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

TL;DR

This paper extends Gor'kov's Ginzburg-Landau equation to a relativistic form at zero temperature to describe overdoped cuprate films, deriving a new scaling law and proposing an experiment to measure a critical exponent.

Contribution

It introduces a relativistic Ginzburg-Landau equation at zero temperature for overdoped cuprates, deriving a novel scaling law and suggesting an experimental method to test it.

Findings

Exact derivation of two-class scaling in overdoped LSCO films.

Prediction of a new scaling law: $\xi(0) \\propto T_c^{-\sigma}$ with \sigma \approx 1.31.

Proposal of a diffraction experiment to measure the critical exponent.

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 $La_{2-x}Sr_xCuO_4$ (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 $\sigma$.