Superfluid density in overdoped cuprates: Thin films versus bulk samples

Recent study of overdoped La$_{2−x}$Sr$_x$CuO$_4$ cuprate superconductor thin films has revealed

several unexpected findings, most notably the violation of the BCS description which was believed to adequately

describe overdoped cuprates. In particular, it was found that the superfluid density in La$_{2−x}$Sr$_x$CuO$_4$

films decreases on the overdoped side as a linear function of critical temperature T$_c$, which was taken as evidence

for the violation of Homes’ law. We show explicitly that the law is indeed violated, and as the main reason

for violation we find that the superfluid density in La$_{2−x}$Sr$_x$CuO$_4$ films is suppressed more strongly than in bulk

samples. Based on the existing literature data, we show that the superfluid density in bulk cuprate samples does

not decrease with doping, but instead tends to saturate on the overdoped side. The result is also supported by our

recent measurement of a heavily overdoped bulk La$_{2−x}$Sr$_x$CuO$_4$ sample. Moreover, this saturation of superfluid

density might not be limited to cuprates, as we find evidence for similar behavior in two pnictide superconductor

families. We argue that quantum phase fluctuations play an important role in suppressing the superfluid density

in thin films.