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

TL;DR

This paper investigates how the optical spectral weight changes in a superconductor with a van Hove singularity, using a tight-binding model and ARPES data, and finds that simple BCS theory cannot explain recent experimental results.

Contribution

It applies the Kubo sum rule to a detailed tight-binding model of Bi2212 to analyze spectral weight changes and compares theoretical predictions with experimental observations.

Findings

Spectral weight change can be positive or negative depending on parameters.

Kinetic energy change remains negative across conditions.

Simple BCS calculations do not match observed positive spectral weight changes.

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.