Finkel’stein Nonlinear Sigma Model: Interplay of Disorder and Interaction in 2D Electron Systems

Burmistrov, I. S.

doi:10.1134/s1063776119100029

Cited by 13 publications

(8 citation statements)

References 113 publications

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“…According to Eqs. ( 1) and ( 2), T c suppression in thin (d ξ 0 ) superconducting films is entirely determined by the dimensionless sheet conductance g. Such a statement perfectly fits the general theoretical framework of scaling [49], justified by the renormalization-group analysis of the nonlinear sigma model in the 2D space [54][55][56].…”

supporting

confidence: 54%

Superconductivity suppression in disordered films: Interplay of two-dimensional diffusion and three-dimensional ballistics

Antonenko,

Skvortsov

2020

Preprint

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Suppression of the critical temperature in homogeneously disordered superconducting films is a consequence of the disorder-induced enhancement of Coulomb repulsion. We demonstrate that for the majority of thin films studied now this effect cannot be completely explained in the assumption of two-dimensional diffusive nature of electrons motion. The main contribution to the Tc suppression arises from the correction to the electron-electron interaction constant coming from small scales of the order of the Fermi wavelength that leads to the critical temperature shift δTc/Tc0 ∼ −1/kF l, where kF is the Fermi momentum and l is the mean free path. Thus almost for all superconducting films that follow the fermionic scenario of Tc suppression with decreasing the film thickness, this effect is caused by the proximity to the three-dimensional Anderson localization threshold and is controlled by the parameter kF l rather than the sheet resistance of the film.

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confidence: 54%

Superconductivity suppression in disordered films: Interplay of two-dimensional diffusion and three-dimensional ballistics

Antonenko,

Skvortsov

2020

Preprint

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“…The action (1) of the Finkel'stein NLσM for the class C is similar to the one for a standard Wigner-Dyson class A in the presence of spin rotation symmetry (see Refs. [50,51,61] for review). We emphasize two distinctions.…”

Section: A Nlσm Actionmentioning

confidence: 99%

Generalized multifractality in the spin quantum Hall symmetry class with interaction

Babkin¹,

Burmistrov²

2022

Preprint

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Scaling of various local observables with a system size at Anderson transition criticality is characterized by a generalized multifractality. We study the generalized multifractality in the spin quantum Hall symmetry class (class C) in the presence of interaction. We employ Finkel'stein nonlinear sigma model and construct the pure scaling derivativeless operators for class C in the presence of interaction. Within the two-loop renormalization group analysis we compute the anomalous dimensions of the pure scaling operators and demonstrate that they are affected by the interaction. We find that the interaction breaks exact symmetry relations between generalized multifractal exponents known for a noninteracting problem.

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“…The action of the Finkel'stein NLSM is given as the sum of the non-interacting NLSM, S σ , and contributions resulting from electron-electron interactions, S (ρ) int (the particle-hole singlet channel), S (σ) int (the particle-hole triplet channel), and S (c) int (the particle-particle channel) (see Refs. [36][37][38] for a review):…”

Section: Finkel'stein Nlsm Action In the Normal Statementioning

confidence: 99%

“…( 46) they obey Eqs. (40a) -( 40c) and (38). In the arguments given above we neglected this subtlety.…”

Section: Relation Between Renormalization Group Flow and The Modified...mentioning

confidence: 99%

Multifractally-enhanced superconductivity in thin films

Burmistrov,

Gornyi,

Mirlin

2021

Preprint

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The multifractal superconducting state originates from the interplay of Anderson localization and interaction effects. In this article we overview the recent theory of the superconductivity enhancement by multifractality and extend it to describe the spectral properties of superconductors on the scales of the order of the superconducting gap. Specifically, using the approach based on renormalization group within the nonlinear sigma model, we develop the theory of a multifractal superconducting state in thin films. We derive a modified Usadel equation that incorporates the interplay of disorder and interactions at energy scales larger than the spectral gap and study the effect of such an interplay on the low-energy physics. We determine the spectral gap at zero temperature which occurs to be proportional to the multifracally enhanced superconducting transition temperature. The modified Usadel equation results in the disorder-averaged density of states that, near the spectral gap, resembles the one obtained in the model of a spatially random superconducting order parameter. We reveal strong mesoscopic fluctuations of the local density of states in the superconducting state. Such strong mesoscopic fluctuations imply that the interval of energies in which the superconducting gap establishes is parametrically large in systems with multifractally-enhanced superconductivity.

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Finkel’stein Nonlinear Sigma Model: Interplay of Disorder and Interaction in 2D Electron Systems

Cited by 13 publications

References 113 publications

Superconductivity suppression in disordered films: Interplay of two-dimensional diffusion and three-dimensional ballistics

Superconductivity suppression in disordered films: Interplay of two-dimensional diffusion and three-dimensional ballistics

Generalized multifractality in the spin quantum Hall symmetry class with interaction

Multifractally-enhanced superconductivity in thin films

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