Phi Josephson junction


A φ 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 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 at, these minimum correspond to the lowest energy 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 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 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 reported in September 2012 by the group of Edward Goldobin at University of Tübingen. It is based on a combination of 0 and π segments in one superconducting-insulator-ferromagnetic-superconductor hybrid device and clearly demonstrates two critical currents corresponding to two junction states. The proposal to construct a φ Josephson junction out of many 0 and π segments has appeared in the works by R. Mints and coauthors, although at that time there was no term φ junction. For the first time the word φ Josephson junction appeared in the work of Buzdin and Koshelev, whose idea was similar. Following this idea, it was further proposed to use a combination of only two 0 and π segments.
In 2016, a junction based on the nanowire quantum dot was reported by the group of Leo Kouwenhoven at Delft University of Technology. The InSb nanowire has strong spin-orbit coupling, and magnetic field was applied leading to Zeeman effect. This combination breaks both inversion and time-reversal symmetries creating finite current at zero phase difference.
Other theoretically proposed realization include geometric φ junctions. There is a theoretical prediction that one can construct the so-called geometric φ junction based on nano-structured d-wave superconductor. As of 2013, this was not demonstrated experimentally.

Properties of φ junctions