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

Physical Review B

Multiple scattering corrections to the T -matrix approximation: Unified theory of normal and superconducting states

P. Lipavský

Published Dec 5, 2008• 12 citations
Publisher

Abstract

We present unified theory of both normal and superconducting states based on the fully self-consistent $\mathcal{T}$-matrix approximation. We argue that the failure of the customary $\mathcal{T}$-matrix approach below the critical temperature is caused by nonphysical repeated collisions. We eliminated the repeated collisions from the Galitskii-Feynman approximation. Obtained corrections are proportional to the inverse volume in the normal state and, thus, vanish in the thermodynamical limit. In the superconducting state these corrections remain finite and describe the Bardeen-Cooper-Schrieffer (BCS) gap. The $\mathcal{T}$-matrix approach goes beyond mean-field BCS theory. It is, thus, well suited for studies of the systems with large fluctuations such as the BCS--Bose-Einstein-condensate crossover or size effects in small metallic grains and the nuclear matter.

DOI
10.1103/physrevb.78.214506

Related papers

Strong-coupling limit in the evolution from BCS superconductivity to Bose-Einstein condensation

P. Pieri, Giancarlo Calvanese Strinati

We consider the problem of the crossover from BCS superconductivity to Bose-Einstein condensation in three dimensions for a system of fermions with a mutual attractive interaction, for which we adopt the simplifying assumption of a suitably regularized point-contact interaction. We examine in a critical way the fermionic (self-consistent) T-matrix approximation, which has been widely utilized in the literature to describe this crossover above the superconducting critical temperature, and show that it fails to yield the correct behavior of the system in the strong-coupling limit, where composite bosons form as tightly bound fermion pairs. We then set up the correct approximation for a ``dilute'' system of composite bosons and show that a class of diagrams has to be considered in the place of the fermionic T-matrix approximation for the self-energy. This class of diagrams correctly describes both the weak- and strong-coupling limits, and consequently results in an improved interpolation scheme for the intermediate (crossover) region. In this context, we provide also a systematic mapping between the corresponding diagrammatic theories for the composite bosons and the constituent fermions. As a preliminary result to demonstrate the numerical effect of our class of diagrams on physical quantities, we calculate the value of the scattering length for composite bosons in the strong-coupling limit and show that it is considerably modified with respect to the result obtained within the self-consistent fermionic T-matrix approximation.

arXiv:cond-mat/9811166•Physical review. B, Condensed matter•Jun 1, 2000•185 citations

Semiclassical Theory of Bardeen-Cooper-Schrieffer Pairing-Gap Fluctuations

H. Olofsson, Sven Åberg, P. Lebœuf

Superfluidity and superconductivity are genuine many-body manifestations of quantum coherence. For finite-size systems the associated pairing gap fluctuates as a function of size or shape. We provide a theoretical description of the zero temperature pairing fluctuations in the weak-coupling BCS limit of mesoscopic systems characterized by order or chaos dynamics. The theory accurately describes experimental observations of nuclear superfluidity (regular system), predicts universal fluctuations of superconductivity in small chaotic metallic grains, and provides a global analysis in ultracold Fermi gases.

arXiv:0704.2310•Physical Review Letters•Jan 24, 2008•30 citations

Self-consistent T -matrix theory of superconductivity

Břetislav Šopík, P. Lipavský, M. Männel +2 more

Using principles of the Fadeev-Lovelace-Watson multiple scattering expansion, a $T$-matrix approximation is derived which coincides with the Galitskii-Feynman $T$ matrix in the normal state and yields the gap in the superconducting state. Unlike other $T$-matrix approaches, the theory satisfies not only the self-consistent Thouless criterion but also the Baym-Kadanoff conditions for a conserving theory in equilibrium. In single-mode approximation it simplifies to the Eliashberg theory.

arXiv:0906.3677•Physical Review B•Sep 27, 2011•12 citations

Excitation properties and effects of mass imbalance in the BCS-BEC crossover regime of an ultracold Fermi gas

Ryo Hanai, Takashi Kashimura, Ryota Watanabe +2 more

We investigate single-particle properties of a mass-imbalanced Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)--BEC (Bose-Einstein condensation) crossover region. In the presence of mass imbalance, we point out that the ordinary $T$-matrix approximation, which has been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically gives a double-valued solution in terms of the superfluid phase transition temperature ${T}_{\mathrm{c}}$ in the crossover region. To overcome this serious problem, we include higher order strong-coupling corrections beyond the $T$-matrix level. Using this extended $T$-matrix theory, we calculate single-particle excitations in the normal state above ${T}_{\mathrm{c}}$. The so-called pseudogap phenomena originating from pairing fluctuations are shown to be different between the light-mass component and heavy-mass component, which becomes more remarkable at higher temperatures. Since Fermi condensates with hetero-Cooper pairs have recently been discussed in various fields, such as exciton (polariton) condensates as well as color superconductivity, our results would be useful for the further development of Fermi superfluid physics, beyond the conventional superfluid state with homo-Cooper pairs.

arXiv:1309.5622•Physical Review A•Nov 18, 2013•23 citations

BCS-BEC Crossover and Pairing Fluctuations in a Two Band Superfluid/Superconductor: A T Matrix Approach

Hiroyuki Tajima, Andrea Perali, Pierbiagio Pieri

We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as the critical temperature, chemical potential, and momentum distributions undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan’s contact to a two band system and report the two contacts for different pair-exchange couplings. The present results are compared with those obtained by the simpler Nozières–Schmitt–Rink approximation. We confirm a pronounced enhancement of the critical temperature due to the multiband configuration, as well as to the pair-exchange coupling.

arXiv:1912.02795•Condensed Matter•Jan 21, 2020•16 citations

Pair excitations, collective modes, and gauge invariance in the BCS–Bose-Einstein crossover scenario

Ioan Kosztin, Qijin Chen, Ying-Jer Kao +1 more

In this paper we study the BCS Bose-Einstein condensation (BEC) crossover scenario within the superconducting state, using a T-matrix approach which yields the ground state proposed by Leggett. Here we extend this ground state analysis to finite temperatures T and interpret the resulting physics. We find two types of bosoniclike excitations of the system: long lived, incoherent pair excitations and collective modes of the superconducting order parameter, which have different dynamics. Using a gauge invariant formalism, this paper addresses their contrasting behavior as a function of T and superconducting coupling constant g. At a more physical level, our paper emphasizes how, at finite T, BCS-BEC approaches introduce an important parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}={\ensuremath{\Delta}}^{2}\ensuremath{-}{\ensuremath{\Delta}}_{\mathrm{sc}}^{2}$ into the description of superconductivity. This parameter is governed by the pair excitations and is associated with particle-hole asymmetry effects that are significant for sufficiently large g. In the fermionic regime, ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}$ represents the difference between the square of the excitation gap ${\ensuremath{\Delta}}^{2}$ and that of the superconducting order parameter ${\ensuremath{\Delta}}_{\mathrm{sc}}^{2}.$ The parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2},$ which is necessarily zero in the BCS (mean field) limit increases monotonically with the strength of the attractive interaction g. It follows that there is a significant physical distinction between this BCS-BEC crossover approach (in which g is the essential variable which determines ${\ensuremath{\Delta}}_{\mathrm{pg}})$ and the widely discussed phase fluctuation scenario in which the plasma frequency is the tuning parameter. Finally, we emphasize that in the strong coupling limit, there are important differences between the composite bosons that arise in crossover theories and the usual bosons of the (interacting) Bose liquid. Because of constraints imposed on the fermionic excitation gap and chemical potential, in crossover theories, the fermionic degrees of freedom can never be fully removed from consideration.

arXiv:cond-mat/9906180•Physical review. B, Condensed matter•May 1, 2000•74 citations
We present unified theory of both normal and superconducting states based on the fully self-consistent T\mathcal{T}T-matrix approximation. We argue that the failure of the customary T\mathcal{T}T-matrix approach below the critical temperature is caused by nonphysical repeated collisions. We eliminated the repeated collisions from the Galitskii-Feynman approximation. Obtained corrections are proportional to the inverse volume in the normal state and, thus, vanish in the thermodynamical limit. In the superconducting state these corrections remain finite and describe the Bardeen-Cooper-Schrieffer (BCS) gap. The T\mathcal{T}T-matrix approach goes beyond mean-field BCS theory. It is, thus, well suited for studies of the systems with large fluctuations such as the BCS--Bose-Einstein-condensate crossover or size effects in small metallic grains and the nuclear matter.
We consider the problem of the crossover from BCS superconductivity to Bose-Einstein condensation in three dimensions for a system of fermions with a mutual attractive interaction, for which we adopt the simplifying assumption of a suitably regularized point-contact interaction. We examine in a critical way the fermionic (self-consistent) T-matrix approximation, which has been widely utilized in the literature to describe this crossover above the superconducting critical temperature, and show that it fails to yield the correct behavior of the system in the strong-coupling limit, where composite bosons form as tightly bound fermion pairs. We then set up the correct approximation for a ``dilute'' system of composite bosons and show that a class of diagrams has to be considered in the place of the fermionic T-matrix approximation for the self-energy. This class of diagrams correctly describes both the weak- and strong-coupling limits, and consequently results in an improved interpolation scheme for the intermediate (crossover) region. In this context, we provide also a systematic mapping between the corresponding diagrammatic theories for the composite bosons and the constituent fermions. As a preliminary result to demonstrate the numerical effect of our class of diagrams on physical quantities, we calculate the value of the scattering length for composite bosons in the strong-coupling limit and show that it is considerably modified with respect to the result obtained within the self-consistent fermionic T-matrix approximation.
Superfluidity and superconductivity are genuine many-body manifestations of quantum coherence. For finite-size systems the associated pairing gap fluctuates as a function of size or shape. We provide a theoretical description of the zero temperature pairing fluctuations in the weak-coupling BCS limit of mesoscopic systems characterized by order or chaos dynamics. The theory accurately describes experimental observations of nuclear superfluidity (regular system), predicts universal fluctuations of superconductivity in small chaotic metallic grains, and provides a global analysis in ultracold Fermi gases.
Using principles of the Fadeev-Lovelace-Watson multiple scattering expansion, a TTT-matrix approximation is derived which coincides with the Galitskii-Feynman TTT matrix in the normal state and yields the gap in the superconducting state. Unlike other TTT-matrix approaches, the theory satisfies not only the self-consistent Thouless criterion but also the Baym-Kadanoff conditions for a conserving theory in equilibrium. In single-mode approximation it simplifies to the Eliashberg theory.
We investigate single-particle properties of a mass-imbalanced Fermi gas in the BCS (Bardeen-Cooper-Schrieffer)--BEC (Bose-Einstein condensation) crossover region. In the presence of mass imbalance, we point out that the ordinary TTT-matrix approximation, which has been extensively used to clarify various BCS-BEC crossover physics in the mass-balanced case, unphysically gives a double-valued solution in terms of the superfluid phase transition temperature Tc{T}_{\mathrm{c}}Tc​ in the crossover region. To overcome this serious problem, we include higher order strong-coupling corrections beyond the TTT-matrix level. Using this extended TTT-matrix theory, we calculate single-particle excitations in the normal state above Tc{T}_{\mathrm{c}}Tc​. The so-called pseudogap phenomena originating from pairing fluctuations are shown to be different between the light-mass component and heavy-mass component, which becomes more remarkable at higher temperatures. Since Fermi condensates with hetero-Cooper pairs have recently been discussed in various fields, such as exciton (polariton) condensates as well as color superconductivity, our results would be useful for the further development of Fermi superfluid physics, beyond the conventional superfluid state with homo-Cooper pairs.
We investigate pairing fluctuation effects in a two band fermionic system, where a shallow band in the Bardeen–Cooper–Schrieffer–Bose–Einstein condensation (BCS-BEC) crossover regime is coupled with a weakly interacting deep band. Within a diagrammatic T matrix approach, we report how thermodynamic quantities such as the critical temperature, chemical potential, and momentum distributions undergo the crossover from the BCS to BEC regime by tuning the intraband coupling in the shallow band. We also generalize the definition of Tan’s contact to a two band system and report the two contacts for different pair-exchange couplings. The present results are compared with those obtained by the simpler Nozières–Schmitt–Rink approximation. We confirm a pronounced enhancement of the critical temperature due to the multiband configuration, as well as to the pair-exchange coupling.
In this paper we study the BCS Bose-Einstein condensation (BEC) crossover scenario within the superconducting state, using a T-matrix approach which yields the ground state proposed by Leggett. Here we extend this ground state analysis to finite temperatures T and interpret the resulting physics. We find two types of bosoniclike excitations of the system: long lived, incoherent pair excitations and collective modes of the superconducting order parameter, which have different dynamics. Using a gauge invariant formalism, this paper addresses their contrasting behavior as a function of T and superconducting coupling constant g. At a more physical level, our paper emphasizes how, at finite T, BCS-BEC approaches introduce an important parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}={\ensuremath{\Delta}}^{2}\ensuremath{-}{\ensuremath{\Delta}}_{\mathrm{sc}}^{2}$ into the description of superconductivity. This parameter is governed by the pair excitations and is associated with particle-hole asymmetry effects that are significant for sufficiently large g. In the fermionic regime, ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2}$ represents the difference between the square of the excitation gap ${\ensuremath{\Delta}}^{2}$ and that of the superconducting order parameter ${\ensuremath{\Delta}}_{\mathrm{sc}}^{2}.$ The parameter ${\ensuremath{\Delta}}_{\mathrm{pg}}^{2},$ which is necessarily zero in the BCS (mean field) limit increases monotonically with the strength of the attractive interaction g. It follows that there is a significant physical distinction between this BCS-BEC crossover approach (in which g is the essential variable which determines ${\ensuremath{\Delta}}_{\mathrm{pg}})$ and the widely discussed phase fluctuation scenario in which the plasma frequency is the tuning parameter. Finally, we emphasize that in the strong coupling limit, there are important differences between the composite bosons that arise in crossover theories and the usual bosons of the (interacting) Bose liquid. Because of constraints imposed on the fermionic excitation gap and chemical potential, in crossover theories, the fermionic degrees of freedom can never be fully removed from consideration.