Abstract :
[en] Topology in condensed matter physics is a field that has exploded in the last two decades. With the realization of its importance, some previously unexplained observations can now be explained. With the progress of time, many new topological phases of matter have been discovered, and topological materials have been shown to be fairly common in nature. Topological materials have further been shown to have properties that may be extremely useful for new technologies, such as spintronics and fault-tolerant quantum computation. The field is however, still evolving, and many properties of these materials are still unknown. In this thesis, we investigate how some of these types of materials react to applied external fields and the theories that can explain these observations.
First, we investigate systems of coupled Majorana bound states. More specifically, we focus on the transport properties of the Majorana box and the T-junction in the presence of charging effects, overlap between the Majorana bound states, and multiple terminals connected to the system. To obtain the transport properties, we apply a master equation and calculate the current through the systems as biases are applied to the different terminals. By tuning the gate voltage, the transport is investigated in both the regime where sequential tunneling is dominating as well as the Coulomb blockaded regime, where cotunneling is the leading transport process. When sequential tunneling is dominating, the transport is mediated by both single electrons tunneling as well as processes that involve the creation and annihilation of Cooper pairs. In the Coulomb blockaded regime, transport is driven by cotunneling processes by transitions via virtual states. The results here show that four-terminal measurements can be a useful tool to characterize the properties of Majorana bound states with finite overlap and charging energy.
Secondly, we study the optical activity of tilted nodal loop semimetals. The inherent Hall conductivity of topological materials makes the Kerr effect an excellent tool for investigating their properties. Here we first calculate the full conductivity tensor for a tilted nodal loop semimetal, where the tilt is in the $ k_{x} - k_{y} $ plane. The conductivity tensor allows us to calculate the Kerr effect. We study this both for a thin film and a bulk material and we fin, in general, that the Kerr effect is large, similar to other topological materials.
Finally, we investigate electronic hydrodynamics in anomalous Hall insulators. First we derive the Navier-Stokes equations for topological materials and show that they are modified due to the Berry curvature. Secondly, we consider the flow in a narrow channel and the application of a small electric field. In this case, the Hall current can be neglected since it is much smaller than the longitudinal current. Flow in narrow channels conventionally leads to Poiseuille flow. However, as shown, the Berry curvature modifies the flow profile and shifts the maximum of the current profile towards one of the edges. Thirdly, we study the flow in an infinite geometry. In this case, it is shown that the Berry curvature induces whirlpools as well as causing an asymmetry in the profile of the electrical potential. Experimentally this can be observed by measuring the non-local resistance.
