Superconductivity is the foundation for modern quantum coherent phenomena in solid-state systems, enabling topological quantum bits, Weyl physics, and macroscopic quantized phenomena. The activation of quantum mechanical phases as degrees of freedom in superconducting multi-terminal structures allows for the realization of complex, topological non-trivial states of matter. This includes Berry spectroscopy of Weyl-Andreev nodes in synthetic dimensions, fractional states of matter of Cooper pair networks, and high-dimensional topology like the Second Chern number with a non-Abelian Berry phase. The talk will discuss theoretical and experimental advancements in realizing effects in spectroscopy, critical currents and quantized transconductance.
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