We propose an exemplary 4-terminal superconducting structure where 4 chaotic cavities are connected by QPCs to the terminals and to each other forming a ring.
The device would provide a practical and comprehensive realization of three distinct topologies that have been recently proposed to explain the properties of the complex energy spectrum of Andreev bound states.
Topology of the first kind is related to the winding of the semiclassical Green's function. It is responsible for the proximity gaps. Topology of the second kind comes about the discreteness of the number of modes and is responsible for the smile gaps. The third topology is manifested in Weyl conical points at Fermi level.