Correlation between anisotropy in the normal-state mass renormalization and anisotropy in the superconducting energy gap for zinc

Abstract

A nonlocal pseudopotential model for the Fermi surface and band structure of zinc together with the cyclotron resonance data is used to calculate the orbital average of the normal-state mass renormalization λCRi for numerous cyclotron orbits on the Fermi surface of zinc. We find that the mass renormalization λk is constant for each sheet of the Fermi surface but that it varies from sheet to sheet. Using the Eliashberg equation, this anisotropy in λk is correlated to anisotropy in the superconducting energy gap Δk. For zinc we predict three distinct energy gaps, in the ratio of 2.30:1.76:1.00, corresponding respectively to the lens, the monster, and the cap sheets of the Fermi surface. Experimental evidence for this anisotropy in Δk is provided by various measurements of the electronic properties in the superconducting state such as the low-temperature specific heat, microwave absorption, ultrasonic attenuation, effect of alloying on the critical temperature, and the temperature dependence of the critical field. We show that the results of these experiments are consistent with our predictions.