Detection of anyon scaling dimension and braiding properties in the fractional Quantum Hall Effect

For the almost half of a century, anyons in the FQHE have been proposed as excitations which carry fractional charge and statistics, thus bridging between fermions and bosons. I will review briefly the protocols and experiments that have allowed over the years to access their fractional charge, scaling dimension and their braiding/statistical angle. Next, I shall propose an experimental setup to measure “directly” the statistical/braiding angle of anyons. The setup involves an omega-shaped junction along a fractional quantum Hall liquid edge, formed by defining an open quantum dot. In the weak tunneling regime, the charge current when an anyon is injected upstream from the omega-junction is computed, showing that its time evolution depends solely on the anyon statistical properties, with temperature and scaling dimension affecting only a constant pre-factor. Next, to connect with experiments, the noise cross-correlation is computed between a Poissonian anyon source impinging on the omega (originating from another tunnel coupled DC biased edge state) and the current downstream from the omega junction, providing a realistic, direct method to detect anyon braiding statistics. As the predicted signal suffers thermal suppression for large open quantum dots, a generalization of the above results including charging effects is proposed, with no major modification of the initial protocol. The robustness of these results against the coupling to a dissipative environment is finally discussed.

Speaker: Thierry Marthn, Aix-Marseille University