University of Twente Student Theses


Topological Insulators: Tight-Binding Models and Surface States

Vliet, Mick van (2019) Topological Insulators: Tight-Binding Models and Surface States.

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Abstract:Topological insulators are relatively recently discovered phases of quantum matter which have exotic electronic properties that have attracted an enormous amount of theoretical and experimental interest in the field of condensed matter physics. They are characterized by being electronically insulating in the bulk, while hosting topologically protected surface or edge states, where the electrons behave like massless particles. The presence of a topological insulator phase is encoded in a topological invariant taking values in Z2, referred to as the Z2-index. We compute the Z2-index of bismuth selenide (Bi2Se3) using two different methods. Subsequently, the presence of surface states in Bi2Se3 is investigated using the method of surface Green’s functions. The results confirm that this material is a topological insulator. The relation between the Z2-index and the existence of surface states is described by a result called the bulk-boundary correspondence, and a proof of this result is reviewed
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics, 33 physics, 51 materials science
Programme:Applied Mathematics BSc (56965)
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