The form of energy gap and critical temperature of superconductor implied by fluctuations of density of states

Abstract

The s-paired BCS superconductor with the electron density of states depending on energy in the vicinity of Fermi level is considered. The existence of such fluctuations of electron density of states may be referred to Van Hove singularities widely discussed in the literature. In the paper three types of small fluctuations of the electron density of states introduced about its average background's value are analysed: Lorentzian, triangle, and logarithmic ones. In order to calculate numerically the energy gap and critical temperature, the formalism of parametric BCS gap equations is applied. The positive fluctuations (peaks) correspond to the increase in occupied states number inducing a higher critical temperature. On the other hand, negative fluctuations, which decrease the number of occupied states, lead to a lower critical temperature. Such decrease in critical temperature can lead, at a specific choice of parameters, to the decease in superconductivity. The presence of fluctuations finds reflection in the shape of energy gap as a function of temperature. In the vicinity of T = 0 an abrupt decrease or increase in the energy gap to the original BCS value, according to the sign of the fluctuation, is observed. In turn, the fluctuations do not change the behaviour of the energy gap near Tc.