Superfluid density in Bi2Sr2CaCu2O8+x from optimal doping to severe underdoping and its implications

TL;DR

This study investigates the superfluid density in underdoped Bi2Sr2CaCu2O8+x, revealing the influence of quantum and thermal fluctuations on superconductivity across a wide doping range, with implications for understanding high-temperature superconductivity.

Contribution

It provides the first detailed measurements of superfluid density at very low doping levels in Bi-2212, highlighting the role of quantum fluctuations and their impact on the superconducting transition.

Findings

Linear Tc vs. ns(0) scaling below 45 K indicates 2D quantum fluctuations.

ns(T) becomes quasi-linear near Tc, suggesting thermal phase fluctuations.

Contrasts with YBCO, showing different fluctuation regimes based on anisotropy.

Abstract

Due to their proximity to an antiferromagnetic phase and to the mysterious pseudogap, underdoped cuprates have attracted great interest in the high Tc community for many years. A central issue concerns the role of quantum and thermal fluctuations of the phase of the superconducting order parameter. The evolution of superfluid density ns with temperature and doping is a powerful probe of this physics. Here, we report superfluid density measurements on underdoped Bi2Sr2CaCu2O8+x (Bi-2212) films at much lower dopings than have been achieved previously, and with excellent control on doping level - Tc ranges from Tc,min ~ 6K to Tc,max ~ 80K in steps of about 5K. Most famous studies on Bi-2212 like angle-resolved photoemission and scanning probe microscopy are surface-sensitive while superfluid density measurements are bulk-sensitive. We find that strong two-dimensional quantum fluctuations are evident in the observed linear scaling of Tc with ns(0) when Tc is below about 45 K, which contrasts with three-dimensional quantum fluctuations evident in the square root scaling, Tc $\propto \sqrt$ns(0), seen in the much less anisotropic cuprate, YBa2Cu3O7 (YBCO). On the other hand, consistent with YBCO, ns(T) in severely underdoped Bi-2212 loses its strong downward curvature near Tc, becoming quasi-linear without any obvious critical behavior near Tc. We argue that the quasi-linear T dependence arises from thermal phase fluctuations, although the current theory needs modification in order to understand some features.