Topological Interface between Pfaffian and Anti-Pfaffian Order in ν=5/2 Quantum Hall Effect

Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise

The nature of the bulk topological order of the 5/2 non-Abelian fractional quantum Hall state and the steady state of its edge are long-studied questions. The most promising non-Abelian model bulk states are the Pfaffian (Pf), anti-Pffafian (APf), and particle-hole symmetric Pfaffian (PHPf). Here, we propose to employ a set of dc current-current correlations (electrical shot noise) in order to distinguish among the Pf, APf, and PHPf candidate states, as well as to determine their edge thermal equilibration regimes: full vs partial. Using other tools, measurements of GaAs platforms have already indicated consistency with the PHPf state. Our protocol, realizable with available experimental tools, is based on fully electrical measurements.

Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength

A successful probing of the neutral Majorana mode in recent thermal Hall conductivity measurements opines in favor of the particle-hole symmetric Pfaffian (PH-Pf) topological order, contrasting the theoretical predictions of Pfaffian or anti-Pfaffian phases. Here we report a reentrant anomalous quantized phase that is found to be gapped in the thermodynamic limit, distinct from the conventional Pfaffian, anti-Pfaffian, or PH-Pf phases, at an intermediate strength of Landau level mixing. Our proposed wave function consistent with the PH-Pf shift in spherical geometry rightly captures the topological order of this phase, as its overlap with the exact ground state is very high and it reproduces low-lying entanglement spectra. A unique topological order, irrespective of the flux shifts, found for this phase, possibly corroborates the experimentally found topological order.

Domain Textures in the Fractional Quantum Hall Effect

Impacts of domain textures on low-lying neutral excitations in the bulk of fractional quantum Hall effect (FQHE) systems are probed by resonant inelastic light scattering. We demonstrate that large domains of quantum fluids support long-wavelength neutral collective excitations with well-defined wave vector (momentum) dispersion that could be interpreted by theories for uniform phases. Access to dispersive low-lying neutral collective modes in large domains of FQHE fluids such as long wavelength magnetorotons at filling factor v=1/3 offer significant experimental access to strong electron correlation physics in the FQHE.

Optical N-invariant of graphene's topological viscous Hall fluid

Over the past three decades, graphene has become the prototypical platform for discovering topological phases of matter. Both the Chern \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C\in {\mathbb{Z}}$$\end{document}C∈Z and quantum spin Hall \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\upsilon \in {{\mathbb{Z}}}_{2}$$\end{document}υ∈Z2 insulators were first predicted in graphene, which led to a veritable explosion of research in topological materials. We introduce a new topological classification of two-dimensional matter – the optical N-phases \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$N\in {\mathbb{Z}}$$\end{document}N∈Z. This topological quantum number is connected to polarization transport and captured solely by the spatiotemporal dispersion of the susceptibility tensor χ. We verify N ≠ 0 in graphene with the underlying physical mechanism being repulsive Hall viscosity. An experimental probe, evanescent magneto-optic Kerr effect (e-MOKE) spectroscopy, is proposed to explore the N-invariant. We also develop topological circulators by exploiting gapless edge plasmons that are immune to back-scattering and navigate sharp defects with impunity. Our work indicates that graphene with repulsive Hall viscosity is the first candidate material for a topological electromagnetic phase of matter.

Graphene is the archetype for realizing two-dimensional topological phases of matter. Here, the authors introduce a new topological classification connected to polarization transport, where the topological number is revealed in the spatiotemporal dispersion of the susceptibility tensor.

Fractional charge and fractional statistics in the quantum Hall effects

Quasiparticles with fractional charge and fractional statistics are key features of the fractional quantum Hall effect. We discuss in detail the definitions of fractional charge and statistics and the ways in which these properties may be observed. In addition to theoretical foundations, we review the present status of the experiments in the area. We also discuss the notions of non-Abelian statistics and attempts to find experimental evidence for the existence of non-Abelian quasiparticles in certain quantum Hall systems.

Noise on the non-Abelian ν=5/2 Fractional Quantum Hall Edge

The recent measurement of a half-integer thermal conductance for the ν=5/2 fractional quantum Hall state has confirmed its non-Abelian nature, making the question of the underlying topological order highly intriguing. We analyze the shot noise at the edge of the three most prominent non-Abelian candidate states. We show that the noise scaling with respect to the edge length can, in combination with the thermal conductance, be used to experimentally distinguish between the Pfaffian, anti-Pfaffian, and particle-hole-Pfaffian edge structures.