Persistent Currents in Superconducting Nanorings

It is well known that superconducting rings pierced by external magnetic flux Φ _x develop circulating persistent currents, which never vanish. This phenomenon is a fundamental consequence of macroscopic phase coherence of Cooper pair wave functions. In bulk superconducting rings (Fig. 20.1), it is responsible for Meissner screening of the magnetic field, which can penetrate inside the ring only at a typical length of order λ _L. For sufficiently thick rings, fluctuations of the amplitude of the order parameter field are negligible, i.e., in this case, we have |Δ(x, τ)| = Δ₀ and quantum phase slip (QPS) effects analyzed in Chapter 19 can be ignored. In addition, we will assume that temperature is sufficiently low, T ≪ Δ₀, in which case overgap quasiparticles are practically irrelevant and, hence, will be disregarded further below in this section. Figure 20.1 Bulk superconducting ring threaded by the magnetic flux Φ. https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429298233/4d96ad44-f659-4a32-b124-f671388ca995/content/fig20_1.tif"/>