Finite-temperature Fermi-liquid theory of electrical conductivity

Toyoda, Tadashi

doi:10.1103/physreva.39.2659

Cited by 22 publications

(18 citation statements)

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“…On the other hand, the proof of the translational invariance along the x 1 direction and the x 3 direction is trivial. 5,7 Therefore, in the following consideration we concentrate on the x 2 direction and shall prove that the temperature Green's function is indeed translationally in-variant along the x 2 direction. Our proof is based on the nonperturbative canonical method proposed in Ref.…”

Section: ͑210͒mentioning

confidence: 97%

“…The use of the FTGWTR in the perturbative calculation of transport coefficients leads to a natural generalization of Baym Kadanoff's conserving approximation, 6 as the conservation laws are nothing else but the consequence of these properties of the Hamiltonian of the system. 7 It has been also shown that the FTGWTR can be applied to spontaneously broken symmetries and lead to a finite-temperature generalization of the Goldstone's theorem. 5,8 Among various transformational properties of the temperature Green's functions, the translational invariance is particularly valuable for theoretical analyses.…”

Section: Introductionmentioning

confidence: 99%

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Translational invariance of the density and current temperature Green’s functions for an electron gas in a uniform magnetic field

1997

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Section: ͑210͒mentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Translational invariance of the density and current temperature Green’s functions for an electron gas in a uniform magnetic field

1997

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“…͑20͒ we have used the previous result on the imaginary part of the proper self-energy at zero frequency obtained in Ref. 7. That is, the contribution from ͕const͖ term to the imaginary part of the self-energy simply vanishes.…”

Section: ͑19͒mentioning

confidence: 99%

“…Hence the same approximation scheme used in the Guiliani-Quinn theory can be safely extended to the calculation of transport coefficients such as electrical conductivity. 7,8 We start with the Hamiltonian of an interacting d-dimensional electron gas (dϭ2 or 3͒,…”

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Nonperturbative approach to the self-energy of interacting electrons

Toyoda

Ito

2001

Phys. Rev. B

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A nonperturbative formula for the imaginary part of the proper self-energy of an interacting electron gas at finite temperatures is derived on the basis of the finite temperature generalized Ward-Takahashi relations ͓Ann. Phys. ͑N.Y.͒ 173, 226 ͑1987͔͒. It is shown that the obtained formula gives a nonperturbative basis for the Guiliani-Quinn's theory on the Coulomb lifetime of the two-dimensional electrons.

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“…("")=IT L: A P P g P A P P g P A P P g P ( + -) (-) (-+) (+) (+ +) ( +) 11 e p,en p En + En En a En En En 11 En En + En + '…”

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A General Expression for Hall Coefficient Based on Fermi Liquid Theory

Kohno

Yamada

1988

Progress of Theoretical Physics

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623A general expression for Hall conductivity including the effects of many-body interaction is derived on the basis of the Fermi liquid theory. It is exact as far as the most singular terms with respect to the quasiparticle damping are concerned. It is applicable for any types of interaction as far as the picture of Fermi liquid holds well. § 1. IntroductionThe systems in which electron-electron interactions cannot be neglected, such as heavy fermion systems!) and high-Tc oxide superconductors, are of current interest_ The former system exhibits the large T2-component of resistivity in its low temperature coherent regime. This behaviour is ascribed to electron-electron scattering with the Umklapp process_ Therefore, Hall coefficient should also be affected by manybody effects. Until now, many-body effects have been treated only within crude approximations. In metals, it seems dangerous to treat them on the basis of such approximate calculations as alloy analogy and Hubbard decoupling which neglect the momentum dependence of the self-energy. Moreover, we should include the vertex corrections originating from electron-electron interactions in order not to violate the Ward identity. These motivated us to seek an exact formula for Hall coefficient including the many-body effects on the basis of the Fermi liquid theory.Such a formula for conductivity was given by Eliashberg 2 ) in 1961. He collected all the terms which are, in the static limit, singular with respect to quasiparticle. damping, namely, divergent terms as the quasiparticle damping goes to zero. The result is given by (for simplicity, we give a static conductivity per spin) (J -e 2 f dp {_I (_ df) }v *v * , ,,11-(2n-)3 2yp de e=E(p) " 11 +f dp f dp' { 1·( df) .} *a 2

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Finite-temperature Fermi-liquid theory of electrical conductivity

Cited by 22 publications

References 20 publications

Translational invariance of the density and current temperature Green’s functions for an electron gas in a uniform magnetic field

Translational invariance of the density and current temperature Green’s functions for an electron gas in a uniform magnetic field

Nonperturbative approach to the self-energy of interacting electrons

A General Expression for Hall Coefficient Based on Fermi Liquid Theory

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