Theoretical model of superconductivity and the martensitic transformation in $A15\mathrm{}$ compounds

The effect of the martensitic transition on superconductivity in the $A15\mathrm{}$ compounds is examined theoretically. The BCS pairing potential is added to the Peierls potential in the Gorkov model of the martensitic transition. We find that the two potentials compete to open an energy gap on the common portion of Fermi surface and that one phase transition depresses the other. It is found that the $T_c=17\mathrm{}$ K in ${\mathrm{V}}_3$Si includes a 0.3-K reduction due to this competition and that superconductivity arrests the development of tetragonality below 17 K. It is predicted that at high pressure (∼ 25 kbar) the martensitic transition will be precluded.