Doping Dependence of the Redistribution of Optical Spectral Weight in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$

TL;DR

This study investigates how the redistribution of optical spectral weight in Bi2212 superconductors varies with doping levels, revealing a sign change near optimal doping and comparing results with theoretical models.

Contribution

It provides detailed experimental data on spectral weight redistribution across doping levels and compares findings with CDMFT calculations, highlighting discrepancies with BCS predictions.

Findings

Spectral weight increases in underdoped samples and decreases in overdoped ones.

Sign change in spectral weight redistribution occurs near optimal doping.

Experimental results align with CDMFT calculations but not with BCS models.

Abstract

We present the ab-plane optical conductivity of four single crystals of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) with different carrier doping levels from the strongly underdoped to the strongly overdoped range with $T_c$=66, 88, 77, and 67 K respectively. We focus on the redistribution of the low frequency optical spectral weight (SW) in the superconducting and normal states. The temperature dependence of the low-frequency spectral weight in the normal state is significantly stronger in the overdoped regime. In agreement with other studies, the superconducting order is marked by an increase of the low frequency SW for low doping, while the SW decreases for the highly overdoped sample. The effect crosses through zero at a doping concentration $\delta$=0.19 which is slightly to the right of the maximum of the superconducting dome. This sign change is not reproduced by the BCS model calculations, assuming the electron-momentum dispersion known from published ARPES data. Recent Cluster Dynamical Mean Field Theory (CDMFT) calculations based on the Hubbard and t-J models, agree in several relevant respects with the experimental data.