TY - JOUR

T1 - Differential sum rule for the relaxation rate in dirty superconductors

AU - Chubukov, Andrey V.

AU - Abanov, Ar

AU - Basov, N.

PY - 2003

Y1 - 2003

N2 - We consider the differential sum rule for the effective scattering rate 1/τ(ω) and optical conductivity σ1(ω) in a dirty BCS superconductor, for arbitrary ratio of the superconducting gap Δ and the normal state constant damping rate 1/τ. We show that if τ is independent of T, the area under 1/τ(ω) does not change between the normal and the superconducting states, i.e., there exists an exact differential sum rule for the scattering rate. For any value of the dimensionless parameter Δτ, the sum rule is exhausted at frequencies controlled by Δ. We show that in the dirty limit the convergence of the differential sum rule for the scattering rate is much faster then the convergence of the f-sum rule, but slower then the convergence of the differential sum rule for conductivity.

AB - We consider the differential sum rule for the effective scattering rate 1/τ(ω) and optical conductivity σ1(ω) in a dirty BCS superconductor, for arbitrary ratio of the superconducting gap Δ and the normal state constant damping rate 1/τ. We show that if τ is independent of T, the area under 1/τ(ω) does not change between the normal and the superconducting states, i.e., there exists an exact differential sum rule for the scattering rate. For any value of the dimensionless parameter Δτ, the sum rule is exhausted at frequencies controlled by Δ. We show that in the dirty limit the convergence of the differential sum rule for the scattering rate is much faster then the convergence of the f-sum rule, but slower then the convergence of the differential sum rule for conductivity.

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U2 - 10.1103/PhysRevB.68.024504

DO - 10.1103/PhysRevB.68.024504

M3 - Article

AN - SCOPUS:0141482107

SN - 1098-0121

VL - 68

JO - Physical Review B - Condensed Matter and Materials Physics

JF - Physical Review B - Condensed Matter and Materials Physics

IS - 2

ER -