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This paper comprises a review of our recent works on fractional chiral modesthat 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$\nu = 2/5$ phase. QH states are topological phases of matter featuring chiralgapless modes at the edge. These edge modes may propagate downstream orupstream, and may support either charge or charge-neutral excitations. Fromtopological considerations, particle-like QH states are expected to supportonly downstream charge modes. However the interplay between the electronicrepulsion and the boundary confining potential may drive certain quantum phasetransitions (called reconstructions) at the edge, which are associated to thenucleation of additional pairs of counter-propagating modes. Employingvariational methods, here we study edge reconstruction in the prototypicalparticle-like phases at $\nu = 1, 1/3$ and $2/5$ as a function of the slope ofthe confining potential. Our analysis shows that subsequent renormalization ofthe edge modes, driven by disorder-induced tunnelling and intermodeinteractions, may lead to the emergence of upstream neutral modes. Thesepredictions may be tested in suitably designed transport experiments. Ourresults are also consistent with previous observations of upstream neutralmodes in these QH phases, and could explain the absence of anyonic interferencein electronic Mach-Zehnder setups.

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