High-resolution measurement of quasiparticle entropy in even-denominator fractional quantum Hall states

Even-denominator fractional quantum Hall states in bilayer graphene are predicted to host quasiparticles with non-Abelian braiding statistics. In thermodynamic equilibrium, the non-Abelian character of these quasiparticles may be reflected in an increase in the bulk entropy per quasiparticle, resulting from the additional ground-state degeneracy associated with the quasiparticle braiding.

We aim to experimentally resolve this effect by measuring the bulk entropy of bilayer graphene fractional quantum Hall states using on-stack aluminum single-electron transistors. Radiofrequency readout of the SET response provides a measurement of the electronic chemical potential with near-ueV resolution – the temperature dependence of this chemical potential then reveals directly the entropy per electron. Our latest experiments integrate primary thermometry using an aluminum SET-based charge sensing scheme to perform direct, non-invasive measurement of the graphene electron temperature, enabling us to resolve the bulk entropy with state-of-the-art sensitivity. We present the dependence of the measured entropy on the quasiparticle density and temperature, and compare observations in the even-denominator states to the (Abelian) odd-denominator states.