Ultra-small metallic grains: effect of statistical fluctuations of the chemical potential on superconducting correlations and vice versa

Abstract

Superconducting correlations in an isolated metallic grain are governed by the interplay between two energy scales: the mean level spacing δ and the bulk pairing gap Δ0, which are strongly influenced by the position of the chemical potential with respect to the closest single-electron level. In turn superconducting correlations affect the position of the chemical potential. Within the parity projected BCS model we investigate the probability distribution of the chemical potential in a superconducting grain with randomly distributed single-electron levels. Taking into account statistical fluctuations of the chemical potential due to the pairing interaction, we find that such fluctuations have a significant impact on the critical level spacing δc at which the superconducting correlations cease: the critical ratio δc/Δ0 at which superconductivity disappears is found to be increased.

Size-dependent electron chemical potential in nanostructures derived from statistical configuration

“…This equation is similar to that previously proposed [21]. Simulation by Croitoru et al showed that for small nanoparticles, the chemical potential can be approximated by [18], with α iℓ the i th zero of a spherical Bessel function of the first kind, j l (x). Kiyonaga et al reported an increase in the Fermi energy in TiO 2 -supported Au particles of sizes ranging between 3.0 and 13 nm, where the Fermi energy increased with diameter [22].…”

“…The distance between the discrete lines decreases as the particle size increases [13][14][15][16][17]. For small particle diameters, the energy spacing in the group is clearly separated [18]. For example, for a spherical particle that is assumed to have a spherical potential well, the energy of each discrete state is given by ε n,ℓ = 2ℏ 2 χ 2 nℓ /m * e D 2 , where n and ℓ are quantum numbers, ℏ is Planck's constant, χ nℓ is the root of a Bessel function, m * e is the effective mass of the electron or the hole, and D is the particle diameter [15,16].…”

“…The chemical potential simulated by Croitoru et al [18]that can be expressed as…”

Phonon limited superconducting correlations in metallic nanograins

“…The experimental results are summarized in Table 1 . The increase of T c observed for In, Sn, and Al was attributed either to quantum-size effects 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 or to the softening of the phonon modes due to the presence of the surface 37 38 39 40 41 42 . The studies showed good agreement between theory and experiment for weak- and intermediate-coupling superconductors.…”

Phase Slip Avalanches in Small Superconductors

“…Phase slip has been the subject of many studies in recent years. It has been widely studied in ultra narrow (width ξ, the coherence length) [3][4][5][6][7][8][9][10][11][12][13] and to a lesser extent in wide (width > ξ) superconducting wires/strips [14,15]. It has been shown that the character of the superconducting phase slip depends on the transverse size of the superconducting nanowires and that for ultra-narrow nanowires, the phase slip ascribes a quantum character that changes the character of the superconducting state and can even completely suppress it [3].…”