Two dimensional electrons subjected to a strong magnetic field form highly degenerate Landau levels, whose flat dispersion makes them highly susceptible to interaction driven instabilities. Among the most spectacular of such ground states are those leading to fractional quantum Hall effects–‘topologically ordered’ collective electron ground states where the elementary excitations of the system carry fractional charge, and follow fractional quantum statistics.
Driven by a string of technical advances in the field of two dimensional layered materials [1-2], including most recently in our group , graphene heterostructures are now among the best material platforms for studying these effects, combining pristine sample quality with highly controllable spin, valley, and orbital degeneracies. The Figure to the left shows data from our lab probing the density of states of a graphene bilayer, as the charge density and interlayer potential are varied. Each thin vertical line is an incompressible fractional quantum Hall liquid, and the interlayer potential drives phase transitions between correlated states with differing layer occupation. (see  for details).
Ongoing projects include using these devices to experimentally detect nonabelian statistics using both interferometric and thermodynamic probes, and engineering nonabelian defect states in abelian fractional quantum Hall and ‘fractional Chern insulator’ phases.
 Dean et al., Nature Nanotechnology, 5:722-726 (2010).
 Wang et al., Science, 342:614-617 (2013).
 Zibrov et al., arXiv:1607.06461 (2016).