Masters defense: Esben Bork Hansen
Unpaired Majorana Fermions in Disordered p-wave Superconductor and Random Matrix Theory
Hamiltonians describing topological insulator and superconductor systems can like random matrices ensembles from random matrix theory be classified into the ten Altland-Zirnbauer symmetry classes. Hamiltonians which exhibits a number of unpaired zero-energy Majorana states share symmetry class with a random matrix ensemble with an equal number of zero eigenvalues. In this thesis, we show that a one-dimensional p-wave superconductor Hamiltonian is able to host unpaired Majorana bound states. Two numerical models of the p-wave Hamiltonian are presented, and disorder effects on the the Majorana bound states are examined. We show that the p-wave Hamiltonian belongs to the BDI symmetry class and attempt to design an equivalent random matrix description of the Majorana physics. We observe a compelling similarity between the average spectral density of the p-wave models and the proposed random matrix models. We believe it is possible to eliminate the remaining discrepancies by finding a more suitable random matrix model.