Master's Defense: Patrick Vendelbo Brouer
Yu-Shiba-Rusinov States in Multi-terminal Josephson Junctions
In recent years it has been proposed that multiterminal Josephson junctions can be used to model topological materials. This have been proposed using a scattering formalism involving Andreev bound states.
I will take this as an inspiration and examine a multiterminal Josephson junction involving a singly occupied Anderson impurity in a magnetic field coupling to N surrounding superconductors, in a Hamiltonian formalism. This will be done in the weak coupling limit by use of a Schrieffer-Wolff transformation.
Here I find an approximate Hamiltonian, for which I will find Yu-Shiba-Rusinov bound states and energies using a Bogoliubov-de Gennes formalism. From the energies I will find the ground state energy and show that all these live in a N-1 + 1 dimensional space of phase differences and a particle-hole asymmetry parameter.
I will show that all energies depend on a variable χ, which fully describe the behavior of the phase differences. I will then examine the symmetries which χ follow.
Lastly, I will find the supercurrent flowing in the junction for different phase differences and use this to construct a simple circuit which possibly can be used as a quantum bit.