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 La2−xSrxCuO4 (LSCO) films (Božović (2016) [7]) 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 ξ(0) and the transition temperature Tc should yield a novel scaling ξ(0)∝Tc−σ with a critical exponent σ≈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 σ.