Critical temperature of MgB${}_2$ ultrathin superconducting films: BCS model calculations in tight-binding approximation

Abstract

We develop the multi-band BCS model of superconductivity in the ultrathin films using the orthogonal tight-binding approximation for constructing the electron wavefunctions. This allows for relatively simple determination of the band structure near the Fermi level as well as the electron-electron interaction matrix elements of the BCS type. The model is applied to the ultrathin MgB${}_2$(0001) films, for which the critical temperature values are calculated in the thickness range 2...10 MgB${}_2$ layers. The importance of the boundary conditions is emphasised, as either boron or magnesium layers may cover the film. It is found that films thinner than 4 layers show substantial decrease in the critical temperature. The charge spillage outside the geometric boundaries of the film, which is allowed in our model, suppresses $T_c$ oscillations and weakens its dependence on film covering layer composition.

References in corpus (3)

• Size dependence of the Tc and the superconducting energy gap in nanocrystalline thin films of Nb
• Definitive experimental evidence for two-band superconductivity in MgB2
• Quantum size effects on the perpendicular upper critical field in ultra-thin lead films

Cited by in corpus (2)

• Evolution of multi-gap superconductivity in the atomically thin limit: Strain-enhanced three-gap superconductivity in monolayer MgB${}_2$
• Quantum size effect on the paramagnetic critical field in Pb nanofilms