Lattice distortion and elasticity change in s-wave and d-wave superconductors

Abstract

The lattice anomaly, i.e., the lattice distortion and the elasticity change, caused by the appearance of superconductivity (SC) is studied by use of the BCS theory. The BCS Hamiltonian with any attractive interaction between electrons is introduced for crystals with the symmetry D4h, so that the s-wave, dx2−y2-wave, and dxy-wave SC’s may appear. The microscopic parameters in the Hamiltonian are expanded in powers of distortions u up to their first order, so as to make the Hamiltonian satisfy the crystal symmetry. The free energy of the system as a function of SC order parameters (SOP) and u’s is obtained to reveal the properties of the lattice anomaly. The temperature dependence of the equilibrium distortion and the elastic constants in the SC phases with the different SOP’s is calculated. The calculated distortion is shown to give its temperature dependence consistent with the observation. The elastic constants obtained can exhibit not only softenings but also hardenings below the transition temperature Tc, depending on the microscopic parameters. This behavior of elastic constant is just that observed in some high-Tc cuprates.

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