Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases

Abstract

This paper comprises a review of our recent works on fractional chiral modes that emerge due to edge reconstruction in integer and fractional quantum Hall (QH) phases. The new part added is an analysis of edge reconstruction of the ν = 2/5 phase. QH states are topological phases of matter featuring chiral gapless modes at the edge. These edge modes may propagate downstream or upstream, and may support either charge or charge-neutral excitations. From topological considerations, particle-like QH states are expected to support only downstream charge modes. However the interplay between the electronic repulsion and the boundary confining potential may drive certain quantum phase transitions (called reconstructions) at the edge, which are associated to the nucleation of additional pairs of counter-propagating modes. Employing variational methods, here we study edge reconstruction in the prototypical particle-like phases at ν = 1, 1/3 and 2/5 as a function of the slope of the confining potential. Our analysis shows that subsequent renormalization of the edge modes, driven by disorder-induced tunnelling and intermode interactions, may lead to the emergence of upstream neutral modes. These predictions may be tested in suitably designed transport experiments. Our results are also consistent with previous observations of upstream neutral modes in these QH phases, and could explain the absence of anyonic interference in electronic Mach-Zehnder setups.Mark Azbel was a physicist in his heart and soul. Beside his major contributions to the quantum theory of electrons in metals, he left his footprints everywhere through talks, arguments and discussions on a broad spectrum of issues (including non-physics themes). He would take an issue that appears all but benign, and expose the intricacy, deep significance, and a scale of insight needed to really penetrate the problem at hand. Among his many notable works was the prediction of the anomalous skin effect in metals [1,2]. It is only natural to devote our manuscript in this commemorative volume to a study of another "skin" effect related to the boundary of a twodimensional electron gas in the presence of a strong perpendicular magnetic field. This concerns the gapless chiral edge modes which emerge at the boundary of quantum Hall phases.