A φ Josephson junction (pronounced phi Josephson junction) is a particular type of the Josephson junction, which has a non-zero Josephson phase φ across it in the ground state. A π Josephson junction, which has the minimum energy corresponding to the phase of π, is a specific example of it.

The Josephson energy ${\displaystyle U}$ depends on the superconducting phase difference (Josephson phase) ${\displaystyle \phi }$ periodically, with the period ${\displaystyle 2\pi }$. Therefore, let us focus only on one period, e.g. ${\displaystyle -\pi <\phi \leq +\pi }$. In the ordinary Josephson junction the dependence ${\displaystyle U(\phi )}$ has the minimum at ${\displaystyle \phi =0}$. The function

where I_c is the critical current of the junction, and ${\displaystyle \Phi _{0}}$ is the flux quantum, is a good example of conventional ${\displaystyle U(\phi )}$.

Instead, when the Josephson energy ${\displaystyle U(\phi )}$ has a minimum (or more than one minimum per period) at ${\displaystyle \phi \neq 0}$, these minimum (minima) correspond to the lowest energy states (ground states) of the junction and one speaks about "φ Josephson junction". Consider two examples.

First, consider the junction with the Josephson energy ${\displaystyle U(\phi )}$ having two minima at ${\displaystyle \phi =\pm \varphi }$ within each period, where ${\displaystyle \varphi }$ (such that ${\displaystyle 0<\varphi <\pi }$) is some number. For example, this is the case for

${\displaystyle U(\phi )={\frac {\Phi _{0}}{2\pi }}\left\{I_{c1}[1-\cos(\phi )]+{\frac {1}{2}}I_{c2}[1-\cos(2\phi )]\right\}}$,

which corresponds to the current-phase relation

${\displaystyle I_{s}(\phi )=I_{c1}\sin(\phi )+I_{c2}\sin(2\phi )}$.