# Topological superconductivity in a phase-controlled Josephson junction

## Abstract

Topological superconductors can support localized Majorana states at their boundaries1,2,3,4,5. These quasi-particle excitations obey non-Abelian statistics that can be used to encode and manipulate quantum information in a topologically protected manner6,7. Although signatures of Majorana bound states have been observed in one-dimensional systems, there is an ongoing effort to find alternative platforms that do not require fine-tuning of parameters and can be easily scaled to large numbers of states8,9,10,11,12,13,14,15,16,17,18,19,20,21. Here we present an experimental approach towards a two-dimensional architecture of Majorana bound states. Using a Josephson junction made of a HgTe quantum well coupled to thin-film aluminium, we are able to tune the transition between a trivial and a topological superconducting state by controlling the phase difference across the junction and applying an in-plane magnetic field22. We determine the topological state of the resulting superconductor by measuring the tunnelling conductance at the edge of the junction. At low magnetic fields, we observe a minimum in the tunnelling spectra near zero bias, consistent with a trivial superconductor. However, as the magnetic field increases, the tunnelling conductance develops a zero-bias peak, which persists over a range of phase differences that expands systematically with increasing magnetic field. Our observations are consistent with theoretical predictions for this system and with full quantum mechanical numerical simulations performed on model systems with similar dimensions and parameters. Our work establishes this system as a promising platform for realizing topological superconductivity and for creating and manipulating Majorana modes and probing topological superconducting phases in two-dimensional systems.

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## Data Availability

The data that support the findings of this study are available within the paper and its Supplementary Information. Additional data are available from the corresponding author upon request.

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## Acknowledgements

This work is supported by the NSF DMR-1708688, by the STC Center for Integrated Quantum Materials under NSF grant number DMR-1231319, and by the NSF GRFP under grant DGE1144152. This work is also partly supported by the US Army Research Office and was accomplished under grant W911NF-18-1-0316. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. A.T.P. is supported by the US Department of Defense through the National Defense Science and Engineering Graduate Fellowship Program. The work at the University of Würzburg is supported by the German Research Foundation (Leibniz Program, Sonderforschungsbereich 1170 ‘ToCoTronics’; Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter, ct.qmat, EXC 2147, project 39085490), the EU ERC-AG programme (Project 4-TOPS) and the Bavarian Ministry of Education, Science and the Arts (IDK Topologische Isolatoren and ITI research initiative).

### Reviewer information

Nature thanks Kaveh Delfanazari and the other anonymous reviewer(s) for their contribution to the peer review of this work.

## Author information

Authors

### Contributions

The experiment is a collaboration between the Harvard and Würzburg experimental groups. A.Y. conceived the experiment and supervised the project. L.L., R.S. and L.W.M. grew the material. H.R., S.H. and A.T.P. fabricated the devices. H.R., S.H., A.T.P. and M.K. performed the measurements. H.R., F.P., B.S., E.M.H., B.I.H. and A.Y. carried out the theoretical modelling and analysis and prepared the manuscript and Supplementary Information.

### Corresponding author

Correspondence to Amir Yacoby.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

This file contains Supplementary Methods and Notes, including a table of contents at the beginning and a list of 22 Supplementary Figures. The display items contain further explanation of our experimental and analytical methods, raw and additional data to support the conclusions presented in the main text, as well as detailed theoretical discussions on our modeling of the current and future devices.

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Ren, H., Pientka, F., Hart, S. et al. Topological superconductivity in a phase-controlled Josephson junction. Nature 569, 93–98 (2019). https://doi.org/10.1038/s41586-019-1148-9

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