Condensed Matter Physics Seminar

We consider a 2D array of superconducting islands with semiconducting nanowires featuring Majorana fermions. We discuss how to control their overlap with Coulomb interactions rather than tunneling. We show that the fermionic Hamiltonian modeling this system is topologically-ordered in a region of parameter space. In particular, we show that Kitaev's toric code emerges in fourth-order perturbation theory. By using a Jordan-Wigner transformation we can map the model onto a family of signed 2D Ising models in a transverse field where the signs (FM or AFM) are determined by additional gauge bits. Our mapping allows an understanding of the non-perturbative regime and the phase transition to a non-topological phase.