The superconducting transition temperatureTc for semimetals like bismuth has been calculated as a function of the densitync of the electron and hole charge carriers. A simplified two-band model for describing the longitudinal dielectric function for such a system has been used in our model calculation. We find that the attractive interaction responsible for the instability of the normal ground state comes not only from the exchange of lattice phonons, but also from the electronhole sound mode, provided the ratio of the averaged hole to electron mass,mh/me ≠ 1. We have compared our theoretical values ofTc(nc) with experimental results for bismuth under hydrostatic pressure, and find reasonable agreement ifmh/me is assumed to have a value which is only slightly larger than that at atmospheric pressures. A linear variation of the negative band gap as a function of pressure has been assumed for the sake of this comparison.
Volume 96, 2022
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