NBIA Condensed Matter Theory Seminar: Graham Kells – University of Copenhagen

NBIA Condensed Matter Theory Seminar: Graham Kells

I will discuss how networks of topological nanowires can realize the physics of exactly solvable Kitaev spin models with two-body interactions. This connection arises from the description of the low-energy theory of both systems in terms of a tight-binding model of Majorana modes. In Kitaev spin models the Majorana description provides a convenient representation to solve the model, whereas in an array of topological nanowires it arises, because the physical Majorana modes localized at wire ends permit tunnelling between wire ends and across different Josephson junctions. We  show that an array of junctions of three wires -- a setup relevant to topological quantum computing with nanowires -- can realize the Yao-Kivelson model, a variant of Kitaev spin models on a decorated honeycomb lattice. Translating the results from the latter,  I will argue that the network could be constructed to give rise to collective states characterized by Chern numbers \nu = 0, +/-1 and +/-2, and that defects in an array can be associated with vortex-like quasi-particle excitations.  I will also discuss the stability of the collective states  and the implications this has for the network as a quantum information processor. In particular I will show that decoherence inducing instabilities,  can be understood in terms of proliferation of the vortex-like quasi-particles of the associated Toric-Code model.