Electronic thermal conductivity and the Wiedemann-Franz law for unconventional superconductors

Journal Article · Sat Jun 01 04:00:00 EDT 1996 · Physical Review, B: Condensed Matter

DOI:https://doi.org/10.1103/PhysRevB.53.15147· OSTI ID:284703

Graf, M J; Yip, S; Sauls, J A ^[1]; Rainer, D ^[2]

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1. Department of Physics and Astronomy, Northwestern University, Evanston, Illinois 60208 (United States)
2. Physikalisches Institut, Universitaet Bayreuth, D-95440 Bayreuth (Germany)

We use the quasiclassical theory of superconductivity to calculate the electronic contribution to the thermal conductivity. The theory is formulated for low temperatures when heat transport is limited by electron scattering from random defects and for superconductors with nodes in the order parameter. We show that certain eigenvalues of the thermal conductivity tensor are universal at low temperature, {ital k}{sub {ital BT}}{lt}{gamma}, where {gamma} is the bandwidth of impurity bound states in the superconducting phase. The components of the electrical and thermal conductivity also obey a Wiedemann-Franz law with the Lorenz ratio {ital L}({ital T})={kappa}/{sigma}{ital T} given by the Sommerfeld value of {ital L}{sub {ital S}}=({pi}{sup 2}/3)({ital k}{sub {ital B}}/{ital e}){sup 2} for {ital k}{sub {ital BT}}{lt}{gamma}. For intermediate temperatures the Lorenz ratio deviates significantly from {ital L}{sub {ital S}}, and is strongly dependent on the scattering cross section, and qualitatively different for resonant vs nonresonant scattering. We include comparisons with other theoretical calculations and the thermal conductivity data for the high-{ital T}{sub {ital c}} cuprate and heavy fermion superconductors. {copyright} {ital 1996 The American Physical Society.}

• OSTI ID: 284703
• Journal Information: Physical Review, B: Condensed Matter, Journal Name: Physical Review, B: Condensed Matter Journal Issue: 22 Vol. 53; ISSN 0163-1829; ISSN PRBMDO
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
BOUND STATES
CRYSTAL DEFECTS
ELECTRON COLLISIONS
ORDER PARAMETERS
SUPERCONDUCTORS
TEMPERATURE DEPENDENCE
THERMAL CONDUCTIVITY
WIEDEMANN-FRANZ LAW