Pressure Dependence of the Superconducting Transition Temperature

A theory of the superconducting transition temperature using a simple model for the electron-phonon interaction has been used to calculate the pressure dependence of the transition temperature for nontransition metals. The pressure dependence of the Debye temperature and phonon frequencies is included by using a Grüneisen model. The theory is compared to experiment for aluminum, lead, zinc, cadmium, indium, and tin, and the agreement is generally quite good. The results have been used to predict the critical pressures at which $T_c=0\mathrm{}$; and for the cases of zinc, cadmium, and possibly aluminum, it should be possible to carry out experiments where $T_c$ is pushed below presently measurable temperatures. The empirical $T_c=f\left(P\right)\mathrm{}$ relations published in the literature are discussed and compared with the present results.