Quantum Fluctuations and the Anomalous Two-Class Scaling in the Overdoped Cuprate Films

By introducing the imaginary time, we show that Gor’kov’s Ginzburg–Landau equation at zero temperature can be extended to an exact relativistic form. Based on this equation, we propose a quantum field theory with the imaginary time, which is intended to describe the quantum critical phenomena in the zero-temperature overdoped cuprate. By using such a quantum field theory, we show that the anomalous two-class scaling between the transition temperature T_c and zero-temperature superfluid phase stiffness \;\rho _s\left( 0 \right) observed in the overdoped side of single-crystal \rmL\rma_2 - x\rmS\rmr_x\rmCu\rmO_4 films can be derived exactly. In this paper, we further theoretically show that, for 2-dimensional overdoped cuprate films, the transition temperature T_c and the zero-temperature coherence length \xi \left( 0 \right) will obey a two-class scaling as well. When the transition temperature T_c is less than a characteristic temperature scale T_Q, the transition temperature T_c and the zero-temperature coherence length \xi(0) obeys the scaling \xi \left( 0 \right) \propto T_c^ - 1.34 , which is a quantum critical behavior. Nevertheless, when the transition temperature is larger than another characteristic temperature scale T_M, the scaling relationship will yield \xi \left( 0 \right) \propto T_c^ - 1 , which is a mean-field behavior.