Differential sum rule for the relaxation rate in the cuprates.
Motivated by recent experiments by Basov et al., we study the differential sum rule for the effective scattering rate 1/tau(omega). We show that, in a dirty BCS superconductor, the area under 1/tau(omega) does not change between the normal and the superconducting states. For magnetically mediated pairing, a similar result holds between T<T(c) and T>or=T(c), while, in the pseudogap phase, 1/tau(omega) is just suppressed compared to 1/tau(omega) in the normal state. We argue that this violation of the differential sum rule in the pseudogap phase is due to the absence of the feedback effects from the pairing.
Abanov
Ar
A
Los Alamos National Laboratory, MS262, Los Alamos, New Mexico 87545, USA.
Chubukov
Andrey V
AV