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.
In the ordinary Josephson junction the dependence
The function where Ic is the critical current of the junction, and
is the flux quantum, is a good example of conventional
, these minimum (minima) correspond to the lowest energy states (ground states) of the junction and one speaks about "φ Josephson junction".
, which corresponds to the current-phase relation
If Ic1>0 and Ic2<-1/2<0, the minima of the Josephson energy occur at
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
, and the corresponding current-phase relation
In this case the ground state is
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:[1] 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
The first indications of φ junction behavior (degenerate ground states[2] or unconventional temperature dependence of its critical current[3]) 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.
[4] 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 (infinitely) many 0 and π segments has appeared in the works by R. Mints and coauthors,[5][6] 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,[1] whose idea was similar.
Following this idea, it was further proposed to use a combination of only two 0 and π segments.
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.
[8] 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.