BCS quantum critical phenomena

College of Economics and Management, Southwest University - Chongqing, China

^(a) taoyingyong@yahoo.com (corresponding author)

Received: 12 January 2017
Accepted: 20 July 2017

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: (Tao Y., Sci. Rep., 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, Božović et al. have observed such a parabolic scaling in the overdoped copper oxides with a sufficiently low transition temperature T_c (Božović I. et al., Nature, 536 (2016) 309). 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.