Bachelor Defense: Peter Tunstall – University of Copenhagen

Bachelor Defense: Peter Tunstall

The Shockley Model for Topological Insulators

In this thesis, the Shockley model for topological insulators is used to analyze
the properties of localized edge states in a 1D system. This was done by deriving
analytical solutions to bulk- and boundary states, and comparing these with
numerical calculations. The relation between the existence of zero-energy edge
states and topological properties of the bulk Hamiltonian is described, and finite
size effects are characterized. The 1D model is generalized to 3D, where spin is
now taken into consideration by adding a Rasha spin-orbit coupling term. The
energy spectrum and wavefunctions are derived, and as an example, the model is
used for a diamond lattice structure. Lastly, the concept of topological invariants
is illustrated and its usage for determining which materials can be topological
insulators is discussed.

Notice: The defense is in Danish.