Lattice distortion and elasticity change caused by the d-wave superconductivity

The lattice distortion and the elasticity change caused by the d-wave superconductivity are studied on the basis of the BCS Hamiltonian, which is constructed for a 2D electron system so as to satisfy its assumed crystal symmetry D-4h. The superconducting order parameters (SOP) considered are those with the symmetries of (k(x)(2) - k(y)(2))/root 2, root 2k(x)k(y) and also (k(x)(2) + k(y)(2))/root 2, k being a 2D wave vector. The obtained free energy as a function of the SOPs and appropriate distortions is used to connect the lattice anomaly and the microscopic parameters in the Hamiltonian. The softening and even the stiffening of the lattice are derived within the present theory to identify their origins. (c) 2006 Elsevier B. V. All rights reserved.