Sum rules and energy scales in BiSrCaCuO

TL;DR

This study investigates the optical spectral weight and energy scales in underdoped Bi-2212, revealing unconventional behavior where the kinetic energy decreases in the superconducting state and the sum rule is violated at 1 eV.

Contribution

It provides high-precision measurements of optical conductivity in Bi-2212, showing the violation of the sum rule and kinetic energy decrease in the superconducting state, which is novel compared to conventional theories.

Findings

Kinetic energy decreases in the superconducting state.

Sum rule is not satisfied up to 1 eV in underdoped Bi-2212.

Contrasts with behavior in overdoped samples.

Abstract

From very high accuracy reflectivity spectra, we have derived the optical conductivity and estimated the spectral weight up to various cut-off frequencies in underdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212). We show that, when evaluating the optical spectral weight over the full conduction band (1 eV), the kinetic energy decreases in the superconducting state, unlike in conventional BCS superconductors. As a consequence, the Ferrell-Glover-Tinkham sum rule is not satisfied up to this energy scale. This stands as a very unconventional behavior, contrasted with the overdoped Bi-2212 sample.