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optical sum rule

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10 - Optical and Thermal Conductivities
Tao Xiang, Chinese Academy of Sciences, Beijing, Congjun Wu, Westlake University, Hangzhou
Book:

D-wave Superconductivity

Published online:

17 June 2022

Print publication:

09 June 2022, pp 240-267
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Summary

Chapter 10 studies the properties of optical conductivity in d-wave superconductors. The optical sum rule is first derived and discussed in connection with the missing low frequency spectral weight in underdoped cuprate superconductors. In the dirty limit, as the coherence length is significantly larger than the mean free path, the light absorption is determined by the optical conductivity in the local limit. Unlike in an s-wave superconductor, there is no absorption edge in a d-wave superconductor. In the limit the elastic scattering rate is significantly lower than the gap amplitude, the conductance is universal, independent on the strength of impurity scattering potential. The microwave conductivity is shown to vary cubically with temperature in cuprate superconductors, resulting from the hot spot nature of the scattering rate. The thermal conductivity of d-wave superconductors with its universal behavior in the zero temperature limit is also discussed and compared with the measurement data.