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 -