Interferometer-Based Studies of Quantum Hall Phenomena

Abstract

The fractional quantum Hall (FQH) effect harbors a wealth of unique phenomena, many of which remain mysterious. Of particular interest is the predicted existence of quasi-particles with unusual topological properties, especially in light of recent proposals to observe these properties using electronic interferometers. An introduction to quantum Hall physics and electronic interferometry is given in Chapter 1 of this thesis. The remaining chapters, summarized below, describe a set of experiments in which FQH systems are studied using electronic Fabry-Perot interferometry and related techniques. Since prior studies of electronic Fabry-Perot interferometers revealed unexpected behavior even in the integer quantum Hall (IQH) regime, we began our measurements there. Our initial experiment, presented in Chapter 2, disentangles signatures of Coulomb interaction effects from those of Aharonov-Bohm (AB) interference and provides the first measurement of pure AB interference in these devices. In our next experiment, presented in Chapter 3, we measure AB interference oscillations as a function of an applied dc bias, use their period to study the velocity of the interfering electrons, and study how the oscillations decay as a function of bias and magnetic field. Moving to the FQH regime, applying a similar-sized bias to a quantum point contact leads to long-lasting changes in the strengths and positions of FQH plateaus. The involvement of lattice nuclear spins in this effect, suggested by the long persistence times, is confirmed using NMR-type measurements. Although the exact physical process responsible for the effect remains unclear, its filling-factor dependence provides a striking illustration of composite fermion physics. These measurements are described in Chapter 4. In certain devices, interference oscillations associated with several FQH states are observed. Interpretation of their magnetic-field and gate-voltage periods provides a measurement of quasi-particle charge, and temperature dependence measurements suggest differences between the edge structure of IQH and FQH states. These measurements are described in Chapter 5. Finally, Chapter 6 presents some recent, not-yet-published observations that may shed light on ways to improve the visibility of existing oscillations and potentially observe interference at additional FQH states. This chapter concludes with a discussion of possible next steps toward achieving these goals.