Counting Statistics in Strongly Interacting Systems: Non-Markovian Effects
We present a theory of full counting statistics for electron transport
through interacting electron systems with non-Markovian dynamics. We illustrate
our approach for transport through a single-level quantum dot and a metallic
single-electron transistor to second order in the tunnel-coupling strength, and
discuss under which circumstances non-Markovian effects appear in the transport
properties.Comment: 4 pages, 2 figures, LaTeX; typos added, references adde
Full Current Statistics in Diffusive Normal-Superconductor Structures
We study the current statistics in normal diffusive conductors in contact
with a superconductor. Using an extension of the Keldysh Green's function
method we are able to find the full distribution of charge transfers for all
temperatures and voltages. For the non-Gaussian regime, we show that the
equilibrium current fluctuations are enhanced by the presence of the
superconductor. We predict an enhancement of the nonequilibrium current noise
for temperatures below and voltages of the order of the Thouless energy
E_Th=D/L^2. Our calculation fully accounts for the proximity effect in the
normal metal and agrees with experimental data. We demonstrate that the
calculation of the full current statistics is in fact simpler than a concrete
calculation of the noise.Comment: 4 pages, 2 figures (included
Electron Interactions in Bilayer Graphene: Marginal Fermi Liquid Behaviour and Zero Bias Anomaly
We analyze the many-body properties of bilayer graphene (BLG) at charge
neutrality, governed by long range interactions between electrons. Perturbation
theory in a large number of flavors is used in which the interactions are
described within a random phase approximation, taking account of dynamical
screening effect. Crucially, the dynamically screened interaction retains some
long range character, resulting in renormalization of key quantities.
We carry out the perturbative renormalization group calculations to one loop
order, and find that BLG behaves to leading order as a marginal Fermi liquid.
Interactions produce a log squared renormalization of the quasiparticle residue
and the interaction vertex function, while all other quantities renormalize
only logarithmically. We solve the RG flow equation for the Green function with
logarithmic accuracy, and find that the quasiparticle residue flows to zero
under RG. At the same time, the gauge invariant quantities, such as the
compressibility, remain finite to order, with subleading logarithmic
corrections. The key experimental signature of this marginal Fermi liquid
behavior is a strong suppression of the tunneling density of states, which
manifests itself as a zero bias anomaly in tunneling experiments in a regime
where the compressibility is essentially unchanged from the non-interacting
value.Comment: 12 pages, 3 figure
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