The spectrum of Andreev bound states in N-terminal Josephson Junctions (MulTJJ) may be viewed as a pseudo-bandstructure of N-1 dimension Bloch electrons. As we recently showed this pseudo-bandstructure may have interesting topological properties. (i) Topological transitions between ground states with different fermion parity may occur in a 3-terminal JJ upon varying the superconducting phases. (ii) In 4- or more terminal JJs, the pseudo-bandstructure may display Weyl nodes, that entail a non-trivial 1st Chern number in a 2D plane in the space of SC phase differences and lead to a measureable quantized transconductance under DC-bias voltage.
However, questions concerning how to characterize, classify, and manipulate the topological states in MulTJJ are still open. The aim of this proposal is to continue to study this unexplored novel platform of topological matters.
We start to study approaches to measure and manipulate topological states of MulTJJ in several more complicated nanostructures. These structures are interesting because topological properties are expected to be easily detected in similar experimental setups. We hope to observe exotic phenomena such as quantized transconductance, non-trivial modifications to the supercurrent and to waiting times due to the Berry phase. Moreover topological states are proposed to be manipulated in a gate-bias controllable dynamical process in a non-adiabatic driven quantum dot.
We then propose to study the symmetry of MulTJJ in higher dimensions. In particular, we are interested in realizing a non-trivial 2nd Chern number, that would show up in the non-linear response of the system. For example we plan to study 6-/5-terminal JJ with/without time-reversal-symmetry in order to realize an analogue of the 4D quantum Hall effect. Finally, we seek to clarify the possible topological classes of MulTJJs.
At the end of our research, we expect to obtain insights in understanding the topological properties of MulTJJs.
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