ABSTRACT
Recent advances in nanofabrication technology resulted in high-quality metallic nanoscale structures like single-crystalline lms with thickness down to a few monolayers (Guo et al., 2004; Bao et al., 2005; Zhang et al., 2005; Eom et al., 2006; Özer et al., 2006a,b, 2007) and wires (both single crystalline and made of strongly coupled grains) with width down to 5-10 nm (Savolainen et al., 2004; Tian et al., 2005; Zgirski et al., 2005; Altomare et al., 2006; Jankovič et al., 2006; Tombros et al., 2008; Wang et al., 2008). In most fabricated samples, the electron mean-free path ℓ was found to scale with the nanowire/nano lm thickness d (Savolainen et al., 2004; Zgirski et al., 2005; Altomare et al., 2006; Özer et al., 2006b, 2007). In particular, Matthiessen-like approximation 1/ℓ = 1/2d + 1/ℓimp was used by Özer et al. (2007), where 1/2d represents the contribution of the boundaries (d is the sample thickness) and imp >> d stands for the mean-free path due to impurities. Based on experimental results reported in this chapter, one can nd that ℓimp ∼ 200-400 nm in Pb single-crystalline atomically uniform nanoislands with thickness about 30-40 Å and with area ∼400 nm × 400 nm. In high-quality nanowires, disorder is more signi cant but due to the scaling ℓ ∝ d, one is also able to expect that the boundary scattering controls ℓ and, hence, ℓimp >> d. So, the present-day technologies make it possible to fabricate superconducting nanostructures with minor disorder, i.e., ℓimp/d >> 1 and kFℓimp >> 1, where kF stands for the threedimensional (3D) Fermi wavevector. An important consequence is that the discrete transverse electron spectrum is not smeared by impurity scattering in this case, and, as a result, the conduction band splits up into a series of single-electron subbands, which move in energy with changing d. As was established
half a century ago (Abrikosov and Gor’kov, 1958a,b; Anderson, 1959), the superconducting equilibrium properties are not very sensitive to minor disorder, when kFℓimp >> 1 [for instance, in Pb single-crystalline nano lms fabricated by Özer et al. (2007), kFℓimp ∼ 103]. us, to rst approximation, such high-quality superconducting nano lms and nanowires can be treated in the clean limit.
