# Josephson junctions of topological nodal superconductors

### Submission summary

 As Contributors: Dganit Meidan · Ranjani Seshadri Preprint link: scipost_202204_00032v1 Date accepted: 2022-05-09 Date submitted: 2022-04-19 15:19 Submitted by: Seshadri, Ranjani Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Approach: Theoretical

### Abstract

Transition metal dichalcogenides (TMDs) offer a unique platform to study unconventional superconductivity, owing to the presence of strong spin-orbit coupling and a remarkable stability to an in-plane magnetic field. A recent study found that when an in-plane field applied to a superconducting monolayer TMD is increased beyond the Pauli critical limit, a quantum phase transition occurs into a topological nodal superconducting phase which hosts Majorana flat bands. We study the current-phase relation of this nodal superconductor in a Josephson junction geometry. We find that the nodal superconductivity is associated with an energy-phase relation that depends on the momentum transverse to the current direction, with a $4\pi$ periodicity in between pairs of nodal points. We interpret this response as a result of a series of quantum phase transitions, driven by the transverse momentum, which separate a topological trivial phase and two distinct topologically non-trivial phases characterized by different winding invariants. This analysis sheds light on the stability of the Majorana flat bands to symmetry-breaking perturbations.

Published as SciPost Phys. 12, 197 (2022)

We hereby resubmit the manuscript "Josephson junctions of topological nodal superconductors"
by Ranjani Seshadri, Maxim Khodas and Dganit Meidan to Scipost Physics.

We thank the referees for their careful reading of our paper and all the constructive comments,
to which we have submitted our responses.

We have now made a few changes in the paper following the questions and comments from the referees.
These are mentioned in the List of Changes.

### List of changes

The following is a section-wise list of changes we have made to the manuscript.

1. The format is now changed from two column to one column

Sec I
1. We have now added a sentence mentioning the importance of Josephson junctions to study the current phase relation
where we refer to the newly added references 36 and 37.
2. A typo (in-plain) has now been corrected to in-plane.

Sec II
1. Fig 1 has now been changed to provide a better viewing angle as suggested by the referee.

Sec III
1. Fig 3 has been modified and we have now indicated the different topological/non-topological regions.

Sec IV
1. Following the comments from the referee, we have now added a paragraph summarizing the method of
calculating the Josephson energies (before Eq. 12) .

Sec V
1. Fig 5 has now been changed so the the different curves corresponding to the energies and currents
in different topological regimes can now be distinguished more easily.

Appendix C
1. Fig 8 has now been changed so the the different curves corresponding to the energies and currents
in different topological regimes can now be distinguished more easily.

References
1. We have now added references 36 and 37.

### Submission & Refereeing History

Resubmission scipost_202204_00032v1 on 19 April 2022
Submission 2201.11514v1 on 2 February 2022

## Reports on this Submission

### Report

In their response the authors have clarified all the issues that I have raised. I recommend this paper for publication.

• validity: -
• significance: -
• originality: -
• clarity: -
• formatting: -
• grammar: -

### Report

The authors have addressed all the questions raised before. Here I can recommend the publication of the manuscript in SciPost.

• validity: high
• significance: good
• originality: good
• clarity: high
• formatting: good
• grammar: excellent