Relativistic Ginzburg-Landau equation: An investigation for overdoped cuprate films

Abstract

By introducing the imaginary time, Gor'kov's Ginzburg-Landau equation at zero temperature can be extended to an exact relativistic form without any phenomenological parameter, which is intended to describe the zero-temperature overdoped cuprate. By using such a relativistic equation, we have shown that the two-class scaling observed in the overdoped side of single-crystal $L{a}_{2-x}S{r}_{x}Cu{O}_4$ (LSCO) films [Nature 536, 309-311 (2016)] can be derived exactly. In this paper, we further test the validity of the relativistic Ginzburg-Landau equation. By applying the perturbation method into this equation, we theoretically predict that near the superconductor-metal transition point in the overdoped side of LSCO films, the zero-temperature correlation length $\xi (0)$ and the transition temperature $T_c$ should yield a novel scaling $\xi (0)\propto T_c^{-\sigma }$ with a critical exponent $\sigma \approx 1.31$ (up to the two-loop approximation). Here, we propose a diffraction experiment between $X$-rays and zero-temperature LSCO films to measure the critical exponent $\sigma$.

References in corpus (5)

• Quantum critical behaviour in the superfluid density of strongly underdoped ultrathin cuprate films
• Scaling of the superfluid density in high-temperature superconductors
• BCS quantum critical phenomena
• Parabolic Scaling in Overdoped Cuprate Films
• Parabolic Scaling in Overdoped Cuprate: a Statistical Field Theory Approach

Cited by in corpus (2)

• Scanning SQUID characterization of extremely overdoped $L{a}_{2-x}S{r}_{x}Cu{O}_4$
• Superconducting quantum criticality and the anomalous scaling: A nonlinear relativistic equation