Higher-dimensional topological solids realized with multiterminal superconducting junctions

Project Information

HITSUPERJU

Grant agreement ID: 694272

DOI

10.3030/694272

Project closed

EC signature date 16 June 2016

Start date 1 August 2016

End date 31 July 2021

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 522 810,00

EU contribution

€ 1 522 810,00

Coordinated by

TECHNISCHE UNIVERSITEIT DELFT
Netherlands

Periodic Reporting for period 4 - HITSUPERJU (Higher-dimensional topological solids realized with multiterminal superconducting junctions)

Reporting period: 2021-02-01 to 2021-07-31

Summary of the context and overall objectives of the project

The project aim is to bring higher artificial dimensions to the use in electronic devices, in the context of multi-terminal superconducting nano-structures. The physical basis for this is that the quantum states in the nano-structure with N terminals depend periodically on the superconducting phase differences in full similarity with a bandstructure of a hypothetical N-1 dimensional material. In most research, we concentrated on magic topologically stable points, Weyl points, where the energy bands cross at zero energy in a 4-terminal nanostructure. The points are manifested in a topologically quantized transconductance. The research in this project addressed theoretically a wide set of topics related to topological singularities, and the role of quantum fluctuations in the nanostructure. We managed to come up with concrete device proposals and address experimentally relevant setups.

In conclusion, we have proven the potential of multi-terminal superconducting nanostructures as nanodevices. The field is rich with very interesting theoretical ideas and proposals, that are ready for experimental realization.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

We have revealed drastic effects of weak interaction on the properties of superconducting nanostructures with topological components. We did it in two complementary limits: 1. discrete spectrum of Andreev states, where we have discovered Weyl disks: degenerate manifolds in the vicinity of the Weyl points 2. continuous spectrum, where the topological protection was shown to fail in the vicinity of the special point .We have analysed quantum superpositions of topologically distinct manifolds, and determine the governing topological numbers. We have found the effects of continuous spectrum on topological for gapped (Phys. Rev. B 99, 165414 (2019)) and ungapped spectrum . We have the abundance of closely spaced Weyl points in generic semiclassical nanostructures.
We have proposed several novel device setups: spin-Weyl quantum unit that is a non-trivial combination of spin and Andreev qubit, Weyl point based minimal spintronic device ,holonomic quantum computation setup based on discovery of Weyl disks.
Concentrating on the experimentally realized setups, we have addressed superconductor-seminconductor nanowires that are now in focus of experimental attention in view of Majorana applications. As a highlight, we propose a scheme to perform braiding and all other unitary operations with Majorana modes in 1D wire (rather than in 2D) that is solely based on resonant manipulation. We have proven the emergence of Weyl points in these topological nanowires and investigated the non-trivial microscopic mechanisms of the Andreev states overlap.

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The discovery of Weyl disks and the drastic effect of weak interaction in semiclassical nanostructures are significant advances beyond the state of the art in this emerging field. These discoveries are interrelated and complimentary addressing the limits of discrete and quasi-continuous spectrum. Both concern the topological singularities of different kinds and show that a weak interaction that can be safely ignored far from topological singularity results in qualitative modification of all properties in the small vicinity of a singularity. So that the interaction can never be ignored in the presence of topological singularities.

The Weyl disk in the parameter space