Universität zu Köln

Legg, Henry ORCID: 0000-0003-0400-5370 (2019). Transport and disorder in Dirac materials. PhD thesis, Universität zu Köln.

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Abstract

The Dirac equation was able to unite relativity with quantum mechanics and successfully describe the behaviour of spin-1/2 particles. Over the past few decades it has been discovered that the electronic properties of many materials is also governed by emergent physics akin to that described by the Dirac equation, these materials are known a ``Dirac materials''. Often there is a deep connection between topology and the appearance of linearly dispersing electronic bands which result in a material's Dirac-like physics. In this thesis we will investigate the impact disorder has on Dirac materials. In particular we will be interested in the theoretical description of transport properties - such as the electrical conductivity of a material - that result from their Dirac physics. Dirac materials provide a fascinating playground for the study of novel quantum mechanical phenomena, both theoretically and in the lab. As such, many of the examples in this thesis are the product of close theoretical and experimental collaborations. We begin this thesis with a detailed overview of the ever-growing class of materials which obey a Dirac-like description and by introducing many of the concepts used in later chapters. Having done this we turn to a discussion of disorder. Of particular importance will be that Dirac electrons are protected from back-scattering off impurity potentials that retain the symmetries protecting the Dirac point. We will use our knowledge of disordered Dirac materials to calculate the conductivity of the surface of a topological insulator. In the second half of this thesis we will discuss three novel phenomena which we theoretically describe and have been experimentally observed in Dirac materials: Firstly, we will discuss how it is possible to enable back-scattering in a Dirac material, in a controlled manner. We will see that this is achieved by the application of a magnetic field in the plane of a topological insulator's surface which leads to an anisotropy of magnetoresistance and, associated to this, a planar Hall effect. Secondly, we will discuss confinement of Dirac surface states on a very thin nanowire. We will show that the quantisation of the wave-function around the wire leads to oscillatory behaviour of the resistivity that has also been experimentally observed. Finally, we turn to 3d Dirac semi-metals, we will show that their quasi-1d physics in a strong magnetic field leads to a magnetoresistivity that is strongly dependent on the angle of the applied magnetic field when there are multiple Fermi-surfaces in the Brillouin zone.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Legg, Henry henrylegg@live.com orcid.org/0000-0003-0400-5370 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-112916
Date:	2019
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Physics > Institute for Theoretical Physics
Subjects:	Physics
Uncontrolled Keywords:	Keywords Language Dirac materials UNSPECIFIED Transport UNSPECIFIED Disorder UNSPECIFIED
Date of oral exam:	29 November 2019
Referee:	Name Academic Title Rosch, Achim Prof. Dr. Scherer, Michael Priv.-Doz. Dr. Trebst, Simon Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/11291