Rise and fall of shape resonances in thin films of BCS superconductors

D. Valentinis; D. van der Marel; C. Berthod

doi:10.1103/PhysRevB.94.054516

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Rise and fall of shape resonances in thin films of BCS superconductors

D. Valentinis, D. van der Marel, C. Berthod

DOI 10.1103/PhysRevB.94.054516 · Physical Review B

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Abstract

The confinement of a superconductor in a thin film changes its Fermi-level density of states and is expected to change its critical temperature Tc. Previous calculations have reported large discontinuities of Tc when the chemical potential coincides with a subband edge. By solving the BCS gap equation exactly, we show that such discontinuities are artifacts and that Tc is a continuous function of the film thickness. We also find that Tc is reduced in thin films compared with the bulk if the confinement potential is lower than a critical value, while for stronger confinement Tc increases with decreasing film thickness, reaches a maximum, and eventually drops to zero. Our numerical results are supported by several exact solutions. We finally interpret experimental data for ultrathin lead thin films in terms of a thickness-dependent effective mass.

Source-reported materials — not catalogue approval

Formula	Reported Tc (K)	Pressure (GPa)	Type
Al Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Ga Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Sn Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
In Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Pb Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
Bi Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
NbN Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
FeSe Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown
SrTiO3 Archive — visibility unverified Source-occurrence policy only; no material identity or catalogue acceptance is inferred from the formula.	—	Pressure not reported	unknown