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.

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Cited by in corpus (7)

• Evolution of multi-gap superconductivity in the atomically thin limit: Strain-enhanced three-gap superconductivity in monolayer MgB${}_2$
• Mapping of the unoccupied states and relevant bosonic modes via the time dependent momentum distribution
• Rise and fall of shape resonances in thin films of BCS superconductors
• Shape resonances and shell effects in thin-film multiband superconductors
• Multigap superconductivity and interaction driven resonances in superconducting nanofilms with an inner potential barrier
• Quantum size effect on the paramagnetic critical field in Pb nanofilms
• Orbital effect on the in-plane critical field in free-standing superconducting nanofilms