Tunneling, Spin Dynamics and Interference at the Fractional Quantum Hall Edge

Abstract

The quantum Hall effect, the first topological quantum phase of matter ever observed, remains today an important framework for the advancement of fundamental physics. With the advent of the topological model of quantum computation and the prediction of nonabelian braiding statistics in the ν=5/2 state, it further gained technological relevance as a potential platform for proof-of-concept demonstration of an intrinsically noise-resistant qubit. Both for enabling technological advances and answering fundamental questions, it is essential to understand transport of fractional quasiparticles across narrow constrictions. The edges of fractional quantum Hall (FQH) fluids are predicted to form strongly interacting chiral one-dimensional systems, resulting in unique dynamics of the tunneling processes coupling them. We investigate the validity of the existing theory in relatively simple, well-understood states, closing a gap in the available literature. Our data agree partially with the theoretical model, with an effective quasiparticle charge of e/3 obtained in a nonlinear regression analysis in parts of the parameter space. The phenomenology is more complex than anticipated, highlighting the need for further theoretical efforts. As the material system which can be grown with the highest purity, GaAs is the platform of choice for research into the fractional quantum Hall effect. The presence of spinful nuclei with a sizeable hyperfine interaction of the conduction electrons is both a blessing and a curse, resulting in a considerable enrichment of transport phenomena in the fractional quantum Hall effect whenever two ground states of opposite spin are energetically close. Well documented in extended areas of 2DEG, those effects have so far not been thoroughly explored in confined systems. We study the dynamic interaction of a quantum point contact with its nuclear environment, and show that neighboring structures can be coupled by the diffusion of nuclear spins. Lastly, we report studies of electronic interferometers designed to probe braiding statistics in fractional quantum Hall states. More than ten years after the publication of first theoretical proposals and experimental efforts, path interference of quasiparticles has proven difficult to realize. We set limits on the dimensions of conventional geometries susceptible of probing braiding statistics and introduce a new promising design, reporting indications of the Aharonov-Bohm effect in the ν=4/3 state. The insights we provide open questions with respect to fundamental aspects of the dynamics of edge states and to properties of unconventional interferometers geometries, motivating extensive theoretical investigations. Further, we propose new experimental approaches to the study of fractional quantum Hall edge states, potentially guiding further experimental work. Finally, our report of a signature of path interference in a fractional state together with a first characterization of more advanced gating techniques is an encouraging step towards the successful demonstration of noncommutative braiding statistics.