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 $\nu =2/5$ 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 $\nu =1,1/3$ 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.

arXiv comment7 pages, 6 figures. Submitted to the special issue Azbel-90 of Low Temperature Physics, dedicated to Mark Azbel. This article comprises a review of two of our recent works, drawing heavily from arXiv:2007.11092 and arXiv:2109.15293, as well as an analysis of edge reconstruction in new phases

References in corpus (42)

• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Observation of neutral modes in the fractional quantum Hall regime
• Impurity scattering and transport of fractional Quantum Hall edge state
• Quantum Dots in Strong Magnetic Fields: Stability Criteria for the Maximum Density Droplet
• Local Thermometry of Neutral Modes on the Quantum Hall Edge
• Reconstruction of Fractional Quantum Hall Edges
• Edge reconstruction in the fractional quantum Hall regime
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Proliferation of neutral modes in fractional quantum Hall states
• Field Theoretical Description of Quantum Hall Edge Reconstruction
• A New Paradigm for Edge Reconstruction in Fractional Quantum Hall States
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Transport in a disordered $\nu =2/3$ fractional quantum Hall junction
• Spontaneous breakdown of topological protection in two dimensions
• Textured Edges in Quantum Hall Systems
• Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes
• Incoherent transport on the $\nu =2/3$ quantum Hall edge
• Topological classification of shot noise on fractional quantum Hall edges
• Synthesizing a Fractional v=2/3 State from Particle and Hole States
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Edge-mode velocities and thermal coherence of quantum Hall interferometers
• Noise on complex quantum Hall edges: Chiral anomaly and heat diffusion
• Imaging the Conductance of Integer and Fractional Quantum Hall Edge States
• Edge reconstructions in fractional quantum Hall systems
• Imaging fractional incompressible stripes in integer quantum Hall systems
• Suppression of interference in quantum Hall Mach-Zehnder geometry by upstream neutral modes
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Counter-propagating charge transport in the quantum Hall effect regime
• Conductance plateaus and shot noise in fractional quantum Hall point contacts
• Realization of supersymmetry and its spontaneous breaking in quantum Hall edges
• Angular Momentum Distribution Function of the Laughlin Droplet
• Contacts, equilibration, and interactions in fractional quantum Hall edge transport
• Robust integer and fractional helical modes in the quantum Hall effect
• Ground state and edge excitations of quantum Hall liquid at filling factor 2/3
• Theoretical investigation of edge reconstruction in the $\nu$=5/2 and 7/3 fractional quantum Hall states
• Spin Mode-Switching at the Edge of a Quantum Hall System
• Magnetic field dependent equilibration of fractional quantum Hall edge modes
• Density matrix renormalization group study of the $\nu =1/3$ edge states in fractional quantum Hall systems
• Edge spin excitations and reconstructions of integer quantum Hall liquids
• Emergence of spin-active channels at a quantum Hall interface
• Symmetry-related transport on a fractional quantum Hall edge

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• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Can Majorana zero modes in quantum Hall edges survive edge reconstruction?