Identifying Topological Semimetals

Abstract

Geometric properties of electron states in crystalline solids lead to a topological classification of materials. A remarkable consequence of this topological viewpoint is that it reveals a deep link between the bulk properties of a material and electronic states which form on its surface. This leads to unique transport properties, the most well-known example being the integer quantum Hall effect. In topological semimetals, the bulk features of interest are nodes in the band structure, where occupied and unoccupied states are not separated by an energy gap. This leads to interesting low-energy excitations, some of which are the condensed matter equivalent of fundamental particles. The Weyl Fermion for example is realized in topological semimetals, which is theoretically postulated but eludes experimental verification in high-energy physics. Crystals however do not have a continuous translational symmetry, and thus do not need to fulfill the so-called Lorentz invariance present in high-energy physics. This allows for Fermions to exist in materials which do not have a fundamental counterpart. The main topic of this thesis is the study and identification of topological semimetals. We propose a mechanism for Weyl Fermions to form under the influence of an external magnetic field. This effect could help explain the anisotropic negative magnetoresistance in transition metal dipnictides. We also study several novel topological material candidates, hosting a plethora of Weyl Fermions and topological nodal lines. In addition to studying specific material examples, we also present several tools and algorithms which enhance the process of identifying topological materials. First, we present an algorithm for evaluating the phase diagram of a system with discrete phases. This is useful in identifying topological phases, but also applicable to other fields of computational physics. Furthermore, we develop tools that simplify the creation of k·p and tight-binding models to study crystalline systems. A particular focus lies on the construction of models which preserve the crystal symmetries, since these play a crucial role in determining the topology of a material. And finally, we develop an algorithm that reliably finds and classifies topological nodal features.