Is There a Lower Size Limit for Superconductivity?

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 <i>bcc</i>-Ta remains superconducting (with ordering temperature, <i>T</i>_C ≈ 0.9 K) down to sizes 40% below the conventional estimate of the Anderson limit of 4.0 nm. Further, both the <i>T</i>_C 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 <i>T</i>_C 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

Effect of Mo-Incorporation in the TiO₂ Lattice: A Mechanistic Basis for Photocatalytic Dye Degradation

Photocatalytic activity of TiO₂ (anatase) is appreciably enhanced by substitutional doping of Mo in anatase lattice, in conjunction with the incorporation of nanostructured MoO₃ within the parent anatase lattice. The photocatalyst material was characterized in detail using X-ray diffraction, Raman spectroscopy, diffuse reflectance (DR-UV–Vis spectroscopy), X-ray photoelectron spectroscopy, and electron microscopy. Photocatalysis experiments were conducted using a model rhodamine-B (Rh–B) dye reaction using both UV and visible irradiation sources. The observed trends in the case of visible irradiative source can be summarized as follows: Mo-1 < Mo-2 < Mo-5 ≫ Mo-10. Attempts were made to isolate the structural factors that control photochemical behavior of these Mo–TiO₂ photocatalysts and to correlate photocatalytic activity with different structural aspects like oxidation state, band gap, surface species, etc. Mechanistic insights were acquired from ex situ ¹H NMR studies showing different intermediates and different probable routes for the Rh–B dye degradation with UV and visible radiations. The stable intermediates were formed by a direct oxidative fragmentation route, without any evidence of the initial deethylation route. The intermediates found were benzoic acid, different amines, diols, and certain acids (mostly formic and acetic acid). The adsorption of the Rh–B dye on the catalytic surface via the N-charge centers of the Rh–B was also observed