Various effects of anisotropy of the superconducting energy gap are theoretically considered. In order to estimate the effects of anisotropy upon the thermodynamic properties of pure, single-crystal superconductors, a factorable BCS-like model for the effective electron-electron matrix element V pp′ = (1 + a p ) V(1 + a p′ ) is used. The effects of anisotropy upon the temperature dependence of the gap parameter, the critical field, and the specific heat near the critical temperature are then shown to be small and proportional to the mean-squared anisotropy 〈 a 2〉, which is of the order of 0.02 for typical superconductors. Theoretical expressions which explicitly include the anisotropy of a general gap parameter are given for low-temperature specific heat, nuclear spin-lattice relaxation time, tunneling, surface resistance, and longitudinal ultrasonic attenuation. These processes are seen to be more sensitive to the details of the anisotropy than are the above thermodynamic properties.
Read full abstract