UC Santa Cruz

\qquad Topology is a branch of mathematics that describes the connectedness of closed surfaces. In condensed matter, ideas from topology have been used to classify electronic and magnetic states. Here we discuss how topological considerations arise in three different contexts: Bulk transport in a Weyl semimetal, sub-gap excitations in a magnetization plateau, and quantum oscillations in a topological Kondo insulator. In the Weyl semimetal candidate, $Y_2Ir_2O_7$, below $T = 60K$ a bulk transport signature emerges that follows $\rho = \rho_0 T^{-4}$ consistent with the thermally screened charged impurity (TSCI) model for a charge compensated disordered Weyl semimetal. Surprisingly the $T^{-4}$ behavior extends far beyond the Ioffe-Regel criterion $k_fl$ $\mathtt{\sim}$ $O(1)$ similar in spirit to the so-called “bad metals” such as $SrRuO_3$, suggesting $Y_2Ir_2O_7$ is a 'bad' Weyl semimetal. The metamagnet $CeSb$ showcases a manifestation of topological quantization involving only local magnetic moments where sub-gap mini-plateaus that imply broken translational symmetry in a 2D ferromagnetic sublattice emerge within the 1/3rd magnetically ordered plateau state. Additionally, the specific heat increases within the 1/3rd plateau incorporating up to 10\% of the total spin entropy identifying the coexistence of seemingly non-interacting $\Delta S_z = 0$ excitations. We also measured the low temperature high field specific heat of $Al$-flux grown $SmB_6$ to further understand the presence of de Haas van Alphen (dHvA) oscillations and absence of Shubnikov de Haas (SdH) oscillations in this material. We found experimental support for Magnetoquantum Oscillations in the specific heat of heavy excitations, that coexist with light effective mass dHvA oscillations, the amplitude of which grow dramatically below $\mathtt{\sim}$ $T = 0.5 K$. This anomalous growth deviates from Lifshitz-Kosevich behavior as expected from the formation of a magnetoexciton-condensate. Lastly, we developed an apparatus and software for the measurement of non-local resistance signatures as a general probe for the discovery and study of topological transport phenomena.