133 research outputs found
Renormalization group analysis of thermal transport in the disordered Fermi liquid
We present a detailed study of thermal transport in the disordered Fermi
liquid with short-range interactions. At temperatures smaller than the impurity
scattering rate, i.e., in the diffusive regime, thermal conductivity acquires
non-analytic quantum corrections. When these quantum corrections become large
at low temperatures, the calculation of thermal conductivity demands a
theoretical approach that treats disorder and interactions on an equal footing.
In this paper, we develop such an approach by merging Luttinger's idea of using
gravitational potentials for the analysis of thermal phenomena with a
renormalization group calculation based on the Keldysh nonlinear sigma model.
The gravitational potentials are introduced in the action as auxiliary sources
that couple to the heat density. These sources are a convenient tool for
generating expressions for the heat density and its correlation function from
the partition function. Already in the absence of the gravitational potentials,
the nonlinear sigma model contains several temperature-dependent
renormalization group charges. When the gravitational potentials are introduced
into the model, they acquire an independent renormalization group flow. We show
that this flow preserves the phenomenological form of the correlation function,
reflecting its relation to the specific heat and the constraints imposed by
energy conservation. The main result of our analysis is that the
Wiedemann-Franz law holds down to the lowest temperatures even in the presence
of disorder and interactions and despite the quantum corrections that arise for
both the electric and thermal conductivities.Comment: 30 pages, 37 figure
Suppression of \bbox{T_c} in superconducting amorphous wires
The suppression of the mean field temperature of the superconducting
transition, , in homogeneous amorphous wires is studied. We develop a
theory that gives in situations when the dynamically enhanced Coulomb
repulsion competes with the contact attraction. The theory accurately describes
recent experiments on --suppression in superconducting wires, after a
procedure that minimizes the role of nonuniversal mechanisms influencing
is applied.Comment: RevTeX, 4 pages, 3 figure
Keldysh approach to the renormalization group analysis of the disordered electron liquid
We present a Keldysh nonlinear sigma-model approach to the renormalization
group analysis of the disordered electron liquid. We include both the Coulomb
interaction and Fermi-liquid type interactions in the singlet and triplet
channels into the formalism. Based on this model, we reproduce the coupled
renormalization group equations for the diffusion coefficient, the frequency,
and interaction constants previously derived with the replica model in the
imaginary time technique. With the help of source fields coupling to the
particle-number and spin densities, we study the density-density and spin
density-spin density correlation functions in the diffusive regime. This allows
us to obtain results for the electric conductivity and the spin susceptibility
and thereby to re-derive the main results of the one-loop renormalization group
analysis of the disordered electron liquid in the Keldysh formalism.Comment: 29 pages, 15 figure
Metal-Insulator Transition in Disordered Two-Dimensional Electron Systems
We present a theory of the metal-insulator transition in a disordered
two-dimensional electron gas. A quantum critical point, separating the metallic
phase which is stabilized by electronic interactions, from the insulating phase
where disorder prevails over the electronic interactions, has been identified.
The existence of the quantum critical point leads to a divergence in the
density of states of the underlying collective modes at the transition, causing
the thermodynamic properties to behave critically as the transition is
approached. We show that the interplay of electron-electron interactions and
disorder can explain the observed transport properties and the anomalous
enhancement of the spin susceptibility near the metal-insulator transition
Branch-cut Singularities in Thermodynamics of Fermi Liquid Systems
The recently measured spin susceptibility of the two dimensional electron gas
exhibits a strong dependence on temperature, which is incompatible with the
standard Fermi liquid phenomenology. Here we show that the observed temperature
behavior is inherent to ballistic two dimensional electrons. Besides the
single-particle and collective excitations, the thermodynamics of Fermi liquid
systems includes effects of the branch-cut singularities originating from the
edges of the continuum of pairs of quasiparticles. As a result of the
rescattering induced by interactions, the branch-cut singularities generate
non-analyticities in the thermodynamic potential which reveal themselves in
anomalous temperature dependences. Calculation of the spin susceptibility in
such a situation requires a non-perturbative treatment of the interactions. As
in high-energy physics, a mixture of the collective excitations and pairs of
quasiparticles can be effectively described by a pole in the complex momentum
plane. This analysis provides a natural explanation for the observed
temperature dependence of the spin susceptibility, both in sign and magnitude.Comment: 8 pages, 3 figure
Heat diffusion in the disordered electron gas
We study the thermal conductivity of the disordered two-dimensional electron
gas. To this end we analyze the heat density-heat density correlation function
concentrating on the scattering processes induced by the Coulomb interaction in
the sub-temperature energy range. These scattering processes are at the origin
of logarithmic corrections violating the Wiedemann-Franz law. Special care is
devoted to the definition of the heat density in the presence of the long-range
Coulomb interaction. To clarify the structure of the correlation function, we
present details of a perturbative calculation. While the conservation of energy
strongly constrains the general form of the heat density-heat density
correlation function, the balance of various terms turns out to be rather
different from that for the correlation functions of other conserved quantities
such as the density-density or spin density-spin density correlation function.Comment: 23 pages, 12 figure
Kinetics of the disordered Bose gas with collisions
We discuss the kinetics of the disordered interacting Bose gas using the
Boltzmann transport equation. The theory may serve as a unifying framework for
studying questions of dynamics of the expanding Bose gas at different stages of
the expansion. We show that the transport theory allows us to straightforwardly
reproduce and generalize a number of results previously obtained from
microscopic models in different formalisms. Based on estimates for the
interparticle scattering rates, we discuss the relevance of interaction effects
for the localization problem in the interacting disordered Bose gas. We argue
that, if the number of particles is large enough, the size of the expanding
cloud may exceed the localization length. We describe the spreading of the wave
packet in this regime as collision-induced diffusion and compare the obtained
rate of expansion to known results on subdiffusive spreading in nonlinear
disordered lattices.Comment: 7 page
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