Marginal Fermi liquid analysis of 300 K reflectance of Bi2Sr2CaCu2O8+x

TL;DR

This study uses 300 K reflectance data to analyze the normal-state electrodynamics of Bi2Sr2CaCu2O8+x, revealing doping-dependent coupling consistent with Marginal Fermi Liquid theory and providing a new method for doping level estimation.

Contribution

It demonstrates that the Marginal Fermi Liquid model effectively describes the reflectance spectra across doping levels and introduces a doping estimation method based on spectral slope.

Findings

Coupling constant decreases with doping from 0.93 to 0.53.

Deviations from MFL spectrum are symmetric around optimal doping.

MFL spectrum is essential for fitting reflectance data up to 2000 cm$^{-1}$.

Abstract

We use 300 K reflectance data to investigate the normal-state electrodynamics of the high temperature superconductor Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ over a wide range of doping levels. The data show that at this temperature the free carriers are coupled to a continuous spectrum of fluctuations. Assuming the Marginal Fermi Liquid (MFL) form as a first approximation for the fluctuation spectrum, the doping-dependent coupling constant $\lambda (p)$ can be estimated directly from the slope of the reflectance spectrum. We find that $\lambda (p)$ decreases smoothly with the hole doping level, from underdoped samples with $ p=0.103$ ($T_c = 67$ K) where $\lambda (p)= 0.93$ to overdoped samples with $p=0.226$, ($T_c= 60$ K) where $\lambda(p)= 0.53$. An analysis of the intercept and curvature of the reflectance spectrum shows deviations from the MFL spectrum symmetrically placed at the optimal doping point $p=0.16$. The Kubo formula for the conductivity gives a better fit to the experiments with the MFL spectrum up to 2000 cm$^{-1}$ and with an additional Drude component or an additional Lorentz component up to 7000 cm$^{-1}$. By comparing three different model fits we conclude that the MFL channel is necessary for a good fit to the reflectance data. Finally, we note that the monotonic variation of the reflectance slope with doping provides us with an independent measure of the doping level for the Bi-2212 system.