Green's function and density of states of bounded P-wave superconductors

Official URL: https://risc01.sabanciuniv.edu/record=b2711502_(Table of contents)

In this thesis, we consider the density of states of bounded chiral p-wave superconductors, particularly focusing on the available Majorana edge modes. Majorana edge modes are among the candidates for developing structures for braiding operations and hence realizing topological quantum computers. The main aim of this thesis is to develop a novel analytical machinery to describe these Majorana edge modes in p-wave superconductors. To this end, we adopt the Multiple Reflection Expansion method developed by Balian and Bloch for the Green’s function of the Helmholtz wave equation and extend this method to the Green’s function of a chiral p-wave superconductor. We thus obtain an analytical expression of the Green’s function near the edge of a chiral p-wave superconductor, analytically calculate the quasiparticle density of states and find signatures of the Majorana edge modes.