Anomalous Nernst Effect in High-$T_c$ Superconductors by Layer Decoupling

The extended vortex-liquid phase found in high-$T_c$ superconductors at temperatures and magnetic fields that lie above the vortex-lattice melting line can be attributed to weak inter-layer coupling. We compute the diamagnetic contribution to the equilibrium magnetization there, $M$, using the corresponding uniformly frustrated $XY$ model, given in terms of the phase of the superconducting order parameter[1]. A high-temperature expansion that is valid in the vicinity of the mean-field phase transition yields (i) that $-M$ increases monotonically with the external magnetic field, and (ii) that it vanishes as the mean-field phase transition is approached from below. Further, we show (iii) that the assumption of a direct dependence between $M$ and the Peltier transport coefficient results in an anomalous Nernst signal inside of the vortex-liquid phase. These results are compared to recent experimental determinations of the equilibrium magnetization and of the Nernst effect in the vortex-liquid phase of high-$T_c$ superconductors[2]. \newline \newline [1] J.P. Rodriguez, PRB {\bf 66}, 214506 (2002); {\bf 69}, 069901(E) (2004). \newline [2] Y. Wang, et al., PRL, in press (arXiv: cond-mat/0503190).