Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Acta Physica Polonica A

Electromagnetic Response of the BCS Superconductor: Flow Equation Approach

M. Zapalska, T. Domański

Published Apr 1, 2012• 1 citation
Publisher

Abstract

We address the linear response for superconductors using the non-perturbative technique based on the continuous unitary transformation.We discuss how this method rigorously reproduces the standard BCS solution and point out how such result can be generalized to the case of electron systems with strong pairing uctuations and in presence of the nonequilibrium phenomena.

DOI
10.12693/aphyspola.121.854

Related papers

The linear response of electron systems with the pairing instabilities - the flow equation study

M. Curie

We address the linear response of the electron system with the pairing instabilities using nonperturbative framework of the continuous unitary transformation technique. For the case of the Bose-Einstein condensed pairs we have analytically derived the BCS result, which in the static and long wavelength limit accounts for the Meissner effect. We next apply our treatment to the mixture of the non-condensed (preformed) pairs interacting with the mobile electrons through the charge-exchange Andreev scattering. We determine the leading contributions to the current-current response function, expressing the vertices by the set of the corresponding flow equations. Our study indicates that the residual diamagnetic behavior detected by the torque magnetometry well above the transition temperature [L. Li et al, Phys. Rev. B 81, 054510 (2010)] can originate from the noncondensed preformed pairs.

•Jan 1, 2011•0 citations

Flow equation approach to the linear response theory of superconductors

M. Zapalska, T. Domański

We apply the flow equation method for studying the current-current response function of electron systems with the pairing instability. To illustrate the specific scheme in which the flow equation procedure determines the two-particle Green's functions, we reproduce the standard response kernel of the BCS superconductor. We next generalize this nonperturbative treatment considering the pairing field fluctuations. Our study indicates that the residual diamagnetic behavior detected above the transition temperature in the cuprate superconductors can originate from the noncondensed preformed pairs.

arXiv:1108.5638•Physical Review B•Nov 23, 2011•7 citations

Exact expectation values within Richardson's approach for the pairing Hamiltonian in a macroscopic system

G. Gorohovsky, Eldad Bettelheim

BCS superconductivity is explained by a simple Hamiltonian describing an attractive pairing interaction between pairs of electrons. The Hamiltonian may be treated using a mean-field method, which is adequate to study equilibrium properties and a variety of nonequilibrium effects. Nevertheless, in certain nonequilibrium situations, even in a macroscopic rather than a microscopic superconductor, the application of mean-field theory may not be valid. In such cases, one may resort to the full solution of the Hamiltonian, as given by Richardson in the 1960s. The relevance of Richardson's solution to macroscopic nonequilibrium superconductors was pointed out recently based on the existence of quantum instabilities out of equilibrium. It is then of interest to obtain analytical expressions for expectation values between exact eigenvalues of the pairing Hamiltonian within the Richardson approach for macroscopic systems. We undertake this task in the current paper. It should be noted that Richardson's approach yields the full set of eigenvalues of the Hamiltonian, while BCS theory yields only a subset. The results obtained here, then, generalize the familiar BCS expressions (e.g., for the electron occupation or pairing correlations) to cases where the spectrum of excitations diverges from BCS theory (e.g., in cases where the spectrum exhibits multiple gaps).

arXiv:1111.1519•Physical Review B•Dec 14, 2011•19 citations

Continuous unitary transformation approach to pairing interactions in statistical physics

T. Domański

We apply the flow equation method to the study of the fermion systems with pairing interactions which lead to the BCS instability signalled by the appearance of the off-diagonal order parameter.For this purpose we rederive the continuous Bogoliubov transformation in a fashion of renormalization group procedure where the low and high energy sectors are treated subsequently.We further generalize this procedure to the case of fermions interacting with the discrete boson mode.Andreev-type interactions are responsible for developing a gap in the excitation spectrum.However, the long-range coherence is destroyed due to strong quantum fluctuations.

Condensed Matter Physics•Jun 1, 2008•0 citations

Renormalization Group Methods: Landau-Fermi Liquid and BCS Superconductor

Jürg Martin Fröhlich, T. Chen, Maximilian Seifert

This is the second part of the notes to the course on quantum theory of large systems of non-relativistic matter taught by J. Fröhlich at the 1994 Les Houches summer school. It is devoted to a sketchy exposition of some of the beautiful and important, recent results of J.Feldman and E.Trubowitz, and J. Feldman, H. Knörrer, D. Lehmann, J. Magnen, V. Rivasseau and E. Trubowitz. Their results are about a mathematical analysis of non-relativistic many-body theory, in particular of the Landau-Fermi liquid and BCS superconductivity, using Wilson's renormalization group methods and the techniques of the $1/N$-expansion. While their work is ultimately aimed at a complete mathematical control (beyond perturbative expansions) of systems of weakly coupled electron gases at positive density and small or zero temperature, we can only illustrate some of their ideas within the context of perturbative solutions of Wilson-type renormalization group flow equations (we calculate leading-order terms in a $1/N$-expansion, where $N$ is an energy scale) and of one-loop effective potential calculations of the BCS superconducting ground state. Contents: 1. Background material 2. Weakly coupled electron gases 3. The renormalization group flow 4. Spontaneous breaking of gauge invariance, and superconductivity

arXiv:cond-mat/9508063•Aug 16, 1995•10 citations

Flow equation approach to the pairing problems

T. Domański

We apply the flow equation method for studying the fermion systems where pairing interactions can either trigger the BCS instability with the symmetry breaking manifested by the off-diagonal order parameter or lead to the gaped single particle spectrum without any symmetry breaking. We construct the continuous Bogoliubov transformation in a scheme resembling the renormalization group procedure. We further extend this continuous transformation to a case where fermion pairs interact with the boson field. Due to temporal quantum fluctuations the single particle excitation spectrum develops a gap which is centered around the renormalized boson energy. When bosons undergo the Bose Einstein condensation this structure evolves into the BCS spectrum.

arXiv:cond-mat/0602236•Feb 9, 2006•0 citations
We address the linear response for superconductors using the non-perturbative technique based on the continuous unitary transformation.We discuss how this method rigorously reproduces the standard BCS solution and point out how such result can be generalized to the case of electron systems with strong pairing uctuations and in presence of the nonequilibrium phenomena.
We address the linear response of the electron system with the pairing instabilities using nonperturbative framework of the continuous unitary transformation technique. For the case of the Bose-Einstein condensed pairs we have analytically derived the BCS result, which in the static and long wavelength limit accounts for the Meissner effect. We next apply our treatment to the mixture of the non-condensed (preformed) pairs interacting with the mobile electrons through the charge-exchange Andreev scattering. We determine the leading contributions to the current-current response function, expressing the vertices by the set of the corresponding flow equations. Our study indicates that the residual diamagnetic behavior detected by the torque magnetometry well above the transition temperature [L. Li et al, Phys. Rev. B 81, 054510 (2010)] can originate from the noncondensed preformed pairs.
We apply the flow equation method for studying the current-current response function of electron systems with the pairing instability. To illustrate the specific scheme in which the flow equation procedure determines the two-particle Green's functions, we reproduce the standard response kernel of the BCS superconductor. We next generalize this nonperturbative treatment considering the pairing field fluctuations. Our study indicates that the residual diamagnetic behavior detected above the transition temperature in the cuprate superconductors can originate from the noncondensed preformed pairs.
BCS superconductivity is explained by a simple Hamiltonian describing an attractive pairing interaction between pairs of electrons. The Hamiltonian may be treated using a mean-field method, which is adequate to study equilibrium properties and a variety of nonequilibrium effects. Nevertheless, in certain nonequilibrium situations, even in a macroscopic rather than a microscopic superconductor, the application of mean-field theory may not be valid. In such cases, one may resort to the full solution of the Hamiltonian, as given by Richardson in the 1960s. The relevance of Richardson's solution to macroscopic nonequilibrium superconductors was pointed out recently based on the existence of quantum instabilities out of equilibrium. It is then of interest to obtain analytical expressions for expectation values between exact eigenvalues of the pairing Hamiltonian within the Richardson approach for macroscopic systems. We undertake this task in the current paper. It should be noted that Richardson's approach yields the full set of eigenvalues of the Hamiltonian, while BCS theory yields only a subset. The results obtained here, then, generalize the familiar BCS expressions (e.g., for the electron occupation or pairing correlations) to cases where the spectrum of excitations diverges from BCS theory (e.g., in cases where the spectrum exhibits multiple gaps).
We apply the flow equation method to the study of the fermion systems with pairing interactions which lead to the BCS instability signalled by the appearance of the off-diagonal order parameter.For this purpose we rederive the continuous Bogoliubov transformation in a fashion of renormalization group procedure where the low and high energy sectors are treated subsequently.We further generalize this procedure to the case of fermions interacting with the discrete boson mode.Andreev-type interactions are responsible for developing a gap in the excitation spectrum.However, the long-range coherence is destroyed due to strong quantum fluctuations.
This is the second part of the notes to the course on quantum theory of large systems of non-relativistic matter taught by J. Fröhlich at the 1994 Les Houches summer school. It is devoted to a sketchy exposition of some of the beautiful and important, recent results of J.Feldman and E.Trubowitz, and J. Feldman, H. Knörrer, D. Lehmann, J. Magnen, V. Rivasseau and E. Trubowitz. Their results are about a mathematical analysis of non-relativistic many-body theory, in particular of the Landau-Fermi liquid and BCS superconductivity, using Wilson's renormalization group methods and the techniques of the 1/N1/N1/N-expansion. While their work is ultimately aimed at a complete mathematical control (beyond perturbative expansions) of systems of weakly coupled electron gases at positive density and small or zero temperature, we can only illustrate some of their ideas within the context of perturbative solutions of Wilson-type renormalization group flow equations (we calculate leading-order terms in a 1/N1/N1/N-expansion, where NNN is an energy scale) and of one-loop effective potential calculations of the BCS superconducting ground state. Contents: 1. Background material 2. Weakly coupled electron gases 3. The renormalization group flow 4. Spontaneous breaking of gauge invariance, and superconductivity
We apply the flow equation method for studying the fermion systems where pairing interactions can either trigger the BCS instability with the symmetry breaking manifested by the off-diagonal order parameter or lead to the gaped single particle spectrum without any symmetry breaking. We construct the continuous Bogoliubov transformation in a scheme resembling the renormalization group procedure. We further extend this continuous transformation to a case where fermion pairs interact with the boson field. Due to temporal quantum fluctuations the single particle excitation spectrum develops a gap which is centered around the renormalized boson energy. When bosons undergo the Bose Einstein condensation this structure evolves into the BCS spectrum.