en>Elcap at 10:41, 1 February 2014

2014-02-01T10:41:24Z

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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 [[Pi Josephson junction|π Josephson junction]], which has the minimum energy corresponding to the phase of π, is a specific example of it.

== Introduction ==
An ordinary [[Josephson junction]] has a Josephson energy profile given by
: <math>U(\phi) = \frac{\Phi_0 I_c}{2\pi}[1-\cos(\phi)]</math>,
where {{math|''Ic''}} is the critical current of the junction and {{math|φ}} is the Josephson phase. This potential has only one trivial minimum <math>\phi=0</math> within the interval <math>-\pi<\phi\leq+\pi</math>. (Reminder: the Josephson phase is {{math|2π}}-periodic, so the same picture is repeated in each other interval different by {{math|2πn}}).

φ [[Josephson junction]] appears because of unusual [[Josephson energy]] profile. Consider two examples.

# Consider the junction with the Josephson energy given by
:: <math>U(\phi) = \frac{\Phi_0}{2\pi} \left\{ I_{c1}[1-\cos(\phi)] + \frac{1}{2}I_{c2}[1-\cos(2\phi)]\right\}</math>,
:which corresponds to the [[Josephson energy|current-phase relation]]
:: <math>I_s(\phi) = I_{c1}\sin(\phi) + I_{c2}\sin(2\phi)</math>.
:If {{math|''Ic1''>0}} and {{math|''Ic2''<-1/2<0}}, the minima of the [[Josephson energy]] occur at
: <math>\phi=\pm\varphi</math>, where <math>\varphi=\arccos\left(-2I_{c1}/I_{c2}\right)</math>.
It is clear that {{math|0<φ<π}} (with accuracy of {{math|2π''n''}}). Note, that the ground state of such a [[Josephson junction]] is doubly degenerate.

# Another example is the junction with
::<math>U(\phi) = \frac{\Phi_0 I_{c}}{2\pi}[1-\cos(\phi-\varphi_0)]</math>,
:and the corresponding current-phase relation
::<math>I_s(\phi) = I_{c}\sin(\phi-\varphi_0)</math>.
In this case the ground state is <math>\phi=\varphi_0</math> and it is simple (not degenerate).

The above two examples show that the Josephson energy profile in φ [[Josephson junctions|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:<ref name=Buzdin:2003:phi-LJJ /> the [[Josephson junctions|Josephson junction]] with double degenerate ground state <math>\phi=\pm\varphi</math>, similar to the first example above, are indeed called φ [[Josephson junction]], while the junction with shifted argument in the CPR, similar to the second example above, are called <math>\varphi_0</math> Josephson junctions.

== Realization of φ junctions ==

* '''Based on combination of 0 and π segments'''. 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,<ref name=Mints:1998:SelfGenFlux@AltJc /><ref name=Mints:2001:FracVortices@GB /> 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,<ref name=Buzdin:2003:phi-LJJ /> whose idea was similar. Following this idea, it was further proposed to use a combination of only two 0 and π segments.<ref name=Goldobin:2011:H-TunableEffCPR /> This idea was successfully demonstrated experimentally<ref name=Sickinger:2012:varphiExp /> shortly thereafter using superconductor|insulator|ferromagnet|superconductor 0-π Josephson junctions.

* '''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.<ref name=Gumann:2007:Geometric-pi-JJ /> As of 2013, this was not demonstrated experimentally.

== Properties of φ junctions ==

* Two critical currents related to the escape (depinning) of the phase from two different wells of the Josephson potential. The lowest critical current can be seen experimentally only at low damping (low temperature). The measurements of the critical current can be used to determine the (unknown) state (+φ or -φ) of φ junction.
* In the case of φ junction constructed out of 0 and π segments, magnetic field can be used to change the asymmetry of the Josephson energy profile up to the point that one of the minima disappears. This allows to prepare the desired state (+φ or -φ). Also, asymmetric periodic Josephson energy potential can be used to construct ratchet-like devices.
* Long φ junctions allow special types of soliton solutions --- the ''splintered vortices''<ref name=Mints:2002:SplinteredVortices@GB /> of two types: one carries the magnetic flux {{math|Φ1<Φ0}}, while the other carries the flux {{math|Φ2{{=}}Φ0−Φ1}}. Here {{math|Φ0}} is the [[magnetic flux quantum]]. These vortices are the solitons of a [[double sine-Gordon]] equation.<ref name=Goldobin:2007:CPR2 /> They were observed in d-wave grain boundary junctions.<ref name=Mints:2001:FracVortices@GB />

== Applications ==

* Similar to [[Pi Josephson junction]] φ junctions can be used as a phase battery.
* Two stable states +φ and -φ can be used to store a digital information. To write the desired state one can apply magnetic field, so that one of the energy minima disappears, so the phase has no choice as to go the the remaining one. To read out an unknown state of the φ junctions one can apply the bias current with value between the two critical currents. If the φ junctions switches to the voltage state, its state was −φ, otherwise, it was +φ. The use of φ junctions as a memory cell (1 bit) was already demonstrated.<ref name=Goldobin:2013:varphi-bit />
* In quantum domain the φ junction can be used as a two-level system (qubit).

==See also==
*[[Josephson junction]]
*[[Josephson energy]]
*[[Pi Josephson junction|π Josephson junction]]
*[[Fractional vortices]]
*[[double sine-Gordon equation]]

== References ==
{{reflist|2|refs=
<ref name=Buzdin:2003:phi-LJJ>{{cite journal|last=Buzdin|first=A.|coauthors=Koshelev, A.|title=Periodic alternating 0- and π-junction structures as realization of φ-Josephson junctions|journal=Physical Review B|year=2003|month=June|volume=67|issue=22|doi=10.1103/PhysRevB.67.220504}}</ref>
<ref name=Mints:1998:SelfGenFlux@AltJc>{{cite journal|last=Mints|first=R.|title=Self-generated flux in Josephson junctions with alternating critical current density|journal=Physical Review B|year=1998|month=February|volume=57|issue=6|pages=R3221–R3224|doi=10.1103/PhysRevB.57.R3221}}</ref>
<ref name=Mints:2001:FracVortices@GB>{{cite journal|last=Mints|first=R.|coauthors=Papiashvili, Ilya|title=Josephson vortices with fractional flux quanta at YBa2Cu3O7-x grain boundaries|journal=Physical Review B|year=2001|month=August|volume=64|issue=13|doi=10.1103/PhysRevB.64.134501}}</ref>
<ref name=Goldobin:2011:H-TunableEffCPR>{{cite journal|last=Goldobin|first=E.|coauthors=Koelle, D.; Kleiner, R.; Mints, R. G.|title=Josephson Junction with a Magnetic-Field Tunable Ground State|journal=Physical Review Letters|year=2011|month=November|volume=107|issue=22|doi=10.1103/PhysRevLett.107.227001}}</ref>
<ref name=Sickinger:2012:varphiExp>{{cite journal|last=Sickinger|first=H.|coauthors=Lipman, A.; Weides, M.; Mints, R. G.; Kohlstedt, H.; Koelle, D.; Kleiner, R.; Goldobin, E.|title=Experimental Evidence of a φ Josephson Junction|journal=Physical Review Letters|year=2012|month=September|volume=109|issue=10|doi=10.1103/PhysRevLett.109.107002}}</ref>
<ref name=Gumann:2007:Geometric-pi-JJ>{{cite journal|last=Gumann|first=A.|coauthors=Iniotakis, C.; Schopohl, N.|title=Geometric π Josephson junction in d-wave superconducting thin films|journal=Applied Physics Letters|year=2007|volume=91|issue=19|pages=192502|doi=10.1063/1.2801387}}</ref>

<ref name=Mints:2002:SplinteredVortices@GB>{{cite journal|last=Mints|first=R.|coauthors=Papiashvili, Ilya; Kirtley, J.; Hilgenkamp, H.; Hammerl, G.; Mannhart, J.|title=Observation of Splintered Josephson Vortices at Grain Boundaries in YBa2Cu3O7-δ|journal=Physical Review Letters|year=2002|month=July|volume=89|issue=6|doi=10.1103/PhysRevLett.89.067004}}</ref>

<ref name=Goldobin:2007:CPR2>{{cite journal|last=Goldobin|first=E.|coauthors=Koelle, D.; Kleiner, R.; Buzdin, A.|title=Josephson junctions with second harmonic in the current-phase relation: Properties of φ junctions|journal=Physical Review B|year=2007|month=December|volume=76|issue=22|doi=10.1103/PhysRevB.76.224523}}</ref>

<ref name=Goldobin:2013:varphi-bit>{{cite journal|last=Goldobin|first=E.|coauthors=Sickinger, H.; Weides, M.; Ruppelt, N.; Kohlstedt, H.; Kleiner, R.; Koelle, D.|title=Memory cell based on a ϕ Josephson junction|journal=Applied Physics Letters|year=2013|volume=102|issue=24|pages=242602|doi=10.1063/1.4811752}}</ref>
}}

[[Category:Superconductivity]]
[[Category:Josephson effect]]

Pseudocapacitance - Revision history

en>Elcap at 10:41, 1 February 2014