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A. M. Finkel'stein

Publications and source records attributed to A. M. Finkel'stein.

At least 19 recordsLinked to original sources
arXiv2023

Scale-dependent theory of the disordered electron liquid

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.

cond-mat.str-el↗
arXiv2015

Theory of Thermal Conductivity in the Disordered Electron Liquid

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.

cond-mat.mes-hall↗
arXiv2015

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.

cond-mat.mes-hall↗
arXiv2015

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.

cond-mat.mes-hall↗
arXiv2014

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.

cond-mat.mes-hall↗
arXiv2014

Thermal Transport and Wiedemann-Franz Law in the Disordered Fermi Liquid

We study thermal transport in the disordered Fermi liquid at low temperatures. Gravitational potentials are used as sources for finding the heat density and its correlation function. For a comprehensive study, we extend the renormalization group (RG) analysis developed for electric transport by including the gravitational potentials into the RG scheme. Our analysis reveals that the Wiedemann-Franz law remains valid even in the presence of quantum corrections caused by the interplay of diffusion modes and the electron electron interaction. In the present scheme this fundamental relation is closely connected with a fixed point in the multi-parametric RG-flow of the gravitational potentials.

cond-mat.mes-hall↗
arXiv2013

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.

cond-mat.quant-gas↗
arXiv2013

Spectral non-uniform temperature, non-local heat transfer, and the spin Seebeck effect

We present a theory of the spin Seebeck effect driven by subthermal non-local phonon heat transfer and spectral non-uniform temperature distribution. The theory explains the non-local behavior of the effect arising from the fact that phonons that store the energy (thermal) and the phonons that transfer it (subthermal) are located in different parts of the spectrum and have very different kinetics. This gives rise to a spectral phonon distribution function that deviates from local equilibrium along the substrate and is sensitive to boundary conditions. The theory also predicts a non-magnon origin of the effect in ferromagnetic metals in agreement with observations in recent experiments. Equilibration of the heat flow out of the substrate to the Pt probe and backwards leads to a measurable vertical spin-current produced by the spin polarized electrons dragged by the local thermal phonons. We predict specific sample length limits and other dependencies that can be probed experimentally, and obtain the correct magnitude of the effect.

cond-mat.mes-hall↗
arXiv2009

Nonlinear wave-packet dynamics in a disordered medium

In this article we develop an effective theory of pulse propagation in a nonlinear and disordered medium. The theory is formulated in terms of a nonlinear diffusion equation. Despite its apparent simplicity this equation describes novel phenomena which we refer to as "locked explosion" and "diffusive" collapse. In this sense the equation can serve as a paradigmatic model, that can be applied to such distinct physical systems as laser beams propagating in disordered photonic crystals or Bose-Einstein condensates expanding in a disordered environment.

cond-mat.mes-hall↗
arXiv2007

Suppression of Tunneling of Superconducting Vortices Caused by a Remote Gate: Example of an Extended Object Tunneling

We discuss a recent experiment in which the resistance of a superconducting film has been measured in magnetic field. A strong decrease of the superconducting film resistance has been observed when a metallic gate is placed above the film. We study how the magnetic coupling between vortices in a thin superconducting film and electrons in a remote unbiased gate suppresses the tunneling rate of the vortices. We examine two general approaches to analyze tunneling in the presence of slow low-energy degrees of freedom: the functional-integral and scattering formalisms. In the first one, the response of the electrons inside the metallic gate to a change in the vortex position is described by the "tunneling with dissipation". We consider the Eddy current induced in the gate by the magnetic flux of the vortex as a result of tunneling. In the second approach, the response is given in terms of scattering of the electrons by the magnetic flux of the vortex in a way similar to the Aharonov-Bohm scattering. A sudden change in the vortex position leads to the Orthogonality Catastrophe that opposes the vortex tunneling. We show that the magnetic coupling between the vortices and the electrons inside the gate can lead to a dramatic suppression of the vortex tunneling, restoring the superconducting property in accord with the experiment.

cond-mat.supr-con↗
arXiv2007

Flow diagram of the metal-insulator transition in two dimensions

The discovery of the metal-insulator transition (MIT) in two-dimensional (2D) electron systems challenged the veracity of one of the most influential conjectures in the physics of disordered electrons, which states that `in two dimensions, there is no true metallic behaviour'; no matter how weak the disorder, electrons would be trapped and unable to conduct a current. However, that theory did not account for interactions between the electrons. Here we investigate the interplay between the electron-electron interactions and disorder near the MIT using simultaneous measurements of electrical resistivity and magnetoconductance. We show that both the resistance and interaction amplitude exhibit a fan-like spread as the MIT is crossed. From these data we construct a resistance-interaction flow diagram of the MIT that clearly reveals a quantum critical point, as predicted by the two-parameter scaling theory (Punnoose and Finkel'stein, Science 310, 289 (2005)). The metallic side of this diagram is accurately described by the renormalization group theory without any fitting parameters. In particular, the metallic temperature dependence of the resistance sets in when the interaction amplitude reaches gamma_2 = 0.45 - a value in remarkable agreement with the one predicted by the theory.

cond-mat.str-el↗
arXiv2006

Temperature dependence of spin susceptibility in two-dimensional Fermi liquid systems

We consider the non-analytic terms in the spin susceptibility arising as a result of rescaterring of pairs of quasiparticles. We emphasize the importance of rescattering in the Cooper channel for the analysis of the temperature dependences in the two-dimensional electron systems in the ballistic regime. In the calculation of the linear in $T$ term we use angular harmonics in the Cooper channel, because for each harmonic the interaction amplitude is renormalized independently. We observe, that as a consequence of strong renormalizations in the Cooper ladder, the temperature derivative of the spin susceptibility may change its sign at low temperatures.

cond-mat.str-el↗
arXiv2006

Metal-Insulator Transition in a System of Superconducting Vortices Caused by a Metallic Gate

We address a recent experiment in which a strong decrease of the resistance of a superconducting film has been observed when a remote unbiased gate was placed above the film. Here we explain the experimental finding as a suppression of the vortex tunneling due to the Orthogonality Catastrophe of the electrons inside the gate. We interpret the change in the resistance of the film as a "metal-insulator" transition in the system of vortices induced by the gate.

cond-mat.supr-con↗
arXiv2005

Chiral spin resonance and spin-Hall conductivity in the presence of the electron-electron interactions

We discuss the electron spin resonance in two-dimensional electron gas at zero external magnetic field. This spin-resonance is due to the transitions between the electron states, which are split by the spin-orbit (SO) interaction, and is termed as the chiral spin resonance (CSR). It can be excited by the in-plane component of the electric field of microwave radiation. We show that there exists an inherent relationship between the spin-Hall conductivity and the CSR in a system with the SO interaction. Since in the presence of the SO interaction spin is not conserved, the electron-electron interaction renormalizes the spin-Hall conductivity as well as the frequency of the CSR. The effects of the electron interaction in systems with the SO interaction are analyzed both phenomenologically and microscopically.

cond-mat.str-el↗
arXiv2005

Diffuse emission in the presence of inhomogeneous spin-orbit interaction for the purpose of spin filtration

A lateral interface connecting two regions with different strengths of the Bychkov-Rashba spin-orbit interaction can be used as a spin polarizer of electrons in two dimensional semiconductor heterostructures. [Khodas \emph{et al.}, Phys. Rev. Lett. \textbf{92}, 086602 (2004)]. In this paper we consider the case when one of the two regions is ballistic, while the other one is diffusive. We generalize the technique developed for the solution of the problem of the diffuse emission to the case of the spin dependent scattering at the interface, and determine the distribution of electrons emitted from the diffusive region. It is shown that the diffuse emission is an effective way to get electrons propagating at small angles to the interface that are most appropriate for the spin filtration and a subsequent spin manipulation. Finally, a scheme is proposed of a spin filter device, see Fig. 9, that creates two almost fully spin-polarized beams of electrons.

cond-mat.mes-hall↗
arXiv2004

Spin polarization of electrons by non-magnetic heterostructures : basics of spin-optics

We propose to use the lateral interface between two regions with different strengths of the spin-orbit interaction(s) to spin-polarize the electrons in gated two dimensional semiconductor heterostructures. For a beam with a non zero angle of incidence the transmitted electrons will split into two spin polarization components propagating at different angles. We analyze the refraction at such an interface and outline the basic schemes for filtration and control of the electron spin.

cond-mat.mes-hall↗
arXiv2004

Hall Coefficient in an Interacting Electron Gas

The Hall conductivity in a weak homogeneous magnetic field, $ω_{c}τ\ll 1$, is calculated. We have shown that to leading order in $1/ε_{F}τ$ the Hall coefficient $R_{H}$ is not renormalized by the electron-electron interaction. Our result explains the experimentally observed stability of the Hall coefficient in a dilute electron gas not too close to the metal-insulator transition. We avoid the currently used procedure that introduces an artificial spatial modulation of the magnetic field. The problem of the Hall effect is reformulated in a way such that the magnetic flux associated with the scattering process becomes the central element of the calculation.

cond-mat.str-el↗