Competing orders and inter-layer tunnelling in cuprate superconductors: A finite temperature Landau theory

We propose a finite temperature Landau theory that describes competing orders and interlayer tunneling in cuprate superconductors as an important extension to a corresponding theory at zero temperature [Nature {\bf 428}, 53 (2004)], where the superconducting transition temperature $T_c$ is defined in three possible ways as a function of the zero temperature order parameter. For given parameters, our theory determines $T_c$ without any ambiguity. In mono- and double-layer systems we discuss the relation between zero temperature order parameter and the associated transition temperature in the presence of competing orders, and draw a connection to the puzzling experimental fact that the pseudo-gap temperature is much higher than the corresponding energy scale near optimum doping. Applying the theory to multi-layer systems, we calculate the layer-number dependence of $T_c$. In a reasonable parameter space the result turns out to be in agreement with experiments.Comment: 5 pages, 3 figure

3-Isopropyl-2-(4-methoxy­phen­oxy)-1-benzo­furo[3,2-d]pyrimidin-4(3H)-one

In the title compound, C20H18N2O4, all non-H atoms of the three fused rings of the benzofuro[3,2-d]pyrimidine system are almost coplanar (r.m.s. deviation 0.021 Å). The dihedral angle between the fused ring system and the benzene ring is 1.47 (12)°. Intra­molecular and inter­molecular C—H⋯O hydrogen bonds together with weak C—H⋯π inter­actions stabilize the structure

1-{1-[(2-Chloro­thia­zol-5-yl)meth­yl]-5-methyl-1H-1,2,3-triazol-4-yl}ethanone

In the title compound, C9H9ClN4OS, the two rings enclose a dihedral angle of 84.67 (11)°. Inter­molecular C—H⋯O and C—H⋯N hydrogen bonds stabilize the crystal packing