Intraband Optical Spectral Weight in the presence of a van Hove singularity: application to Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

Abstract

The Kubo single band sum rule is used to determine the optical spectral weight of a tight binding band with further than nearest neighbour hopping. We find for a wide range of parameters and doping concentrations that the change due to superconductivity at low temperature can be either negative or positive. In contrast, the kinetic energy change is always negative. We use an ARPES determined tight binding parametrization of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ to investigate whether this can account for recent observations of a positive change in the spectral weight due to the onset of superconductivity. With this band structure we find that in the relevant doping regime a straightforward BCS calculation of the optical spectral weight cannot account for the experimental observations.

arXiv comment10 page 9 figures

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• Photo-enhanced antinodal conductivity in the pseudogap state of high Tc cuprates
• Optical Integral in the Cuprates and the Question of Sum Rule Violation
• Dipole matrix element approach vs. Peierls approximation for optical conductivity
• Superconductivity-induced spectral weight transfer due to quantum geometry
• Optical sum rule anomalies in the cuprates: interplay between strong correlation and electronic bandstructures
• Optical Integral and Sum Rule Violation
• Impact of a finite cut-off for the optical sum rule in the superconducting state
• Optical conductivity for a dimer in the Dynamic Hubbard model
• Optical Sum Rule anomalies in the High-Tc Cuprates