The mass enhancement and the specific heat of disordered and amorphous metals

The reduction of the mean free path in metals causes a change of the electronphonon interaction and the Eliashberg function α²(Ω)F(Ω). The values of α²(Ω)F(Ω) for pure, disordered and amorphous lead are used to calculate the enhancement of the density of states and the electronic specific heat in these materials. In pure lead the cyclotron mass (1+λ) has a maximum at 11 °K and the Sommerfeld constant (γ) has a maximum at 5 °K. In disordered lead with a mean free path of about 70 Å, both, 1+λ and γ are almost constant in this temperature range. For amorphous lead there is no temperature range where 1+λ and γ are sufficiently constant. A measurement of the specific heat in disordered non-superconducting metals could answer the question whether these metals are closer to the superconducting state when their mean free path is reduced, a fact which is true for all weak-coupling superconductors.