Four-flux fractional quantum Hall states in suspended graphene

The interactions between charge carriers in ultra-clean graphene subject to a perpendicular magnetic field can drive the system to condense into one of a set of incompressible fractional quantum Hall (FQH) states. We use a scanning single-electron transistor to measure the local electronic compressibility of suspended graphene. In addition to observing incompressible behavior at fractional filling factors in the two-flux composite fermion sequence, we also observe FQH states arising from four-flux composite fermions, including states at filling factors $\nu =$ 1/5, 2/7, 2/9, 3/11, 5/7 and 6/5. We measure the energy gaps of these states as a function of magnetic field; most display approximately linear scaling. Interestingly, several four-flux FQH states are conspicuously absent near filling factors $\nu =$ 1 and 2, despite the robust appearance of their counterparts near $\nu =$ 0.