Superconductivity and lattice distortions in high-Tcsuperconductors

A thermodynamic analysis of the behavior of the lattice parameters and elastic properties at $T_c$ in the orthorhombic high-$T_c$ superconductors ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x\mathrm{Cu}{\mathrm{O}}_4$ and Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ is presented. Expressions for the singularities in the specific heat, lattice parameters, and sound velocities are derived using a mean-field expression for the superconducting free energy, and Gaussian fluctuation corrections and critical behavior are discussed. The mean-field expressions are used to interpret presently available data on the thermal, structural, and elastic properties of polycrystalline samples, and additional measurements necessary to complete the determination of the theoretical parameters are suggested. The usefulness of the theory in providing quantitative consistency checks among different types of experimental measurements and in understanding the coupling between crystal structure and superconductivity is emphasized. It is found that although the first strain derivatives of $T_c$ are comparable in magnitude to those in conventional superconductors, some second strain derivatives of $T_c$ are anomalously large.