Size-dependent enhancement of superconductivity in Al and Sn nanowires: Shape-resonance effect

Abstract

A shape-dependent superconducting resonance can be expected when an energy level associated with the transverse motion in a wire passes through the Fermi surface. We show that the recently observed widthdependent increase of T c in Al and Sn nanowires is a consequence of this shape-resonance effect.Increasing the critical temperature ͑T c ͒ of a superconductor ͑SC͒ has been a major challenge. On the one hand one can look for different materials that exhibit a higher T c . Such a search has been very successful over the last 20 years. On the other hand microstructuring of a superconductor is a different and new road that is able to modify T c ͑i.e., increase and/or decrease it͒ and may also give us further insight in the basic mechanism of superconductivity.In earlier works on microstructuring of SCs in the mesoscopic regime, enhancement of the critical current ͑j c ͒ was demonstrated to occur due to trapping of vortices. Also a large increase of the critical magnetic field ͑H c ͒ was realized through such mesoscopic structuring, which is mostly a consequence of surface superconductivity. But in both cases the zero-magnetic-field critical temperature was unaltered. The enhancement of j c and H c could be accurately described by phenomenological theories such as the London approach and the ͑time-dependent͒ Ginzburg-Landau theory.In the present Brief Report we are interested in modifying a SC on the nanoscale. We deal with systems where the electron motion is limited to quasi-one-dimension ͑1D͒. During the last decade nanowires have attracted much attention in the context of phase fluctuations of the order parameter ͑i.e., quantum phase slips͒. 1 But quantization of the electron motion in the transverse direction was not investigated in much detail. However, very recently numerical investigation of the Bogoliubov-de Gennes equations has shown 2 that this quantization results in significant shape-dependent superconducting resonances with a profound effect on the nanowire T c . Such systems have been the subject of recent experimental studies, 3-5 and we demonstrate here that the widthdependent increase of T c found in these experiments is a manifestation of these shape resonances.More than 40 years ago, Blatt and Thompson 6 calculated a remarkable sequence of peaks in the thickness dependence of the energy-gap parameter of single-crystalline superconducting nanofilms in the clean limit. They called these spikes shape resonances. At that time it was not possible to produce high-quality SCs with nanoscale dimensions ͑only very recently were the thickness-dependent oscillations of T c observed experimentally in ultrathin Pb films 7 ͒. For decades atomic nuclei were the only systems where the interplay between quantum confinement and pairing of fermions could be studied experimentally and where the expectations of Blatt and Thompson were confirmed as a series of size resonances in the pairing energy gap of nuclei. 8 Very recently high-quality nanowires have become available, where this resonance effect is expected 2 to b...

Thickness-Dependent Oscillations of the Critical Magnetic Field Induced by the Quantum Size Effect in Superconducting Nanofilms

“…[10], the oscillations of the critical temperature as a function of the number of atomic monolayers have been found for ultra-thin Pb films grown on Si(111) substrate. This experiment reopens an extensive research concerning the interplay of the superconductivity and the quantum confinement in nanoscale systems [1,3,11,14,18,19,22]. The study of the superconductivity in Pb nanofilms has been extended by Eom et al [8].…”

Visualizing superconductivity in FeSe nanoflakes onSrTiO3by scanning tunneling microscopy

“…Superconductivity in reduced dimensions, including ultrathin films, 1-3 nanowires 4 and nanograins, [5][6][7][8][9][10] has still been a hot topic of interest due to its potential for developing dissipationless nanoelectronics. However, as the size of a superconductor is shrunk to nanoscale, quantum size effects (QSE) would become important and can dramatically change its superconducting properties.…”

“…Many fascinating phenomena, such as the parity effect and shell effect on gap magnitude ∆, have been predicted theoretically [11][12][13] and ascertained experimentally in several conventional BCS-type superconductors. [5][6][7][8]10 Superconductivity can be eventually quenched if the nanograin size is small enough so that the QSE induced discrete energy level spacing (∼ 2π 2 2 /(mk F V )) exceeds the bulk gap magnitude ∆ 0 , where , m, k F and V denote the reduced Planck constant, the mass of an electron, the Fermi wave vector and nanograin volume, respectively. In order to study these phenomena, nanostructures with extremely small k F V are particularly interesting.…”

“…In order to study these phenomena, nanostructures with extremely small k F V are particularly interesting. Compared to conventional metal superconductors, [1][2][3][4][5][6][7][8]10 the layered superconducting compounds (e.g. cuprates and iron-based superconductors) generally exhibit a smaller k F and represent ideal systems to test the intriguing superconductivity in confined systems.…”

Bardeen-Cooper-Schrieffer Theory of Finite-Size Superconducting Metallic Grains

“…In particular, finite-size corrections to the predictions of the Bardeen-CooperSchrieffer (BCS) theory for bulk superconductors [4] have been studied [5][6][7][8][9][10] within the exactly solvable Richardson model [11]. Pairing in specific potentials, such as a harmonic oscillator potential [12] and a rectangular box, [13,14] and mesoscopic fluctuations of the energy gap [15,16] have been explored as well. Nevertheless, a comprehensive theoretical description of the combined effect of the discrete energy spectrum and fluctuating interaction matrix elements has not yet emerged.…”