Theoretical Study of Orthorhombic Distortions in High-Temperature Superconductors

Using a Fermi-liquid-based theory we calculate the response function for various spectroscopic probes in hole-doped high-T$_C$ superconductors, and determine the effects of orthorhombic distortions in the crystal lattice and asymmetry in the superconducting gap function. Employing the two-dimensional one-band Hubbard model and a generalized RPA-type theory we consider anisotropic hopping parameters ($t_x \ne t_y$) and a mixing of $d$- and $s$-wave symmetry of the superconducting order parameter. Within this model, both the electronic Raman spectra and the dynamical magnetic susceptibility~[1] are studied in detail. The relevance of these calculations to electronic Raman scattering measurements and inelastic neutron scattering experiments~[2] on untwinned YBa$_2$Cu$_3$O$_{6+x}$ are discussed. [1]~A.~P.~Schnyder, D.~Manske, C.~Mudry, and M. Sigrist, cond-mat/0510790. [2]~V.~Hinkov, S.~Pailhes, P.~Bourges, Y.~Sidis, A.~Ivanov, A.~Kulakov, C.~T.~Lin, D.~P.~Chen, C.~Bernhard, and B.~Keimer, Nature \textbf{430}, 650 (2004).