Masters Defense: Mathias Rosdahl Jensen

In this thesis, we give a thourough investigation of the basic physics of bismuth selenide, a recently discovered three-dimensional topological insulator. We give a detailed and pedagogical introduction to group theory, describing the symmetry operations of the crystal lattice, in order to construct the minimal effective model, describing the topological features of bismuth selenide. Qualitatively, we discuss the physical principles of the band structure around the Fermi level, which is found to consist of linear combinations of p-orbitals. Specifically, we see that a strong spin-orbit coupling leads to a band inversion. This band inversion gives rise to a non-trivial topology. Within this model, we calculate the topological surface states by imposing hard-wall boundary conditions. For a single isolated surface we find the conditions on the parameters of the model, for the existence of surface states. We analytically find the spectrum and wave functions of the surface states. These have a Dirac-like spectrum, and a helical spin structure. In a thin film, the overlap of wavefunctions on opposite surfaces, leads to a gap in the spectrum. We discuss the dependence of the gap on the thickness, as well as the parameters of the model and compare to experimental measurements of the gap. For a thin film, the spin structure is dependent on position. The helical spin structure, gets opposite vorticity on the two surfaces, which is a result of the inversion symmetry of the crystal.