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Multi-Terminal Josephson Junctions as a novel platform for high dimensional topological matter

Periodic Reporting for period 1 - TopoInMulTermJJ (Multi-Terminal Josephson Junctions as a novel platform for high dimensional topological matter)

Reporting period: 2017-10-01 to 2019-09-30

Josephson junctions host so-called Andreev bound states. As has been shown recently, the spectrum of Andreev bound states in an N-terminal Josephson junction as function of the superconducting phases can be viewed as a pseudo-bandstructure in N-1 dimension. This pseudo-bandstructure may have interesting topological properties. However, many questions concerning the characterization, classification, and manipulation of the topological states in multi-terminal Josephson junctions are still open. The objective of the project was to further explore this novel platform for topological matter.
In the beginning of the project, general properties of multi-terminal Josephson junctions were investigated. Furthermore, it was shown that coupling two 3-terminal junctions via a common superconducting island makes it impossible to reach the Weyl points that may be present in the Andeev spectrum of a single junction. This rules out one of the original ideas in the proposal.

Subsequently, the effect of Berry curvature on electronic transport was studied. While the appearance of a first Chern number can be seen in the first order perturbation correction to the adiabatic result, here a second order perturbation expansion was performed to explore whether new phenomena appear. The results still have to be applied to a concrete realization that would allow one to interpret them
The researcher is planning to continue the investigation on the last project after the end of the fellowship. The identification of a measurable quantity probing the higher order terms is expected to stimulate further activity in the research field of topological properties of matter.
Examples of geometric setups of Multi-terminal Josephson junctions