Transport Experiments on Topological and Strongly Correlated Conductors

Abstract

Band theory categorizes solid materials based of the presence or lack of an energy gap in the electronic density of states at the Fermi level: metal, insulator, or semiconductor. However, in topological and strongly correlated phases of matter, this simple classification breaks down.In topological materials, Berry curvature (even in bands far-removed from the Fermi level) gives rise to conducting surface and edge states. This thesis studies two topological conductors. The first is the Weyl semimetal Co2MnGa in which we discover an unexpected resistance anisotropy that twists by 90 degrees between the upper and lower surfaces of thin lamellar crystals. We show that this twisted anisotropy arises from distinct surface states that are prevented from hybridizing with gapless states in the bulk. The second system is the original topological insulating phase: the quantum Hall state. We develop high-mobility two-dimensional electron gases based on graphene that exhibit both the integer and fractional quantum Hall effects in strong magnetic fields at cryogenic temperatures. We engineer a quantum point contact in these devices and demonstrate that it can selectively control the transmission of the dissipationless quantum Hall edge modes, reaching full pinch-off. We also describe the development of a sensitive system to measure noise (Johnson and shot) in these devices. This system can be used to study properties of interesting quantum phases that are inaccessible to standard resistive transport techniques. In addition to the fractional quantum Hall effect in graphene, we study another strongly correlated system: unconventional type-II superconductivity in infinite-layer nickelates. We probe vortices in the superconducting order parameter through measurements of the off-diagonal component of the thermoelectric response tensor (Nernst effect) in strong magnetic fields. We provide the first evidence that these nickelates have a robust vortex-liquid phase, which we show has strong similarities to that of the high-Tc cuprate superconductors.