# A proposal to extract and enhance four-Majorana interactions in hybrid nanowires

### Submission summary

 Authors (as Contributors): Sergey Frolov
Submission information
Arxiv Link: https://arxiv.org/abs/2110.04778v2 (pdf)
Date accepted: 2022-10-14
Date submitted: 2022-05-24 23:28
Submitted by: Frolov, Sergey
Submitted to: SciPost Physics
Ontological classification
Specialties:
• Condensed Matter Physics - Theory
• Condensed Matter Physics - Computational
Approaches: Theoretical, Computational

### Abstract

We simulate the smallest building block of the Sachdev-Ye-Kitaev (SYK) model, a system of four interacting Majorana modes. We propose a 1D Kitaev chain that has been split into three segments, i.e., two topological segments separated by a non-topological segment in the middle, hosting four Majorana Zero Modes at the ends of the topological segments. We add a non-local interaction term to this Hamiltonian which produces both bilinear (two-body) interactions and a quartic (four-body) interaction between the Majorana modes. We further tune the parameters in the Hamiltonian to reach the regime with a finite quartic interaction strength and close to zero bilinear interaction strength, as required by the SYK model. To achieve this, we map the Hamiltonian from Majorana basis to a complex fermion basis, and extract the interaction strengths using a method of characterization of low-lying energy levels and then finding the differences in energies between odd and even parity levels. We show that the interaction strengths can be tuned using two methods - (i) an approximate method of tuning overlapping Majorana wave functions (without non-local interactions) to a zero energy point followed by addition of a non-local interaction, and (ii) a direct parameter space optimization method using a genetic algorithm. We propose that this model could be further extended to more Majorana modes, and show a 6-Majorana model as an example. Since eigenspectral characterization of one-dimensional nanowire devices can be done via tunneling spectroscopy in quantum transport measurements, this study could be performed in experiment.

Published as SciPost Phys. 13, 120 (2022)

### Author comments upon resubmission

Dear editors and referees,

We have expanded the paper and clarified several points. Please see replies to referees for details.

On the topic of the goal and impact of this work, we would like to clarify - this is not a proposal to implement an SYK model in nanowires. This is a proposal for a future experiment in which the strength of 4-Majorana terms can be extracted for tunneling data, and possibly enhanced, relative to two-Majorana interaction terms. The paper introduces quantities that relate to interaction strengths.

What the paper does not do is study all conditions for the realization of the large N SYK model. This is not the value of this work. Not every paper must do that. There are many important questions to ask and explore that are not full SYK demonstration pathways. The question of how to study interacting Majorana modes is an important one. The proposal paper like this one opens path for future experiments, hence it satisfies SciPost Physics acceptance criteria.

### List of changes

1) Clarified motivation - not full SYK but study interactions

2) Performed additional simulations of tuning via other Kitaev model parameters, rather than the interaction strength U

3) Created a section on the experimental protocol for tunneling experiments

4) Added a figure with a two-wire design which can help enhanece the 4-Majorana term that is non-local

5) Addressed other referee questions

### Submission & Refereeing History

Resubmission 2110.04778v2 on 24 May 2022
Submission 2110.04778v1 on 1 November 2021

## Reports on this Submission

### Anonymous Report 2 on 2022-10-10 (Invited Report)

• Cite as: Anonymous, Report on arXiv:2110.04778v2, delivered 2022-10-10, doi: 10.21468/SciPost.Report.5867

### Report

The Authors clarified their goal to engineer, tune, and characterize the four-Majorana zero modes (MZM) interaction in the nanowire devices rather than to build the SYK model in a condensed matter platform. The Introduction section was updated accordingly.
In the conclusive Section VII the Authors state that ''... it is indeed possible to design a low $N_γ$ (particularly $N_γ = 4, 6$) SYK model in a 1D nanowire system. It might be possible to extend this model to a $N_γ > 6$ system in future work.'' I believe it would be beneficial for readers to reinstate the initial goal to characterize and control the four-MZM interaction in this Section and specify that achieving scalability for the large-$N$ regime and random character of the SYK interaction is not a part of the paper.
I think the Authors addressed my questions adequately, and I recommend the paper for publication in SciPost.

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### Report

The authors have satisfied my questions, and I recommend publication.

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