Title: 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.