BCS quantum critical phenomena

Abstract

Theoretically, we recently showed that the scaling relation between the transition temperature T_c and the superfluid density at zero temperature n_s (0) might exhibit a parabolic pattern [Scientific Reports 6 (2016) 23863]. It is significantly different from the linear scaling described by Homes' law, which is well known as a mean-field result. More recently, Bozovic et al. have observed such a parabolic scaling in the overdoped copper oxides with a sufficiently low transition temperature T_c [Nature 536 (2016) 309-311]. They further point out that this experimental finding is incompatible with the standard Bardeen-Cooper-Schrieffer (BCS) description. Here we report that if T_c is sufficiently low, applying the renormalization group approach into the BCS action at zero temperature will naturally lead to the parabolic scaling. Our result indicates that when T_c sufficiently approaches zero, quantum fluctuations will be overwhelmingly amplified so that the mean-field approximation may break down at zero temperature.

A potential technique capturing quantum fluctuations

References in corpus (12)

• Universal scaling relation in high-temperature superconductors
• Generalized Ginzburg-Landau theory for non-uniform FFLO superconductors
• Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films
• Superfluid Density in a Highly Underdoped YBCO Superconductor
• Correlation between superfluid density and Tc of underdoped YBa2Cu3O6+x near the superconductor-insulator transition
• Scaling of the superfluid density in high-temperature superconductors
• Phenomenological description of the two energy scales in underdoped superconducting cuprates
• Homes scaling and BCS
• Universal scaling relations in molecular superconductors
• Electron-fluctuation interaction in a non-Fermi superconductor
• Scaling Laws for Thin Films near the Superconducting-to-Insulating Transition
• Ginsburg-Landau Expansion in a non-Fermi Superconductor

Cited by in corpus (7)

• Scanning SQUID characterization of extremely overdoped $L{a}_{2-x}S{r}_{x}Cu{O}_4$
• Relativistic Ginzburg-Landau equation: An investigation for overdoped cuprate films
• Parabolic Scaling in Overdoped Cuprate Films
• Universal scaling relations in electron-phonon superconductors
• Parabolic Scaling in Overdoped Cuprate: a Statistical Field Theory Approach
• Superconducting quantum criticality and the anomalous scaling: A nonlinear relativistic equation
• Spatial Chern-Simons Interactions and Complex Magnetic Penetration Depth