Universität zu Köln

Bömerich, Thomas ORCID: 0000-0001-9868-1497 (2025). Nonlinear Transport and Disorder Effects in Nodal Line Semimetals. PhD thesis, Universität zu Köln.

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Abstract

Symmetries manifest themselves everywhere in nature with invariance under symmetry transformations influencing the properties of many systems. They are also directly connected to conservation laws which often are cornerstones of physical theories. In solids, the Bloch theorem takes advantage of crystalline translation symmetry, giving rise to the band structure of electrons. Of particular interest are so-called ”Dirac materials”, for which in the last years a whole zoo of examples have been found and researched. Such systems have low-energy excitations that behave like massless, relativistic particles described by a Dirac equation. These materials therefore connect symmetries, topology, and linear electron dispersions. In this thesis we will mainly work on one example of such materials where the band structure has a nodal line consisting of linear crossings along a ring in momentum space. The main goal will be to investigate different transport properties beyond the linear response to the external fields. Here, symmetries will play a major role as certain responses can only be finite if particular symmetries are absent. At the start of this thesis we review some of the above mentioned Dirac systems with a focus on the role of symmetries. Afterwards we develop the tools to calculate transport properties of solids both semi-classically as well as from a fully quantum mechanical approach. In both cases, disorder will play an important role. The main results of this thesis will be on models describing 3d crystals of zirconium pentatelluride (ZrTe5). We will discuss four different transport phenomena in this material: Firstly, we will show how a nonreciprocal response can be created due to the spin texture of the Fermi surface. In this case the resistance will depend on the direction of the applied current which is only possible if inversion symmetry is broken. Secondly, we discuss the current-voltage relation at large magnetic fields which will deviate strongly from the linear Ohm’s law. We will see that such an enhancement of nonohmic effects can be achieved in a nodal line system when all electrons sit in the same quasi-1d band. For both of these phenomena it will be necessary to consider inhomogeneous electron distributions due to charged impurities. Next, we consider unconventional Hall effects where the applied current and magnetic field are parallel to each other. Here, broken symmetries will result in a tilted Fermi surface enabling the parallel-field Hall response. Lastly, we will investigate nonlocal transport beyond the effects caused by contact geometries. As a possible mechanism we explore the coupling of charge to additional degrees of freedom.

Item Type:	Thesis (PhD thesis)
Creators:	Creators Email ORCID ORCID Put Code Bömerich, Thomas tboemerich@gmail.com https://orcid.org/0000-0001-9868-1497 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-799502
Date:	2025
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 Nonlinear Transport English Dirac Materials English Nodal-Line Semimetals English Magnetochiral Anisotropy English Symmetry Breaking English Resistor Networks English Anisotropic Transport English Landau Levels English Hall Effects English Boltzmann Equation English Nonlocal Transport English Disorder English
Date of oral exam:	26 March 2025
Referee:	Name Academic Title Rosch, Achim Prof. Dr. Trebst, Simon Prof. Dr. Bocquillon, Erwann Prof. Dr.
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/79950