The conductivity of Kitaev’s chain

Abstract

In 2001, Alexei Kitaev proposed a 1D model for spinless fermions that hosts non-local (spatially separated) Majorana fermions as zero-energy modes. The Kitaev model corresponds to a tight-binding p-wave superconductor which has two phases, a trivial one and a topological. It’s doubly degenerate ground state is responsible for non-Abelian exchange statistics among the Majorana fermions hosted. The non-Abelian exchange statistics nature of Majoranas and their zero-energy “cost” existence make them an ideal candidate for qubits. As qubits they may build a topological quantum memory that is protected from decoherence. The current thesis consists of two main parts. In the first one, we investigate the ground state of the model in several representations, in order to understand it’s nature. In the second part, we couple Kitaev's model to Fermi gas reservoirs and calculate it's conductivity using non-equilibrium Green’s functions.