Parity effect and spontaneous currents in superconducting nanorings

TL;DR

This paper explores how electron parity influences persistent currents in superconducting nanorings, revealing phenomena like spontaneous supercurrents and a novel $\

Contribution

It introduces the concept of a $\

Findings

Odd electron addition induces countercurrents.

Odd electron number can cause spontaneous supercurrents.

Normal metal layers enable $\

Abstract

New physical effects emerge from an interplay between the electron parity number and persistent currents in superconducting nanorings. An odd electron, being added to the ring, produces a countercurrent which may substantially modify the ground state properties of the system. In superconducting nanorings with an embedded normal metal layer a novel ``$\pi /N$-junction'' state can occur for the odd number of electrons. Changing this number from even to odd yields spontaneous supercurrent in the ground state of such rings without any externally applied magnetic flux. Further peculiar features of the parity effect are expected in structures with resonant electron transport across the weak link.