Phonon limited superconducting correlations in metallic nanograins

Abstract

Conventional superconductivity is inevitably suppressed in ultra-small metallic grains for characteristic sizes smaller than the Anderson limit. Experiments have shown that above the Anderson limit the critical temperature may be either enhanced or reduced when decreasing the particle size, depending on the superconducting material. In addition, there is experimental evidence that whether an enhancement or a reduction is found depends on the strength of the electron-phonon interaction in the bulk. We reveal how the strength of the e-ph interaction interplays with the quantum-size effect and theoretically obtain the critical temperature of the superconducting nanograins in excellent agreement with experimental data. We demonstrate that strong e-ph scattering smears the peak structure in the electronic density-of-states of a metallic grain and enhances the electron mass, and thereby limits the highest Tc achievable by quantum confinement.

Lattice dynamics in Sn nanoislands and cluster-assembled films

“…A future challenge is to correlate the changes in the phonon density of states at the nanoscale to changes in the superconducting behaviour. β-Sn is a low temperature superconductor with a bulk superconducting transition temperature (T C ) of 3.7 K. A substantial increase in (T C ) of Sn nanostructures has been experimentally observed [66][67][68] with origins in the subtle interplay of the quantum confinement for the electronic degrees of freedom and a phonon environment 69 . Our work enables further analysis of the role of phonon confinement in nanoscale superconductivity, and its precise account in Sn nanostructures.…”

The influence of phonon softening on the superconducting critical temperature of Sn nanostructures

“…For Sn nanostructures an increase in T C of up to 10% has been observed [3][4][5][6][7][8][9][10] . The mechanism of this T C enhancement is not well understood and is suggested to be caused by changes in the phonon density of states 3,5,[11][12][13][14] , changes in the electron density of states [15][16][17][18][19][20][21][22][23] or a combination of these effects [24][25][26][27][28][29][30] .…”

Experimental observation of electron-phonon coupling enhancement in Sn nanowires caused by phonon confinement effects

“…As mentioned before, T c of weak-coupling superconductors increases upon size reduction while no impact or even a reduction of T c is observed in strong coupling materials. Note that, according to theoretical calculations, strongcoupling superconducting nanograins exhibit a larger broadening of single electron levels and a heavier electron mass than weak-coupling superconductors [52]. QSE are inversely proportional to the electron mass, thus making them more relevant in strong-coupling superconductors.…”