Manuscript N: NCOMMS-13-09832
Authors: G. R. Berdiyorov et al.
Title: Josephson vortex loops in nanostructured Josephson junctions
Dear Editor,
Thank you for your new communication about our manuscript and for your positive inclination towards our work.
In the new version of the manuscript, we have addressed all your concerns with respect to the presentation and
style of the paper and its Supplementary Materials.
We also thank the referee for his time and for his useful comments. To accommodate the remarks of the referee
we have conducted additional simulations. On the following pages we give the point-by-point response to the
referee and list the changes made in the revised version of the manuscript.
The main concern of the referee is about the Josephson currents flowing across the junction. As we have stated in
the manuscript, our approach does describe the Josephson tunneling, and the expression for the current across the
junction is available in the Methods section. The source of misunderstanding with the referee is in the scale we
used for the current distribution near the superconducting pillars (Supplementary Figures 2 and 3), where the
Josephson current was not visible due to coarse-graining of the superconducting current density. The Josephson
current does exist, and will be clearly seen if one plots the current distribution away from the pillars, which is now
discussed in the new version of the manuscript (with accompanying equations in Methods section and
comparative plots in Supplementary Figure 4). It is indeed that this current carries information about the
Josephson vortices travelling across the sample, as expected by the referee.
Since there is no conceptual problem here, and referees have otherwise been very supportive to our work, we
expect that the manuscript will now be accepted for publication in Nature Communications. Please do not hesitate
to contact us should we improve anything else in the presentation, since we would like to avoid any further delay.
Sincerely yours,
Authors
Responses to Recommendation and Comments of the Secon Referee
Recommendation
I think that the Authors have done their best to revise the manuscript, trying to respond to all comments raised by
the Referees.
Our response
We thank the referee for acknowledging our effort. We are very pleased to have suitably covered the issues raised
in the first round of refereeing.
Comment 1
However I still believe that there is one relevant issue which still needs to be clarified, connected with one
comment that both referees have raised (comment 1 of the first referee, comment 3 of the second referee).
When somebody mentions a Josephson vortex in a Josephson junction, the reader expects that the Josephson
current will pass through the barrier carrying phase information. In this manuscript (see Fig. 1 of the rebuttal
letter) supercurrent seems to flow only through the pillars (it is very very hard to believe that a supercurrent in
presence of an available superconducting short would prefer to flow through a tunnel barrier! Where would be
the Josephson vortex generated? ....). As a consequence it is very hard to understand how much phase
information will be transferred in these conditions.
Therefore the new physics has to be better explained and better justified.
Our response
As we have explained in the manuscript (section Methods) our approach can describe both supercurrents flowing
through the pillars and Josephson tunnel currents flowing across the junction. The current flowing through the
pillars is always larger in magnitude than the Josephson current alone, and therefore the Josephson current was
not clearly visible in Figs. S2 and S3 in the supplemental materials (see also Fig. 1 below).
To see the distribution of the Josephson current in the system, we plotted in Fig. 2 of this reply the vector plots of
the supercurrent density in a vertical plane not crossing the pillars (see the contour plots of the Cooper-pair
density in the column of Fig. 2). Color plot in panel 1 clearly shows the presence of the Josephson currents across
the junction. Note that global circulation of the supercurrent in this plot is due to the Meissner response of the
system to the applied magnetic field. The current distribution changes considerably when the Josephson vortices
are present in the system (see panels 2 and 3, where the vector plots of the supercurrent are superimposed onto the
contourplot of the phase of the order parameter for facilitated view of the vortex position).
As was mentioned by the referee, the Josephson current should carry phase information across the junction. To
show that our approach can describe such a phase transfer, we plotted in panels (a) and (b) of Fig. 3 below the
̅ (where  is the phase of the order parameter obtained in our simulations and
phase difference ∆θ = θt − θb − δA
indices “t” and “b” indicate to bottom of the top layer and top of the bottom layer, respectively) along the junction
in a plane not crossing the pillars (see the right column, where we present the isosurface plots of the Cooper-pair
density) when a single vortex is present in the system. A clear 2 change of the phase of the order parameter is
seen in these plots due to the vortex. Filled circles in panels (a) and (b) show the calculated Josephson current
(referred to left axis) with (a) and without (b) the presence of applied current. The shape of the vortex current is
slightly different in the presence of the applied current (panel (a)) than the one without the applied current (panel
(b)). Solid blue and solid yellow curves in panel (b) shows the fitting curves for ∆𝜃 and j using the following
Josephson relations: ∆𝜃 = ⁡4atan(𝑒𝑥𝑝[(𝑦0 − 𝑦)/𝜆𝐽 ]) and 𝑗 = 𝑗𝑐 sin⁡{4atan(𝑒𝑥𝑝[(𝑦0 − 𝑦)/𝜆𝐽 ])}, where 𝑦0 =
61.5, 𝜆𝐽 = 4.2 and 𝑗𝑐 = 0.0622. It is seen from this figure that our simulations results can be well described by
the well-known Josephson relations. Small deviation of the fitting curves from the simulation results is due to the
Meissner current, which are not taken into account in the above expressions for the phase difference and
Josephson current.
Panels (a’) and (b’) show the results for the plane crossing the pillars (see the right column). A phase drop by 2
is observed even in this cross section although the shape of the Josephson current is different in this case due to
the presence of pillars.
We are very grateful to the referee for this useful comment, since it allowed us to add important discussion about
the Josephson current in the paper. Figure 3 below is made available to the readers as Supplementary Figure 4.
Comment 2
In the present form, there are still a few misleading aspects. I think it might be also useful to insert in the text a
few formulas where the reader can understand how the energy terms play with clear reference to the phase.
Our response
In the current version of the manuscript we discuss the direct relation of our boundary conditions to the standard
relations of Josephson current and Josephson energy and the phase of superconducting order parameter. The
requested equations can be found in the Methods section.
Conclusion
The manuscript cannot be accepted in the present form.
Our response
We thank the referee once again for his/her useful comments and suggestions. There is no conceptual difference
in opinion between us and the referee, and we have solved the misunderstanding pointed out by the referee. We
presented additional and convincing results, and improved the presentation of the results. We therefore expect that
our revisions are satisfactory and that the referee will recommend our work for publication in Nature
Communications.
Brief list of made changes in the manuscript
The main changes include:
1) Improvements in the abstract and the last paragraph of the introduction, according to Editorial request.
2) Added equations and discussion about Josephson current in the Methods section.
3) Reformatting of the Supplementary Material according to Editorial request; added Supplementary Figure
4, to accommodate the last remarks of the referee.
4) Minor changes in the figures, figure captions, references, and referrals to Supplementary Materials,
according to Editorial request.
Figure 1. Top panel: An example of the voltage vs. time characteristics of the sample (of size L=100ξ, w=100ξ,
d=5ξ and δ = 1ξ) for in-plane magnetic field H = 0.01Hc2 and applied current j = 0.052j0. The size of the pillars
is R = 9ξ. Panels 1-4: (left column) Supercurrent distribution inside the sample at different times (indicated on
the V(t) curve). In panels 2-4 the supercurrent distribution is superimposed on the contourplot of the phase of the
order parameter. (right column) Isosurface plots of the Cooper-pair density (taken isovalue is 30% of |ψ|2max , i.e.
dark blue color outlines the vortex cores) at times indicated on the V(t) curve. The shaded z-y plane is chosen to
plot the current distribution and the phase of the order parameter on the right panels.
Figure 2. The same as in Fig. 1 above, but the current distributions and the phase of the order parameter are
plotted in a z-y plane not crossing the pillars (see panels on the right).
Figure 3. Top panel: An example of the voltage vs. time characteristics of the sample (of size L=100ξ, w=100ξ,
d=5ξ and δ = 1ξ) for in-plane magnetic field H = 0.01Hc2 and applied current j = 0.052j0. The size of the pillars
is R = 9ξ. Panel (a): the Josephson current across the junction (filled black circles, referred to left axis) and the
phase difference ∆𝜃 = ⁡𝜃𝑡 − 𝜃𝑏 − 𝛿𝐴̅ (open red circles), in the plane depicted on the right in the isosurface plots
of the Cooper-pair density, as a function of the y-coordinate. Here  is the phase of the order parameter and
indices “t” and “b” denote the bottom of the top layer and the top of the bottom layer, respectively (see the
manuscript for the definition of 𝐴̅). Panel (b): the same as in panel (a) but when the current was switched off (see
the main panel for points (a) and (b)). Solid blue curve is the fit for∆𝜃 using ∆𝜃 = ⁡4atan(𝑒𝑥𝑝[(𝑦0 − 𝑦)/𝜆𝐽 ]),
where 𝑦0 = 61.5 and 𝜆𝐽 = 4.2. Solid yellow curve is the fit for the current density using 𝑗 =
𝑗𝑐 sin⁡{4atan(𝑒𝑥𝑝[(𝑦0 − 𝑦)/𝜆𝐽 ])} with 𝑗𝑐 = 0.0622. Panels (a’) and (b’): the same as in panels (a) and (b), for
currents and phase plots in the plane crossing the pillars (see panels on the right column).