Parabolic Scaling in Overdoped Cuprate: a Statistical Field Theory Approach

Abstract

Recently, Bozovic et al. reported that [Nature 536, 309-311 (2016)], in the overdoped side of the single-crystal $L{a}_{2-x}S{r}_{x}Cu{O}_4$ (LSCO) films, the transition temperature $T_c$ and zero-temperature superfluid phase stiffness ${\rho }_s(0)$ will obey a two-class scaling law: $T_c=\gamma \cdot \sqrt{{\rho }_s(0)}$ for $T_c\le T_Q$ and $T_c\propto {\rho }_s(0)$ for $T_c\ge T_M$, where $\gamma =(4.2\pm 0.5)K^{1/2}$, $T_Q\approx 15K$, and $T_M\approx 12K$. They further pointed out that the parabolic scaling observed in the highly overdoped side indicates a quantum phase transition from a superconductor to a normal metal. In this paper, we propose a quantum partition function (QPF) for zero-temperature Cooper pairs, by which one can effectively distinguish between mean-field and quantum critical behaviors. We theoretically show that the two-class scaling law can be exactly derived by using the QPF, and the theoretical values of $\gamma$, $T_Q$, and $T_M$ are well in accordance with experimental measure values. Our analyses indicate that the linear scaling $T_c\propto {\rho }_s(0)$ is a mean-field behavior, while the parabolic scaling $T_c=\gamma \cdot \sqrt{{\rho }_s(0)}$ is a quantum critical behavior.

24 pages, 1 figure, 1 table

References in corpus (5)

• Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films
• Scaling of the superfluid density in high-temperature superconductors
• Universal scaling relations in molecular superconductors
• BCS quantum critical phenomena
• Parabolic Scaling in Overdoped Cuprate Films

Cited by in corpus (2)

• Relativistic Ginzburg-Landau equation: An investigation for overdoped cuprate films
• Superconducting quantum criticality and the anomalous scaling: A nonlinear relativistic equation