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.

G. Schwiete A. M. Finkel'stein

We study thermal conductivity in the disordered two-dimensional electron liquid in the presence of long-range Coulomb interactions. We describe a microscopic analysis of the problem using as a starting point the partition function defined on the Keldysh contour. We extend the Renormalization Group (RG) analysis developed for thermal transport in the disordered Fermi liquid, and include scattering processes induced by the long-range Coulomb interaction in the sub-temperature energy range. For the thermal conductivity, unlike for the electric conductivity, these scattering processes yield a logarithmic correction which may compete with the RG-corrections. The interest in this correction arises from the fact that it violates the Wiedemann-Franz law. We checked that the sub-temperature correction to the thermal conductivity is not modified, neither by the inclusion of Fermi liquid interaction amplitudes nor as a result of the RG flow. We thereby expect that the answer obtained for this correction is final. We use the theory to describe thermal transport on the metallic side of the metal-insulator transition in Si MOSFETs.

G. Schwiete A. M. Finkel'stein

The non-linear sigma model is a well-established theoretical tool for studies of transport and thermodynamics in disordered electronic systems. The conventional sigma model approach for interacting systems does not account for particle-hole asymmetry. It is therefore not suited for studying quantities that are sensitive to this effect such as the thermoelectric transport coefficient. Here, we derive a minimal extension of the Keldysh non-linear sigma model tailored for two-dimensional interacting systems. We argue that this model can be used to systematically study the combined effect of interactions and disorder on thermoelectric transport. As a first step in this direction, we use the model to analyze the structure of the heat density-density correlation function and calculate interaction corrections to its static part. The calculation of interaction corrections to the dynamical part of the correlation function and the thermodynamic transport coefficient is left for future work.

G. Schwiete

We demonstrate theoretically the possibility to produce a pure spin current in graphene by filtering the charge from a spin-polarized electric current. To achieve this effect, which is based on the recently predicted property of specular Andreev reflection in graphene, we propose two possible device structures containing normal-superconductor (NS) junctions.

D. Greenbaum S. Das G. Schwiete P. G. Silvestrov

We consider magnetotransport in a disordered two-dimensional electron gas in the presence of a periodic modulation in one direction. Existing quasiclassical and quantum approaches to this problem account for Weiss oscillations in the resistivity tensor at moderate magnetic fields, as well as a strong modulation-induced modification of the Shubnikov-de Haas oscillations at higher magnetic fields. They do not account, however, for the operation at even higher magnetic fields of the integer quantum Hall effect, for which quantum interference processes are responsible. We then introduce a field-theory approach, based on a nonlinear sigma model, which encompasses naturally both the quasiclassical and quantum-mechanical approaches, as well as providing a consistent means of extending them to include quantum interference corrections. A perturbative renormalization-group analysis of the field theory shows how weak localization corrections to the conductivity tensor may be described by a modification of the usual one-parameter scaling, such as to accommodate the anisotropy of the bare conductivity tensor. We also show how the two-parameter scaling, conjectured as a model for the quantum Hall effect in unmodulated systems, may be generalized similarly for the modulated system. Within this model we illustrate the operation of the quantum Hall effect in modulated systems for parameters that are realistic for current experiments.

G. Schwiete D. Taras-Semchuk K. B. Efetov

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.

G. Schwiete A. M. Finkel'stein

We discuss galvanomagnetic and thermomagnetic effects in disordered electronic systems focusing on intermediate temperatures, for which electron-electron scattering and electron-impurity scattering occur at similar rates, while phonon-related effects can be neglected. In particular, we explore how electric and thermal currents driven either by an electric field or by a temperature gradient are affected by the interplay of momentum-dependent electron-impurity scattering, electron-electron scattering, and the presence of a magnetic field. We find that the electric resistance, the Seebeck coefficient and the Nernst coefficient are particularly sensitive to the momentum dependence of the electron-impurity scattering rate at intermediate temperatures. A sufficiently strong momentum dependence of the electron-impurity scattering rate can induce a sign change of the Seebeck coefficient. This sign change can be suppressed by a perpendicular magnetic field. The temperature and magnetic field dependence of the Seebeck coefficient can be used for measuring the magnitude of the electron-impurity and electron-electron scattering rates. The Nernst coefficient vanishes for momentum-independent electron-impurity scattering, but displays a maximum at finite temperatures once the momentum dependence is accounted for. By contrast, the Hall coefficient and the Righi-Leduc coefficient display only a weak dependence on the momentum dependence of the electron-impurity scattering at intermediate temperatures.

Woo-Ram Lee Alexander Finkel'stein G. Schwiete

We review the scaling theory of disordered itinerant electrons with e-e interactions. We first show how to adjust the microscopic Fermi-liquid theory to the presence of disorder. Then we describe the non-linear sigma model (NLSM) with interactions (Finkel'stein's model). This model is closely connected to the Fermi liquid, but is more generally applicable, since it can also be viewed as a minimal effective functional describing disordered interacting electrons. Our discussion emphasizes the general structure of the theory, and the connection of the scaling parameters to conservation laws. We then move on to discuss the metal-insulator transition (MIT) in the disordered electron liquid in two and three dimensions. This MIT is a non-trivial example of a quantum phase transition. The NLSM approach allows to identify the dynamical exponent connecting the spatial and energy scales, which is central for the description of the kinetic and thermodynamic behavior in the critical region of the MIT in three dimensions. In two dimensions, the system can be discussed in terms of a flow in the disorder-interaction phase plane, which is controlled by a fixed point. We demonstrate that the two-parameter RG-equations accurately describe electrons in Si-MOSFETs including the observed non-monotonic behavior of the resistance and its strong drop at low temperatures. The theory can also be applied to systems with an attractive interaction in the Cooper channel, where it describes the suppression of superconductivity in disordered amorphous films. We extend our discussion to heat transport in the two-dimensional electron liquid. Similar to the electric conductivity, the thermal conductivity also acquires logarithmic corrections induced by electron interaction and disorder. The resulting thermal conductivity can be calculated in the NLSM formalism after introducing so-called gravitational potentials.

A. M. Finkel'stein G. Schwiete

Using a supersymmetry formalism, we reduce exactly the problem of electron motion in an external potential to a new supermatrix model valid at all distances. All approximate nonlinear sigma models obtained previously for disordered systems can be derived from our exact model using a coarse-graining procedure. As an example, we consider a model for a smooth disorder and demonstrate that using our approach does not lead to a 'mode-locking' problem. As a new application, we consider scattering on strong impurities for which the Born approximation cannot be used. Our method provides a new calculational scheme for disordered and chaotic systems.

K. B. Efetov G. Schwiete K. Takahashi

We formulate the perturbative QCD approach to coherent diffractive dijet production in pion-nucleon and pion-nucleus collisions at high energy. For hard dijets the Pomeron splitting mechanism in which both helicity amplitudes are proportional to the unintegrated gluon structure function of the proton and the pion distribution amplitude is shown to dominate. In nuclear diffraction multiple Pomeron splitting components are found to give antishadowing contributions at large jet momentum. To leading twist there is an exact cancelation of effects of nuclear attenuation and antishadowing/broadening of multiple Pomeron splitting contributions. The next-to-leading higher twist correction driven by nuclear rescatterings is calculable in hard QCD and proves to be numerically very large. We argue that large higher twist effects do not preclude the determination of gross features of the pion distribution amplitude. Our results on the atomic mass number and momentum dependence of dijet cross sections agree well with the preliminary findings from the E791 experiment.

N. N. Nikolaev W. Schäfer G. Schwiete