Topological Phases, Majorana Modes, Dynamics and Transport in One-Dimensional Systems

Abstract

This thesis presents work done on topological phases, Majorana modes, dynamics and transport in various system like the Kitaev models in one and two dimensions and systems with junctions of a p-wave superconductor and normal metal leads in one dimension. The systems we have studied are a one-dimensional spin-1/2 model placed in a transverse magnetic field [1,2], a lattice model of spinless electrons with p-wave superconductivity (Kitaev chain) [3,4], the Kitaev model of spin- 1/2’s placed on the sites of a honeycomb lattice [5], and continuum and lattice models of one-dimensional systems with junctions of a p-wave superconductor and normal metal leads [6].