Optical Sum Rule in Finite Bands

Abstract

In a single finite electronic band the total optical spectral weight or optical sum carries information on the interactions involved between the charge carriers as well as on their band structure. It varies with temperature as well as with impurity scattering. The single band optical sum also bears some relationship to the charge carrier kinetic energy and, thus, can potentially provide useful information, particularly on its change as the charge carriers go from normal to superconducting state. Here we review the considerable advances that have recently been made in the context of high $T_c$ oxides, both theoretical and experimental.

Review article accepted for publication in J. Low Temp. Phys. 29 pages, 33 figures

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• Dipole matrix element approach vs. Peierls approximation for optical conductivity
• Kinetic energy driven superconductivity, the origin of the Meissner effect, and the reductionist frontier
• Characteristics of oxygen isotope substitutions in the quasiparticle spectrum of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$
• Detecting a preformed pair phase: The response to a pairing forcing field
• Optical sum rule anomalies in the cuprates: interplay between strong correlation and electronic bandstructures
• Optical Integral and Sum Rule Violation
• Kinetic energy driven superconductivity and superfluidity
• Robustness of the optical-conductivity sum rule in Bilayer Graphene