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. Introduction The Josephson energy depends on the superconducting phase difference (Josephson phase) periodically, with the period . Therefore, let us focus only on one period, e.g. . In the ordinary Josephson junction the dependence has the minimum at . The function , where is the critical current of the junction, and is the flux quantum, is a good example of conventional . Instead, when the Josephson energy has a minimum (or more than one minimum per period) at , 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 having two minima at within each period, where (such that ) is some number. For example, this is the case for , which corresponds to the current-phase relation . If and , the minima of the Josephson energy occur at , where . Note, that the ground state of such a Josephson junction is doubly degenerate because . Another example is the junction with the Josephson energy similar to conventional one, but shifted along -axis, for example , and the corresponding current-phase relation . In this case the ground state is and it is not degenerate. The above two examples show that the Josephson energy profile in φ Josephson junction can be rather different, resulting in different physical properties. Often, to distinguish, which particular type of the current-phase relation is meant, the researches are using different names. At the moment there is no well-accepted terminology. However, some researchers use the terminology after A. Buzdin: the Josephson junction with double degenerate ground state , similar to the first example above, are indeed called φ Josephson junction, while the junction with non-degenerate ground state, similar to the second example above, are called Josephson junctions. Realization of φ junctions The first indications of φ junction behavior (degenerate ground states or unconventional temperature dependence of its critical current) were reported in the beginning of the 21st century. These junctions were made of d-wave superconductors. The first experimental realization of controllable φ junction was