## SciPost Submission Page

# Supercurrent-induced Majorana bound states in a planar geometry

### by André Melo, Sebastian Rubbert, Anton R. Akhmerov

### Submission summary

As Contributors: | Anton Akhmerov · André Melo |

Arxiv Link: | https://arxiv.org/abs/1905.02725v2 |

Date submitted: | 2019-06-06 |

Submitted by: | Melo, André |

Submitted to: | SciPost Physics |

Domain(s): | Theoretical |

Subject area: | Condensed Matter Physics - Theory |

### Abstract

We propose a new setup for creating Majorana bound states in a two-dimensional electron gas Josephson junction. Our proposal relies exclusively on a supercurrent parallel to the junction as a mechanism of breaking time-reversal symmetry. We show that combined with spin-orbit coupling, supercurrents induce a Zeeman-like spin splitting. Further, we identify a new conserved quantity---charge-momentum parity---that prevents the opening of the topological gap by the supercurrent in a straight Josephson junction. We propose breaking this conservation law by adding a third superconductor, introducing a periodic potential, or making the junction zigzag-shaped. By comparing the topological phase diagrams and practical limitations of these systems we identify the zigzag-shaped junction as the most promising option.

###### Current status:

### Submission & Refereeing History

## Reports on this Submission

### Anonymous Report 1 on 2019-7-2 Invited Report

### Strengths

1. Relates to a field of high current experimental and theoretical interest

2. Offers a new way to create a topological superconductor

3. Is written in a way that is accessible and useful also for experimentalists, and might inspire future experimental works

4. Uses an open source software and provides links to codes and parameters used in the paper

### Weaknesses

1. The numerics are not always supported with analytical or intuitive insights

2. The dependence of the results on the various different parameters remains unclear

3. The predicted superconducting gaps in the proposed systems are very small, which seriously limits the experimental relevance

### Report

The paper "Supercurrent-induced Majorana bound states in a planar geometry" is a theoretical proposal for realizing Majorana bound states (MBS) in planar Josephson junction devices, which relies entirely on using a supercurrent to break time-reversal symmetry (meaning that no external magnetic field is needed). The authors use a rather simple 2D model of a 2DEG partly covered by a superconductor and then discretize this and solve it as a tight-binding problem. They find that in the simplest geometry there is no gapped topological phase, and then investigate three different ways (adding a third superconductor, adding a periodic potential or making the Josephson junction zagzag-shaped) to break the symmetry and induce a topological phase. They scan the parameter space and calculate where a topological phase can be expected and give an estimate of the superconducting gap in the topological regions.

In short, I believe that the results are scientifically sound, the paper is well-written, and the work represents a substantial advance in a very active scientific field. The strengths and weaknesses, according to my opinion, are given above. In addition to these points, I have a few technical questions:

1. From the text after Eq. 1, I get the impression that the spin-orbit coupling is taken to be zero in the regions with direct superconducting proximity effect. Why? Would this region not just be the same 2DEG as elsewhere, but covered with a superconducting material?

2. On page 7, the authors say that they assume the same phase winding in the zigzag system as in the straight one. I guess this would be the result if the supercurrent density is unaffected by the zigzag pattern. Why, and under which circumstances, do the authors expect this to be a good approximation?

3. Related to weakness 3. above, on page 8 the authors write that the small superconducting gap is "likely due to a suboptimal choice of parameters". Why do they think so?

4. (Minor point) Why is the induced superconducting gap taken to be 1 meV? This seems rather large. Especially considering that they authors use the London penetration depth for Al in their estimate on page 9, and Delta for Al is much smaller.

### Requested changes

I think that my questions 1-4 in the report should be addressed and probably warrants some modifications to the paper. In addition, I think the paper would be improved by addressing the weaknesses 1-3 above. In particular, I think the paper would be greatly improved by additional physical (analytical and/or intuitive) insight into how the result depends on the different parameters. This might also hint at how the central problem for an experimental realization (the small gap) can be solved.