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${}_{7-\delta }$ (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 $\nu \approx 2/3$, ${\nu }^{\prime }\approx 1/3$ and $\alpha \approx 0$, with $\nu$ and $\alpha$ being respectively the correlation lenght and specific heat exponents while ${\nu }^{\prime }$ 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 ${\nu }^{\prime }=1$.

RevTex, 3 pages, 1 figure; misprints corrected and numerical errors removed