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

Abstract

An unifying scenario for the critical behavior of YBa$_{2}$Cu$_{3}$O$_{7-δ}$ (YBCO) and Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+δ}$ (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 $ν\approx 2/3$, $ν'\approx 1/3$ and $α\approx 0$, with $ν$ and $α$ being respectively the correlation lenght and specific heat exponents while $ν'$ 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 $ν=1$ and $α=-1$ which must be compared with the measured values $ν\approx 1$ and $α\approx-0.7$ for BSCCO. For the penetration depth exponent it is predicted the value $ν'=1$.