Energy gap, transition temperature and electron-electron interaction of the weak coupling superconductors tin and indium as a function of the mean free path of the electrons

Abstract

The energy gap and the transition temperature of the weak coupling superconductors tin and indium are measured as a function of the mean free path of the electrons. Both of them increase with decreasing mean free path. The ratioα=2Δ ₀/kT_c increases proportionally to the reciprocal mean free path from 3.6 to 4.0 for tin and from 3.6 to 3.95 for indium. A theoretical consideration is presented showing that the electron-electron interaction is increased in dirty superconductors. Without any fit we find from the theoretical calculation an increase inNV for indium ofδNV=5 · 10⁻¹⁰ m/l _tr and for tinδNV=2 · 10⁻¹⁰ m/l _tr (l_tr is the transport mean free path of the electrons). The experiments give an increase inNV for indium ofδNV=4.2 · 10⁻¹⁰ m/l_tr and for tinδNV=1.7 · 10⁻¹⁰ m/l _tr. The agreement is surprisingly good.