Conserving T-matrix theory of superconductivity

Šopík, Břetislav; Lipavský, Pavel; Männel, Michael; Morawetz, Klaus; Matlock, Peter

doi:10.48550/arxiv.0906.3677

Cited by 3 publications

(5 citation statements)

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“…Recently a new variation of a T -matrix type of theory was proposed by Šopík et al [52]. This new formulation is based on a T -matrix approximation in which one removes certain 'dangerous' contributions to the self-energy arising from a resonance of an interacting pair (see their paper for further details).…”

Section: Discussionmentioning

confidence: 99%

Analyzing the success ofT-matrix diagrammatic theories in representing a modified Hubbard model

Pisarski

Gooding

2011

J. Phys.: Condens. Matter

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We present a systematic study of various forms of renormalization that can be applied in the calculation of the self-energy of the Hubbard model within the T-matrix approximation. We compare the exact solutions of the attractive and repulsive Hubbard models, for linear chains of lengths up to eight sites, with all possible taxonomies of the T-matrix approximation. For the attractive Hubbard model, the success of a minimally self-consistent theory found earlier in the atomic limit (Verga et al 2005 Phys. Rev. B 71 155111) is not maintained for finite clusters unless one is in the very strong correlation limit. For the repulsive model, in the weak correlation limit at low electronic densities-that is, where one would expect a self-consistent T-matrix theory to be adequate-we find the fully renormalized theory to be most successful. In our studies we employ a modified Hubbard interaction that eliminates all Hartree diagrams, an idea which was proposed earlier (Zlatić et al 2000 Phys. Rev. B 63 035104).

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Section: Discussionmentioning

confidence: 99%

Analyzing the success ofT-matrix diagrammatic theories in representing a modified Hubbard model

Pisarski

Gooding

2011

J. Phys.: Condens. Matter

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“…9,10 With the multiple scattering corrections the gap develops. 7,8 The half-selfconsistent theory 10 of Kadanoff and Martin (KM) is recovered if we approximate the Q-reduced propagator by the bare one, G Q↓ ≈ G 0 . The KM theory yields the correct BCS gap but as noticed by Chen et al 11 confirmed below, the KM approximation results in the ideal Bose gas of Cooper pairs.…”

Section: A General Equationsmentioning

confidence: 99%

Stability of condensate in superconductors

Lipavský,

Šopík,

Männel

et al. 2010

Preprint

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According to the BCS theory the superconducting condensate develops in a single quantum mode and no Cooper pairs out of the condensate are assumed. Here we discuss a mechanism by which the successful mode inhibits condensation in neighboring modes and suppresses a creation of noncondensed Cooper pairs. It is shown that condensed and noncondensed Cooper pairs are separated by an energy gap which is smaller than the superconducting gap but large enough to prevent nucleation in all other modes and to eliminate effects of noncondensed Cooper pairs on properties of superconductors. Our result thus justifies basic assumptions of the BCS theory and confirms that the BCS condensate is stable with respect to two-particle excitations.

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“…It was observed by Kadanoff and Martin [2] and used later on [1,3,4,5] that an asymmetric breaking of the selfconsistency in the T-matrix, such that one propagator is used selfconsistently and the other non-selfconsistently, leads immediately to the correct gap dispersion while the symmetric selfconsistent one does not. This so called Prange paradox [6] remains puzzling since a seemingly worse approximation leads to better results.…”

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confidence: 99%

“…The advantage of eliminating only the contributions of single channels as proposed in Refs. [1] and [5] is that the formation of pairs and their condensation can be described within the same approximation. We note that the proposed elimination shemes yield similar results as the often used mean field approximations with anomalous functions [7].…”

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confidence: 99%

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Multiple condensed phases in attractively interacting Bose systems

Männel¹,

Morawetz²,

Lipavský³

2010

New J. Phys.

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We investigate a Bose gas with finite-range interaction using a scheme to eliminate unphysical processes in the T-matrix approximation. In this way the corrected T-matrix becomes suitable to calculate properties below the critical temperature. For attractive interaction, an Evans-Rashid transition occurs between a quasi-ideal Bose gas and a BCS-like phase with a gaped dispersion. The gap decreases with increasing density and vanishes at a critical density where the single-particle dispersion becomes linear for small momenta indicating Bose-Einstein condensation. The investigation of the pressure shows however, that the mentioned quantum phase transitions might be inaccessible due to a preceding first order transition.

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Conserving T-matrix theory of superconductivity

Cited by 3 publications

References 61 publications

Analyzing the success ofT-matrix diagrammatic theories in representing a modified Hubbard model

Analyzing the success ofT-matrix diagrammatic theories in representing a modified Hubbard model

Stability of condensate in superconductors

Multiple condensed phases in attractively interacting Bose systems

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