# Theoretical Physics

**14 January 2016**

**Time:**14:00 to 15:00

**Location:**QI

Internal Seminar: Kristian Patrick

Thursday, Jan 14, 2pm @ QI area

Abstract:

The Kitaev Chain with nearest neighbour hopping and pairing terms has been studied at detail, however, adding long range terms to the Hamiltonian complicates matters. I begin this talk by reviewing the short range case showing that edge modes are in fact zero energy modes exponentially localised at the edges. I consider the conditions required for an edge mode, aiming to reproduce the original results given by Kitaev [1]. I will then add infinite range hopping and pairing terms and, using a similar method to the short range case, find the energy of an edge state, show that it is exponentially localised at the edges and find the conditions required for edge modes.

[1] arXiv:cond-mat/0010440 Majorana fermions in quantum wires - Kitaev (2000)

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