Critical behavior of YBa_{2}Cu_{3}O_{7-\delta} and Bi_{2}Sr_{2}CaCu_{2}O_{8+\delta} from the dual Ginzburg-Landau model

TL;DR

This paper presents a unified theoretical framework using the dual Ginzburg-Landau model to explain the critical behavior and crossover phenomena in high-temperature superconductors YBCO and BSCCO, matching experimental critical exponents.

Contribution

It introduces a dual Ginzburg-Landau model with two scalings to unify the critical behavior of YBCO and BSCCO superconductors, predicting critical exponents consistent with experiments.

Findings

Critical exponents match experimental values for YBCO and BSCCO.

Two different scalings explain observed critical crossovers.

Predicted penetration depth exponent is $ u'=1$.

Abstract

An unifying scenario for the critical behavior of YBa$_{2}$Cu$_{3}$O$_{7-\delta}$ (YBCO) and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (BSCCO) is proposed. It is shown that both critical crossovers observed in these materials follow by considering two different scalings in the dual Ginzburg-Landau model. The first scaling leads to the critical exponents $\nu\approx 2/3$, $\nu'\approx 1/3$ and $\alpha\approx 0$, with $\nu$ and $\alpha$ being respectively the correlation lenght and specific heat exponents while $\nu'$ is the magnetic field penetration depth exponent. These values for the critical exponents agree with the ones obtained experimentally for YBCO single crystals. For the second scaling we obtain $\nu=1$ and $\alpha=-1$ which must be compared with the measured values $\nu\approx 1$ and $\alpha\approx-0.7$ for BSCCO. For the penetration depth exponent it is predicted the value $\nu'=1$.