Is There a Lower Size Limit for Superconductivity?

Abstract

The ultimate lower size limit for superconducting order to exist is set by the "Anderson criterion"-arising from quantum confinement-that appears to be remarkably accurate and universal. We show that carefully grown, phase-pure, nanocrystalline bcc-Ta remains superconducting (with ordering temperature, T ≈ 0.9 K) down to sizes 40% below the conventional estimate of the Anderson limit of 4.0 nm. Further, both the T and the critical magnetic field exhibit an unusual, nonmonotonic size dependence, which we explain in terms of a complex interplay of quantum size effects, surface phonon softening, and lattice expansion. A quantitative estimation of T within first-principles density functional theory shows that even a moderate lattice expansion allows superconductivity in Ta to persist down to sizes much lower than the conventional Anderson limit, which can be traced to anomalous softening of a phonon due to its coupling with electrons. This appears to indicate the possibility of bypassing the Anderson criterion by suitable crystal engineering and obtaining superconductivity at arbitrarily small sizes, an obviously exciting prospect for futuristic quantum technologies. We take a critical look at how the lattice expansion modifies the Anderson limit, an issue of fundamental interest to the study of nanoscale superconductivity.

Molybdenum–Ruthenium–Carbon Solid-Solution Alloy Nanoparticles: Can They Be Pseudo-Technetium Carbide?

“…The lower T c compared with that of bulk cubic MoC y (T c = 12 K 18 ) may be associated with the size-induced discretization of the energy levels. 36 A similar size-dependent behavior was observed in MoC y . 37 The superconducting parameter that was most affected by nanosizing is λ(0) (4.3 × 10 2 nm vs 1.3 × 10 2 nm in bulk MoC y 18 ).…”

“…The lower T c compared with that of bulk cubic MoC y ( T c = 12 K) may be associated with the size-induced discretization of the energy levels . A similar size-dependent behavior was observed in MoC y .…”

A Reduction in Particle Size Generally Causes Body-Centered-Cubic Metals to Expand but Face-Centered-Cubic Metals to Contract

“…Changes are shown as a percentage shift from the corresponding bulk values. Only face centered cubic (fcc) and body-centered cubic metals (bcc) were considered, and the data were obtained from the following references: Al, Au, , Cu, , Pd, Nb, and Ta …”

“…However, a few metals are known to exhibit a systematic lattice expansion in the nanoparticle form. These include Cr, 23 Fe, 24 Nb, 25 V, 26 and Ta, 27 and interestingly, each one happens to have a body-centered cubic (bcc) structure. In order to investigate whether such a correlation is genuine or coincidental, we measured or verified the data for four of the bcc metals (Nb, Ta, V, and Mo), synthesized and analyzed by the same techniques.…”

“…Finally, it is important to appreciate that the size-driven change in the lattice parameters is a nontrivial effect with significant consequences, in some cases dominating over quantum size effects and other types of surface effects. For instance, size-induced lattice expansion plays a crucial role in the: (a) persistence of superconductivity down to unexpectedly small sizes, 27 (b) appearance of a magnetic moment in isolated Fe atoms embedded in a nanocrystalline metals, 30 and (c) destruction of ferroelectricity in nanocrystalline oxides. 4…”