Theory of topological insulators and its applications
Abstract
An important pursuit in semiconductor physics is to discover new materials to sustain the continuous progress and improvements in the current electronic devices. Traditionally, three material types are in use: 1) Metals 2) Semiconductors 3) Insulators. All the three material types are classified according to the energy gap between conduction and valence bands derived from band theory of solids. Recent theoretical predictions and confirmed by experimental observations have provided evidence that there exists materials which behave as insulators in the bulk but possess gapless conducting states on the surface. These new class of materials are called topological insulators (TI). In this work, the electronic structure of TIs would be explained specifically answering the two important questions: 1) What distinguishes a topological insulator from a normal insulator? 2) Why topology is related to the study of insulators? This thesis examines HgTe and Bi2Te3 as 2D and 3D TIs respectively. Design principles for utilizing HgTe based 2D TIs as a switch and tuning the critical width is explained. Further the surface states, which are the counterpart of the edge states in a 3D TI depend on thickness of the film, orientation, inequivalent surface termination, spin-momentum locking etc. Using a four-band k.p model, some of these features are investigated. Further, peculiarities in the electronic structure of TIs do not allow classical methods of band structure calculation possible. A new approach which does not distinguish between electrons and holes will be presented that efficiently computes the self-consistent band structure of Tis within the semi-empirical tight binding model. Almost all known topological insulators are a direct outcome of strong spin-orbit coupling. As a break of this trend, wurtzite based nitrides are shown to possess 2D topological insulator states. The strong internal polarization of wurtzite crystal is used to invert the bands and create a 2D TI. As an application of TIs, the current-voltage characteristics of a Bi2Te3 transistor that utilize the highly mobile surface states are simulated. The characteristics show that in addition to high mobility, it also offers a low-power option for designing a transistor in a fast switching environment. Additionally, a comparison between the I-V characteristics of silicon and graphene ultra-thin bodies further demonstrate the low-power utility of such devices. Difficulties with a transistor that operate exclusively with TI surface states are also highlighted. In the last part of the work, topological insulator nanostructures are considered. In particular, TI nanowires and nanoribbons which distinctly exhibit various manifestations of well-established phenomenon in condensed matter physics such as AB and SdH oscillations, WAL, Kondo effect etc. are studied. The influence of an external magnetic field on surface states is also discussed. Finally, the proximity effect of superconductors that induce a band gap opening in a TI-SC heterostructure is computed with a modified form of the BdG Hamiltonian.
Degree
Ph.D.
Advisors
Klimeck, Purdue University.
Subject Area
Electrical engineering|Computer science
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