Open AccessSuperconducting Quantum Critical Phenomena
Author(s) -
Yong Tao
Publication year - 2018
Publication title -
reports in advances of physical sciences
Language(s) - English
Resource type - Journals
eISSN - 2424-9424
pISSN - 2529-752X
DOI - 10.1142/s2424942418500093
Subject(s) - superfluidity , condensed matter physics , scaling , physics , superconductivity , quantum , quantum phase transition , critical phenomena , function (biology) , quantum critical point , transition temperature , quantum mechanics , critical exponent , zero (linguistics) , quantum fluctuation , phase transition , linguistics , philosophy , geometry , mathematics , evolutionary biology , biology
When the superconducting transition temperature [Formula: see text] 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 [Formula: see text] 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 [Formula: see text] and the zero-temperature superfluid phase stiffness [Formula: see text] will obey a two-class scaling combined by linear and parabolic parts, which agrees with the existing experimental investigation [I. Božović 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.