Electrical and Thermal Transport Studies on Topologically Non-Trivial Systems

Topology has become a topic that has become ubiquitous in Condensed Matter Physics over the last decade or so with the observations of topological insulators, Dirac and Weyl semimetals, topological superconductors, etc. These materials exhibit a wide array of physical properties of both academic and industrial interest. As such, understanding existing topological phases is of interest for both Physics purists (like myself) and those interested in exploiting these properties for technological gains. In this dissertation, I explore the properties of two topologically (potentially) non-trivial systems, the Fractional Quantum Hall state, and proposed topological Kondo insulator SmB6. The observation of voltage oscillations in a single crystal of cryogenically cooled SmB6 that had been proposed to be related to bulk-surface conduction crossover presented a question regarding the implicit thermal mechanism. As such I explored the time dependent thermal oscillations in SmB6 that gave rise to the potential high frequency oscillations. My introduction to uniaxial strain came simultaneously with projects looking to explore the thermal conductivity of SmB6 in order to probe the possible existence of bulk neutral excitations, as well as to study the emergent nematic state in ν = 5/2 state in a two dimensional electron gas hosted in semiconductor quantum wells. By subjecting the two-dimensional electron gas to uniaxial strain while electrons sit in the ν = 5/2 state we found that stripe phases can be made to emerge. In addition to this behavior, we noted the effect of strain was dramatically coupled to the Landau Level at which the electrons sit during the strain application. Finally, the development of a novel thermal transport experimental design for use in uniaxial strain cells was pursued for the purpose of understanding the bulk excitations in SmB6. A symmetrized thermal conductivity technique was developed for single crystals that is compatible with uniaxial strain experiments. Preliminary measurements show that when care is taken in the sample preparation, the measured values of κ(T) are in good agreement with theory and conventional thermal conductivity experiments, making this technique useful for a broad array of experiments