Fractional quantum Hall effects in graphene: thermodynamics, edge tunneling, and a roadmap for topological qubits

The fractional quantum Hall effect remains the preeminent experimental platform for studying topological order, with recent experiments in III-V semiconductor heterostructures demonstrating convincing evidence for fractional statistics. However, limitations inherent to III-V heterostructures stand in the way of further progress. In this talk, I will describe recent progress in graphene based heterostructures where some of these limitations may be overcome.

First, I will describe measurements of the chemical potential ultra-clean heterostructures. In the lowest Landau level of monolayer graphene, pseudopotentials are identical to those of the lowest Landau level in GaAs and we find quantitative agreement between experiment and numerical DMRG calculations. In bilayer graphene, pseudopotentials resemble that of the first Landau level in GaAs, allowing us to measure the chemical potential and entropy in the vicinity of the even denominator fractional quantum Hall state at half filling.

Second, I will describe a new fabrication technique that allows precise local electrostatic control on the nanometer scale, based on local anodic oxidation of graphite gates. As an illustrative example of the resulting possibilities, we study tunneling across a gate-defined quantum point contact separating incompressible states at filling 1/3 and 1. At low tunneling, we observe the universal quadratic power laws in applied bias and temperature expected from the theory of chiral Luttinger liquids. Data at high temperature and bias show saturation of the conductance across the quantum point contact to half the conductance quantum. This can be understood as arising from an Andreev-reflection like process at the point contact in which electrons are transferred across the point contact through a correlated process in which an incoming e/3 quasiparticle is accompanied by retroreflection of a charge -2e/3 hole. In this regime, the device may be operated as a dissipationless direct current voltage step-up transformer.

Finally, I will describe our plans to combine charge sensing and local anodic oxidation lithography to detect fusion and braiding of nonabelian quasiparticles, and a roadmap for building a moderate scale topological quantum computer if these efforts are successful.

Note: In-person only, no zoom.