Universal Mechanism for Breaking the $hc/2e$ Periodicity of Flux-Induced Oscillations in Small Superconducting Rings

A universal mechanism of restoration of minimal $hc/e$ periodicity in the response of small superconducting rings or cylinders to the magnetic flux is proposed. The mechanism is based on the dependence of the Cooper pair’s internal energy on its motion as a whole and does not rely on the presence of quasiparticles in the system. The thermal equilibrium $hc/2e$ periodicity is broken by an offset of the transition between different current-carrying states. The magnitude of the offset is calculated for an $s$-wave superconducting cylinder of radius $R$ in the limit $R\gg {\xi }_0$, where ${\xi }_0$ is the BCS coherence length and turns out to be exponentially small. A possible enhancement of the effect for nodal superconductors is suggested. Similar conclusions should also apply to the response of charged or neutral superfluids to rotation.

Figure 1

Schematic behavior of the internal part of the pair WF as a function of the relative angular coordinate for even (red) and odd (blue) values of the pair’s angular momentum. High frequency oscillations are not shown. (a) The circumference of the ting is much larger than the decay length of the pair WF. (b) The circumference of the ring is comparable with the decay length.

Figure 2

Dependence of the induced flux on the external flux for rings of small and large sizes.