In contrast to a normal metal, in a superconductor, the charge is carried by a pair of electron or hole excitations. Because of that, new phenomena happen on the interface between a normal metal and a superconductor. Electrons and holes make closed trajectories at specific energies corresponding to Andrew Bound states. As free particles, electrons of the normal metal occasionally enter the superconductor and take its shadow electron with them, leaving a hole as a result. Symmetrically the same happens with holes. The energies of this process depend on superconductor order parameters which also determine the supercurrent between SNS sandwiches as in Josephson junction and multi-terminal superconducting junctions. The later ones can be tuned to two Andrew Band crossings (Weyl points), manifesting in a quantised transconductance.
However, the life of an experimentalist is challenging. The tuning of phases could be affected by quantum fluctuations of the superconductor phase due to always present capacities and nonuniform superconductor order parameter distribution in bulk. To model such a problem, we promoted superconducting phases near the Weyl point as dynamical variables and coupled them with external phases by a concave potential. What we found surprised us: in a soft constraint limit (when the fluctuations in phase can be large), two of three directions (in the space defined by superconducting phases) become almost degenerate, forming subspaces in place of Weyl points, which we call Weyl Discs Erdmanis & Lukacs & Nazarov (2018) (with Julia code in here).
A fascinating application of one such subspace would be in quantum computation. A qubit of Andrew-bound states in the Josephson junction was demonstrated by Urbina et al. (2015) where excitation of the state and readout had already been developed. The Weyl discs, in addition, would allow us to perform holonomic computation by changing external superconductor phases and collecting Berry phases. Particularly one could consider a circular orbit on the disc. Due to Berry's curvature, a phase difference would be acquired between the states. Due to the mixing of the lowest levels, the basis (between which a relative phase would be acquired) would depend on the angular velocity Aharanov & Anandan (1986). This effectively allows us to implement any rotation in the Bloch sphere and any single qubit gate (that follows because the time dependence of the Weyl disc Hamiltonian for circular orbit can be factored out as exponentials acting on a time-independent part). However, it is still unknown how effective (for example, how many Rabbi oscillations one could expect to get) the phase difference collection would be compared with parametric noise (which would also affect decoherence time).