25 research outputs found
Interaction corrections to the Hall coefficient at intermediate temperatures
We investigate the effect of electron-electron interaction on the temperature
dependence of the Hall coefficient of 2D electron gas at arbitrary relation
between the temperature and the elastic mean-free time . At small
temperature we reproduce the known relation between the
logarithmic temperature dependences of the Hall coefficient and of the
longitudinal conductivity. At higher temperatures, this relation is violated
quite rapidly; correction to the Hall coefficient becomes whereas
the longitudinal conductivity becomes linear in temperature.Comment: 4 pages, 3 .eps figure
Phase Relaxation of Electrons in Disordered Conductors
Conduction electrons in disordered metals and heavily doped semiconductors at
low temperatures preserve their phase coherence for a long time: phase
relaxation time can be orders of magnitude longer than the momentum
relaxation time. The large difference in these time scales gives rise to well
known effects of weak localization, such as anomalous magnetoresistance. Among
other interesting characteristics, study of these effects provide quantitative
information on the dephasing rate . This parameter is of
fundamental interest: the relation between and the
temperature (a typical energy scale of an electron) determines how well a
single electron state is defined. We will discuss the basic physical meaning of
in different situations and its difference from the energy
relaxation rate. At low temperatures, the phase relaxation rate is governed by
collisions between electrons. We will review existing theories of dephasing by
these collisions or (which is the same) by electric noise inside the sample. We
also discuss recent experiments on the magnetoresistance of 1D systems: some of
them show saturation of at low temperatures, the other do not. To
resolve this contradiction we discuss dephasing by an external microwave field
and by nonequilibrium electric noise.Comment: Order of figures and references corrected; one reference added; 15
pages, 2 figures, lecture given on 10th International Winterschool on New
Developments in Solid State Physics, Mauterndorf, Salzburg, Austria; 23-27
Feb. 199
Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
We consider low-temperature behavior of weakly interacting electrons in
disordered conductors in the regime when all single-particle eigenstates are
localized by the quenched disorder. We prove that in the absence of coupling of
the electrons to any external bath dc electrical conductivity exactly vanishes
as long as the temperatute does not exceed some finite value . At the
same time, it can be also proven that at high enough the conductivity is
finite. These two statements imply that the system undergoes a finite
temperature Metal-to-Insulator transition, which can be viewed as Anderson-like
localization of many-body wave functions in the Fock space. Metallic and
insulating states are not different from each other by any spatial or discrete
symmetries. We formulate the effective Hamiltonian description of the system at
low energies (of the order of the level spacing in the single-particle
localization volume). In the metallic phase quantum Boltzmann equation is
valid, allowing to find the kinetic coefficients. In the insulating phase,
, we use Feynmann diagram technique to determine the probability
distribution function for quantum-mechanical transition rates. The probability
of an escape rate from a given quantum state to be finite turns out to vanish
in every order of the perturbation theory in electron-electron interaction.
Thus, electron-electron interaction alone is unable to cause the relaxation and
establish the thermal equilibrium. As soon as some weak coupling to a bath is
turned on, conductivity becomes finite even in the insulating phase
Inelastic Scattering Time for Conductance Fluctuations
We revisit the problem of inelastic times governing the temperature behavior
of the weak localization correction and mesoscopic fluctuations in one- and
two-dimensional systems. It is shown that, for dephasing by the electron
electron interaction, not only are those times identical but the scaling
functions are also the same.Comment: 10 pages Revtex; 5 eps files include
Low energy transition in spectral statistics of 2D interactingfermions
We study the level spacing statistics and eigenstate properties of
spinless fermions with Coulomb interaction on a two dimensional lattice at
constant filling factor and various disorder strength. In the limit of large
lattice size, undergoes a transition from the Poisson to the
Wigner-Dyson distribution at a critical total energy independent of the number
of fermions. This implies the emergence of quantum ergodicity induced by
interaction and delocalization in the Hilbert space at zero temperature.Comment: revtex, 5 pages, 4 figures; new data for eigenfunctions are adde
Ballistic electron motion in a random magnetic field
Using a new scheme of the derivation of the non-linear -model we
consider the electron motion in a random magnetic field (RMF) in two
dimensions. The derivation is based on writing quasiclassical equations and
representing their solutions in terms of a functional integral over
supermatrices with the constraint . Contrary to the standard scheme,
neither singling out slow modes nor saddle-point approximation are used. The
-model obtained is applicable at the length scale down to the electron
wavelength. We show that this model differs from the model with a random
potential (RP).However, after averaging over fluctuations in the Lyapunov
region the standard -model is obtained leading to the conventional
localization behavior.Comment: 10 pages, no figures, to be submitted in PRB v2: Section IV is
remove
The Parallel Magnetoconductance of Interacting Electrons in a Two Dimensional Disordered System
The transport properties of interacting electrons for which the spin degree
of freedom is taken into account are numerically studied for small two
dimensional diffusive clusters. On-site electron-electron interactions tend to
delocalize the electrons, while long-range interactions enhance localization.
On careful examination of the transport properties, we reach the conclusion
that it does not show a two dimensional metal insulator transition driven by
interactions. A parallel magnetic field leads to enhanced resistivity, which
saturates once the electrons become fully spin polarized. The strength of the
magnetic field for which the resistivity saturates decreases as electron
density goes down. Thus, the numerical calculations capture some of the
features seen in recent experimental measurements of parallel
magnetoconductance.Comment: 10 pages, 6 figure
Linear temperature dependence of conductivity in the "insulating" regime of dilute two-dimensional holes in GaAs
The conductivity of extremely high mobility dilute two-dimensional holes in
GaAs changes linearly with temperature in the insulating side of the
metal-insulator transition. Hopping conduction, characterized by an
exponentially decreasing conductivity with decreasing temperature, is not
observed when the conductivity is smaller than . We suggest that
strong interactions in a regime close to the Wigner crystallization must be
playing a role in the unusual transport.Comment: 3 pages, 2 figure
Dynamics of short time--scale energy relaxation of optical excitations due to electron--electron scattering in the presence of arbitrary disorder
A non--equilibrium occupation distribution relaxes towards the Fermi--Dirac
distribution due to electron--electron scattering even in finite Fermi systems.
The dynamic evolution of this thermalization process assumed to result from an
optical excitation is investigated numerically by solving a Boltzmann equation
for the carrier populations using a one--dimensional disordered system. We
focus on the short time--scale behavior. The logarithmically long time--scale
associated with the glassy behavior of interacting electrons in disordered
systems is not treated in our investigation.
For weak disorder and short range interaction we recover the expected result
that disorder enhances the relaxation rate as compared to the case without
disorder. For sufficiently strong disorder, however, we find an opposite trend
due to the reduction of scattering probabilities originating from the strong
localization of the single--particle states. Long--range interaction in this
regime produces a similar effect. The relaxation rate is found to scale with
the interaction strength, however, the interplay between the implicit and the
explicit character of the interaction produces an anomalous exponent.Comment: 4 pages, 3 EPS figure
A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade
We provide a framework for analyzing the problem of interacting electrons in
a ballistic quantum dot with chaotic boundary conditions within an energy
(the Thouless energy) of the Fermi energy. Within this window we show that the
interactions can be characterized by Landau Fermi liquid parameters. When ,
the dimensionless conductance of the dot, is large, we find that the disordered
interacting problem can be solved in a saddle-point approximation which becomes
exact as (as in a large-N theory). The infinite theory shows a
transition to a strong-coupling phase characterized by the same order parameter
as in the Pomeranchuk transition in clean systems (a spontaneous
interaction-induced Fermi surface distortion), but smeared and pinned by
disorder. At finite , the two phases and critical point evolve into three
regimes in the plane -- weak- and strong-coupling regimes separated
by crossover lines from a quantum-critical regime controlled by the quantum
critical point. In the strong-coupling and quantum-critical regions, the
quasiparticle acquires a width of the same order as the level spacing
within a few 's of the Fermi energy due to coupling to collective
excitations. In the strong coupling regime if is odd, the dot will (if
isolated) cross over from the orthogonal to unitary ensemble for an
exponentially small external flux, or will (if strongly coupled to leads) break
time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we
are treating charge-channel instabilities in spinful systems, leaving
spin-channel instabilities for future work. No substantive results are
change