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Report

Teaser, summary, work performed and final results

Periodic Reporting for period 2 - HITSUPERJU (Higher-dimensional topological solids realized with multiterminal superconducting junctions)

Teaser

Summary

The project aims to bring higher dimensions to the use in electronic devices, in the context of multi-terminal superconducting nano-structures. We live in 3D world, and the materials we synthesize seem to be 3D as well. The project accesses if one can make a usefull device that would work as if it is based on a multi-dimensional material. 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. The preliminary research gave a theoretical prediction of a magic topologically stable point, Weyl point, where the energy bands cross at zero energy in a 4-terminal superconducting nanostructure. The Weyl points are manifested in a topologically quantized transconductance. The research in this project addresses a wide set of topics related to higher-order topological singularities, the role of quantum fluctuations and ordering in charge space, quantum dynamics of the nano-structures in the context of devices that may be built with such multi-terminal nano-structures. The understanding of these phenomena will have a profound impact on the opportunities to engineer quantum structures for sensing and information processing applications.

Work performed

We have discovered Weyl disks: we have demonstrated theoretically that quantum fluctuations in semiclassical limit spread a singular Weyl point into a finite two-dimensional region in the parameter space. This interesting singularity enables new ways of quantum manipulation in superconducting nanostructures. In solids, the same concept result in unusual excitations that can propagate along a single direction only.
We have investigated the role of continuous spectrum on topological properties of the bandstructures inventing a novel theoretical method to access the contribution of infinitely many close-spaced quantum states. We have discovered that a non-quantized contribution to a quantity that previously was thought to be perfectly quantized, may emerge and be controlled by parameters of the nanostructure.
We have found an ideal setup that allows for necessary controls in multi-dimensional space of the superconducting phases: Two nano-structures housing Weyl points that are connected with a tunnel Josephson junction. We have proposed a setup that permits the interplay of spin and Andreev degrees of freedom in the vicinity of a Weyl point. The setup under consideration combines a superconducting nano-structure with a Weyl point and a quantum dot that can house an electron with spin. The hybridization of the states of the dot and the nano-structure will give rise to a spin-Weyl double qubit that promises the applications for quantum manipulations.

Final results

The discovery of Weyl disks and the invention of theoretical method for accounting the topological contribution of continuous spectrum constitute the progress beyond the state of the art.
We will continue our wide-spectrum research to identify the further manifestations of topology in multi-termnal superconducting nano-structures with the aim on possible device applications.