| The concept of the geometric Berry phase of the quantum mechanical wave function has led to a better theoretical understanding of natural phenomena in all fields of fundamental physics research. In condensed matter physics, the impact of this theoretical discovery has been particularly profound: The quantum Hall effect, the anomalous Hall effect, the quantum spin Hall effect, magnetic skyrmions, topological insulators, and topological semimetals are but a few subfields that have witnessed rapid developments over the three decades since Michael Berry's landmark paper. In this thesis, I will present and discuss the results of three experiments where Berry's phase leads to qualitatively new transport behavior of electrons or magnetic spin excitations in solids.;We introduce the theoretical framework that leads to the prediction of a thermal Hall effect of magnons in Cu(1,3-bdc), a simple two-dimensional layered ferromagnet on a Kagome net of spin S = 1/2 copper atoms. Combining our experimental results measured down to very low temperatures T = 0.3 K with published data from inelastic neutron scattering, we report a quantitative comparison with the theory. This confirms the expected net Berry curvature of the magnon band dispersion in this material.;Secondly, we have studied the thermal Hall effect in the frustrated pyrochlore magnet Tb2Ti2O7, where the thermal Hall effect is large in the absence of long-range magnetic order. We establish the magnetic nature of the thermal Hall effect in Tb2Ti2O7, introducing this material as the first example of a paramagnet with non-trivial low-lying spin excitations. Comparing our results to other materials with zero thermal Hall effect such as the classical spin ice Dy2Ti 2O7 and the non-magnetic analogue Y2Ti2O 7, we carefully discuss the experimental limitations of our setup and rule out spurious background signals.;The third and final chapter of this thesis is dedicated to electrical transport and thermopower experiments on the half-Heusler material GdPtBi. A careful doping study of the negative longitudinal magnetoresistance (LMR) establishes GdPtBi as a new material platform to study the physical properties of a simple Weyl metal with only two Weyl points (for magnetic field along the crystallographic ⟨111⟩ direction). The negative LMR is associated with the theory of the chiral anomaly in solids, and a direct consequence of the nonzero Berry curvature of the energy band structure of a Weyl semimetal. We compare our results to detailed calculations of the electronic band structure. Moving beyond the negative LMR, we report for the first time the effect of the chiral anomaly on the longitudinal thermopower in a Weyl semimetal. |
