Electron Interferometry and Magnon Transport in Graphene Quantum Hall Systems

Abstract

The discovery of graphene, an atomically thin layer of carbon, has given the condensed matter community an opportunity to investigate two dimensional (2D) physics with a fresh set of experimental knobs. The quantum Hall (QH) effect is a particularly rich system in which recent experiments in graphene have already revealed novel magnetic ground states, superlattice-induced QH effects, and new fractional QH phases. Experimentalists and theorists alike have been able to re-examine open problems in the field, as well as discover new challenges and physical phenomena. One of the key features of the QHE is the behavior of the electrons at the boundaries of the sample, where one-dimensional edge states exist. This thesis will describe novel manipulations of these edge states, using them to probe the electronic and magnetic properties of graphene quantum Hall states. The first experiment described here will show how we can use QH edge states as solid-state analogues of monochromatic beams of light to study electron interference. Electron interferometry is regarded as one of the most promising routes for studying fractional and non-Abelian statistics and quantum entanglement via two-particle interference. However, creating an edge-channel interferometer in which electron-electron interactions play an important role requires a clean system and long phase coherence lengths. We have achieved this with a simpler Mach-Zehnder design than used in previous 2D systems and are able to realize visibilities of up to 98% using spin and valley polarized edge channels. Surprisingly, our interferometer is robust to dephasing effects at energies an order of magnitude larger than observed in pioneering experiments in semiconductor quantum wells. Our results shed light on the nature of edge-channel equilibration and open up new possibilities for studying exotic electron statistics and quantum phenomena. The second experiment will describe how we use out-of-equilibrium occupation of QH edge channels in graphene to excite and detect spin waves (magnons) in magnetically ordered QH states. Magnons are the elementary spin excitations of magnetic materials and are essential to understanding the intrinsic ordering and thermodynamic properties of magnetic systems. They are able to transmit information without displacing charge, and as such, they are free from the heat production associated with electrical currents, making them promising candidate signal carriers for future information processing. When realized in graphene, spin waves are expected to be particularly long lived due to the weak spin-orbit interaction. However, their charge-neutral nature has made them challenging to detect and study. Our novel method of magnon generation and detection has allowed us to show long distance spin wave propagation through different ferromagnetic phases in the N=0 Landau level, as well as across the insulating canted antiferromagnetic phase. Our results providing insight into the order parameters of magnetic phases in the QH regime and enable experimental investigation of the fundamental magnetic properties of two-dimensional electron systems.