Optical conductivity of granular aluminum films near the Mott metal-to-insulator transition

Abstract

We report measurements of the energy gap of granular aluminum films by THz spectroscopy. We find that as the grains progressively decouple, the coupling ratio 2∆(0)/kBTc increases above the BCS weak coupling ratio 3.53, and reaches values consistent with an approach to BCS-BEC crossover for the high resistivity samples, expected from the short coherence length. The Mattis-Bardeen theory describes remarkably well the behavior of σ1,s/σ1,n for all samples up to very high normal state resistivities. arXiv:1901.02814v2 [cond-mat.supr-con]

Superfluid density from magnetic penetration depth measurements in Nb–Cu 3D nano-composite films

“…4 d), we see that J S ~ ∆(0)/k B for films with thicknesses < 5 nm for the Nb rich nano-composites while for the Cu rich films it becomes comparable at thickness < 25 nm i.e. very close to the 2D regime similar to the granular Al films studied previously 19 – 22 . This is indicative that for Nb–Cu films with higher Cu content (> 60 at%), it is possible to see the effect of phase fluctuations on superconducting properties even for relatively thick films (~ 20–30 nm) i.e.…”

“…Similarly, SPE due to the proximity of the small Cu grains to the nano-grains of Nb may affect the properties of the films, depending on the cleanliness of the Nb–Cu interfaces 16 . Besides, as discussed previously phase fluctuations in the random array of SNS Josephson junctions might also influence the superconducting properties just like it did in 2D granular films having an array of SIS junctions 19 – 22 . To see which of the mechanisms play the dominant role, we analyzed the two-coil mutual inductance data for finite films to obtain the superfluid stiffness (J S ) and the penetration depth (λ).…”

“…Besides, the resistivity of the Cu rich films also becomes lower than the Nb rich films due to the large increase in the Cu content. Thus, all films studied here were purely metallic in nature unlike the granular Al films which were in the insulating regime used to probe the role of phase fluctuations on superconductivity 19 – 22 . From our previous studies on thick films, we had conjectured that phase fluctuations might play a dominant role in controlling the T c with increasing Cu content in these granular Nb–Cu films.…”

“…∆ can be directly measured through spectroscopic techniques like planar tunneling, scanning tunneling spectroscopy (STM) or point contact Andreev reflection spectroscopy (PCAR). In recent times it has been possible to get an accurate estimation of both ∆ and J S by THz optical spectroscopy 19 – 22 . However, this technique limits measurements in extremely thin films which need to be transparent to the THz radiation.…”

The Role of the Short Coherence Length in Unconventional Superconductors

“…The number of pairs within a coherence volume is of the order of the square of the Fermi energy divided by the energy gap. In a typical metal, this number is of the order of 1.10 6 to 1.10 8 . This very large number is the reason why the superconducting state is so robust in the face of local perturbations of the crystal lattice, such as impurities or grain boundaries.…”