# Shot noise distinguishes Majorana fermions from vortices injected in the edge mode of a chiral p-wave superconductor

### Submission summary

 Authors (as Contributors): Carlo Beenakker
Submission information
Date accepted: 2020-11-13
Date submitted: 2020-10-28 22:39
Submitted by: Beenakker, Carlo
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
Approach: Theoretical

### Abstract

The chiral edge modes of a topological superconductor support two types of excitations: fermionic quasiparticles known as Majorana fermions and $\pi$-phase domain walls known as edge vortices. Edge vortices are injected pairwise into counter-propagating edge modes by a flux bias or voltage bias applied to a Josephson junction. An unpaired edge mode carries zero electrical current on average, but there are time-dependent current fluctuations. We calculate the shot noise power produced by a sequence of edge vortices and find that it increases logarithmically with their spacing - even if the spacing is much larger than the core size so the vortices do not overlap. This nonlocality produces an anomalous V log V increase of the shot noise in a voltage-biased geometry, which serves as a distinguishing feature in comparison with the linear-in-V Majorana fermion shot noise.

Published as SciPost Phys. 9, 080 (2020)

We thank both referees for their reports and their favorable recommendation. In response to the reports we have revised the manuscript as detailed below.

### List of changes

In response to the first referee:

1. The edge vortices are mobile: Since the pi-phase domain wall on the edge is pinned to the fermionic degrees of freedom, edge vortices propagate with the same velocity as the Majorana fermions. We stress this key point in the fourth paragraph of the introduction.

2. We have clarified that "inelastic scattering" means "energy-nonconserving scattering".

3. Below equation (2.2) we now note that the energy differences are integer multiples of the driving frequency for a periodic time dependence.

4. The phrase "when the incoming modes are in thermal equilibrium" has been added directly below equation (2.2).

5. D_M has been replaced by D.

6. We have rephrased the discussion above equation (3.8) to avoid the confusion between different meanings of the words "energy dependence".

7. We did not find a natural place to insert a comparison with multiple Andreev reflections.

8. The word "adiabatic" is replaced by "frozen" above equation (4.3).

9. Concerning the logarithmic increase of the charge noise with increasing detection time t_det: This holds as long as the product of t_det/ħ and kT is smaller than unity. At nonzero temperature this product will exceed unity as t_det becomes larger and larger, and then we expect the logarithmic increase to cross over into a linear increase. We have added this to appendix D (last paragraph).

10. The condition of validity of equation (5.4) has been added in equation (5.5).

11. A constant shift in the phase differences across the two Josephson junctions changes the effective separation of the injected vortices. We point this out in a footnote just below equation (E.1) and note that such a shift can be avoided by ensuring that the superconducting phase in the two leads has the same value, fixed by a ground contact to a bulk superconductor.

In response to the second referee:

We are indeed referring to two different devices in Fig. 1a and 1b, the two injection processes need different elements (a Josephson junction versus an STM tip). We have added a comment on this just before equation (5.3).

### Submission & Refereeing History

Resubmission scipost_202010_00027v1 on 28 October 2020
Submission 2009.14173v1 on 30 September 2020

## Reports on this Submission

### Report

The manuscript is now suitable for publication in SciPost.

• validity: -
• significance: -
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### Report

I am satisfied with the revisions and with the authors' response. I enthusiastically recommend publication.

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