Bachelor Defense: Peter Tunstal – University of Copenhagen

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Bachelor Defense: Peter Tunstal

Title: The Shockley Model for Topological Insulators

abstract:

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.