Tunable $\pm \phi$, ${\phi }_0$ and ${\phi }_0\pm \phi$ Josephson junction

Abstract

We study a 0-$\pi$ dc superconducting quantum interference device (SQUID) with asymmetric inductances and critical currents of the two Josephson junctions (JJs). By considering such a dc SQUID as a black box with two terminals, we calculate its effective current-phase relation $I_s(\psi )$ and the Josephson energy $U(\psi )$, where $\psi$ is the Josephson phase across the terminals. We show that there is a domain of parameters where the black box has the properties of a $\phi$ JJ with degenerate ground state phases $\psi =\pm \phi$. The $\phi$ domain is rather large, so one can easily construct a $\phi$ JJ experimentally. We derive the current phase relation and show that it can be tuned \emph{in situ} by applying an external magnetic flux resulting in a continuous transition between the systems with static solutions $\psi =\pm \phi$, $\psi ={\phi }_0$ (${\phi }_0\ne 0,\pi$) and even $\psi ={\phi }_0\pm \phi$. The dependence of ${\phi }_0$ on applied magnetic flux is not $2\pi$ (one flux quantum) periodic.

to be published in Phys. Rev. B (status on June 1st, 2015)