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The study of topological phases of matter is among the most active research fields in modern solid state physics. Over the last couple of years, there has been growing interest in the topological classification of gapless systems. One example of a gapless system, with defining topological properties, is the Weyl semimetal (TWS). In Weyl semimetals, conduction and valence bands touch at isolated points in the Brillouin zone. These Weyl points are topologically pro- tected and can only disappear if they annihilate pairwise. The Weyl semimetal hosts non-trivial surface states, which take the form of open Fermi arcs, connect- ing the projections of two Weyl points to the Brillouin zone of the surface. Due to the robustness of this phase, Weyl semimetals are of interest for applications in quantum computers or electronic devices. In this work, we consider a model for the iridium electrons in pyrochlore iridates. For this material class, a Weyl- semimetal phase has been predicted. We calculate the phase diagram and find a rich variety of phases, the TWS, a strong topological insulator, a type-II Weyl semimetal and various kinds of magnetic order. For the TWS, we study the un- conventional surface states for various geometries. For lower electron densities, we find a plethora of new magnetic configurations. We then turn our attention towards possible instabilities in Weyl semimetals. We study the stability of the Weyl semimetal phase against the formation of charge density waves. In the back- folded Brillouin zone, Weyl points that were originally far apart can be mapped close to each other and annihilate if that reduces the free energy. However we did not find a charge density wave. We therefore study the behavior of Weyl points under the influence of a charge density wave. We find mechanisms, that could possibly avoid the formation of such a charge configuration. For example, one-dimensional Fermi lines emerge.

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Christoph Berke, TU Dresden
Seminarraum E0.02
Contact: Simon Trebst