**Speaker**: Stephanie Goertzen

**Location**: Physics 175

**Time**: 3:30, August 14 2014

**Abstract**: Recently, the discovery of a new class of materials called topological insulators has stimulated much excitement in the field of condensed matter physics. Their discovery has also begun the search for the exotic topological superconductor – a superconductor whose properties are protected by topology. A novel feature of such topological superconductors is the possible existence of the Majorana fermion as an elementary excitation. Traditionally, the Hamiltonian of the system is directly diagonalized in order to calculate the mean-field potentials. However this method is very computationally expensive and is widely regarded as impractical. As such, we make use of two efficient numerical algorithms that have recently been developed in order to self-consistently solve the Bogoliubov-de Gennes equations. The first is Chebyshev polynomial expansion which allows us to bypass directly diagonalizing the Hamiltonian and the second is the Sakurai-Sugiura (SS) method for efficient computation of eigenvalues and eigenvectors. Armed with this combination of techniques, we aim to investigate two-dimensional topological superconductivity.