Interferometry of Integer and Fractional Quantum Hall Edge States in Graphene

Abstract

In this thesis, we develop Fabry-Pérot quantum Hall interferometers in graphene and measure anyon braiding in the fractional quantum Hall effect. Our results demonstrate the potential of van der Waals materials for constructing quantum coherent electronic devices with advanced functionalities in order to unveil a wealth of physics that is otherwise inaccessible via transport measurements. We begin by first demonstrating clear Aharonov-Bohm resistance oscillations in integer quantum Hall states, overcoming a major technical challenge of “Coulomb dominated” oscillations, which plagued decades of experiments in traditional semiconductor-based platforms. Next, we develop an improved, density-tunable interferometer and measure tunable Coulomb coupling between copropagating integer edge states, revealing the physics behind anomalous interference phase jumps and Aharonov-Bohm oscillation frequency doubling in the integer quantum Hall effect. Similar observations in other semiconductor platforms had been unexplained for a decade. The combined theoretical developments and precise tuning knobs added by our work enable further experiments probing correlations in strongly coupled one-dimensional chiral edge channels. Finally, we observe robust Aharonov-Bohm oscillations in two distinct fractional quantum Hall states, filling fractions ν=1/3 and ν=4/3, and discover 3-state telegraph noise consistent with localized anyon number fluctuations, which we put to use to directly measure the 2π/3 abelian anyon braiding phase in both states. This final work enables further experiments to demonstrate control of the localized anyon number and eventually measure the braiding properties of non-abelian anyons in even-denominator fractional quantum Hall states. Many open questions, such as whether non-abelian order describes these states, how robust topological order really is, which excitations belong to which fractional states in real devices, and whether we can build a technology leveraging the exotic physics of the fractional quantum Hall effect will soon be directly addressable.