Superconducting Quantum Critical Phenomena

摘要

When the superconducting transition temperature T c sufficiently approaches zero, quantum fluctuations are expected to be overwhelmingly amplified around zero temperature so that the mean-field approximation may break down. This implies that quantum critical phenomena may emerge in highly underdoped and overdoped regions, where the transition temperature T c is sufficiently low. By using Gor’kov’s Green function method, we propose a superconducting quantum critical equation (SQCE) for describing such critical phenomena. For two-dimensional (2D) overdoped materials, SQCE shows that the transition temperature T c and the zero-temperature superfluid phase stiffness ρ s ( 0 ) will obey a two-class scaling combined by linear and parabolic parts, which agrees with the existing experimental investigation [I. Bo?ovi? et?al. , Dependence of the critical temperature in overdoped copper oxides on superfluid density, Nature 536 (2016) 309–311]. For three-dimensional (3D) overdoped materials, SQCE predicts that the two-class scaling will be replaced by the linear scaling. Furthermore, we show that SQCE can be applied into highly underdoped region by using Anderson’s non-Fermi liquid model.