Phenomenology of the superconducting transition temperatures of pure metals, and specially those not showing isotope effects

摘要

We consider a group of five transition metals all having a bcc structure. Their superconductivity transition temperatures, as pointed out a long time ago by Ledbetter, correlate well with the Cauchy discrepancy in their elastic constants. The absence of any measurable isotope effect distinguishes them from conventional Bardeen-Cooper-Schriefer (BCS) superconductors, which seems the major difficulty in front of a first principle theory of the Tc in those materials. Nevertheless, it remains to be studied a phenomenological connection of Tc with the Debye temperature. The BCS theory precisely describes for these materials the properties determined by broken symmetry requirements, but not Tc. Here we show that Tc is much less sensitive to TD than in BCS conductors. This conclusion seems coherent with the lack of isotope effects in these materials. The analysis leads us to propose a possible mechanism for the existing link between Tc and the Cauchy discrepancy.