Effects of Planar Anisotropy on Eliashberg Superconductors

Abstract

<p>Within the context of Eliashberg theory, we have studied the effects<br />of planar anisotropy on many superconducting properties. Planar anisotropy<br />is of interest for superconductors with layered crystal structure, such as the<br />metallic transition metal dichalcogenide and high-Tc oxide superconductors.</p> <p>To describe planar anisotropy we use a model dispersion relation<br />which gives free-particle-like electronic states in the direction parallel to the<br />layers and the tight-binding form in the direction perpendicular to the layers.<br />Using this dispersion relation and the Fermi-Surface-Harmonic (FSH)<br />expansion technique, we specify the general anisotropic Eliashberg equations<br />for the problem of planar anisotropy.</p> <p>We begin with the study of the effects of planar anisotropy on the superconducting<br />transition temperature, the thermodynamic critical magnetic field, and the quasiparticle density of states in the superconducting state. For all these properties, especially the quasiparticle density of states, the effects<br />of planar anisotropy are usually qnite significant.</p> <p>Next, we study some thermodynamic and transport properties, namely,<br />the specific heat, the thermal conductivity, and the ultrasound attenuation.<br />The effects of planar anisotropy on these properties are closely related to the<br />changes in the quasiparticle density of states due to anisotropy. The changes<br />in the quasiparticle lifetime due to the superconducting phase transition and<br />anisotropy are also important for the unusual behaviors of thermal conductivity<br />at low temperature.</p> <p>Several electromagnetic properties are also studied. The introduction of anisotropy usually reduces the value of the London penetration depth below its isotropic value, and strongly depresses the Hebel-Slichter peak in the nuclear spin relaxation rate. The theorerical results for the nuclear spin relaxation rate with strong coupling, anisotropy and Fermi liquid corrections have been compared with the experimental data for the high-Tc oxides. The<br />major effect of planar anisotropy on the infrared conductivity is to reduce<br />the frequency at which the absorption starts.</p> <p>Finally, we have examined the changes of the phonon self-energy when the superconducting phase transition occurs. It is found that there<br />is a qualitative difference between the results for isotropic superconductors<br />and for anisotropic ones. This may be displayed in experiment under certain<br />conditions. Anisotropy also complicates the analysis of the structures in the<br />phonon self-energy.</p> <p>It is generally true, for all the properties which we have studied,<br />that the effects of anisotropy will be diminished if we increase the coupling<br />strengths, and/or introduce impurity scatterings.</p> <p>Besides the problem of planar anisotropy, we briefly discuss the problem<br />of an energy dependent electronic density of states (EDOS) for Eliashberg<br />superconductors. This is of interest for a model of two-dimensional<br />tight-binding dispersion relation. For a Lorentzian form for EDOS around the<br />Fermi level, we have discussed the modifications of the Eliashberg equations<br />and, then, calculated the quasiparticle density of states in the superconducting<br />state. The effects of an energy dependent electronic density of states on<br />the temperature evolution of the quasiparticle density of states below Tc is<br />particularly interesting.</p>