Superconducting transition temperature of Pb nanofilms: Impact of thickness-dependent oscillations of the phonon-mediated electron-electron coupling

Abstract

To date, several experimental groups reported measurements of the thickness dependence of Tc of atomically uniform single-crystalline Pb nanofilms. The reported amplitude of the Tc-oscillations varies significantly from one experiment to another. Here we propose that the reason for this unresolved issue is an interplay of the quantum-size variations in the single-electron density of states with thickness-dependent oscillations in the phonon mediated electron-electron coupling. Such oscillations in the coupling depend on the substrate material, the quality of the interface, the protection cover and other details of the fabrication process, changing from one experiment to another. This explains why the available data do not exhibit one-voice consistency about the amplitude of the Tc-oscillations. Our analyses are based on a numerical solution of the Bogoliubovde Gennes equations for a superconducting slab.

Relativistic spin-polarized KKR theory for superconducting heterostructures: Oscillating order parameter in the Au layer of Nb/Au/Fe trilayers

“…We mention that T c oscillations due to quantum-well states were also reported for Pb thin films in Ref. [57]. The inclusion of more and more Au layers leads to more and more damped oscillations in the Fe layers similarly as was found in Ref.…”

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

“…Oscillations as a function of film thickness showing larger T c 's for films made of an even number of monolayers (ML) were reported [22,23]. These trends can be understood within the Bogoliubov-de Gennes formalism [34,47]. Other theoretical ideas have also been put forward, such as a change of the electron-phonon coupling in the films [48] or a role played by the interaction with the Si substrate [9].…”

Mass enhancement parameter in free-standing ultrathin Pb(111) films: The effect of spin-orbit coupling

“…2, bottom) and is a flat curve in the vicinity of the BZ center. In general, the oscillation of N (E F ) with thickness in thin Pb films was found 1,9,12,13 to be correlated with the formation of quantum well states that affect strongly the electronic distribution near the Fermi level. With increasing film thickness, the density of states in free-standing Pb(111) films approaches the bulk value of N bulk (E F ) = 0.259 states/eV/atom/spin.…”

“…5 Under the effect of spin-orbit interaction, the critical temperature considerably rises so that it becomes near to the experimental bulk T c = 7.2 K. The values are higher than T c obtained from the measured gaps in Pb(111) films grown on a Si(111) substrate. [1][2][3][4][5] It is obvious that for such small thicknesses the influence of a substrate should be very important 13,54 that is not included in the calculations done for freestanding films. The calculated layer-dependent transition temperatures show quantum oscillations down to the thinnest film considered (four layers) without any suppression.…”

“…[7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] The experimental findings inspired a great amount of theoretical work focused on the thin film properties such as the critical temperature of superconductivity, 5,12,13 the electron-phonon coupling, 5,19,20 film surface vibrations, [17][18][19][20] electronic characteristics 14,15,[22][23][24] as well as on the impact of quantum size effect on the physical properties.…”