Fractional Electron States for Topological Quantum Computing

The fractional quantum anomalous Hall effect (FQAHE), the analogue of the fractional quantum Hall effect1 at zero magnetic field, is predicted to exist in topological flat bands under spontaneous time-reversal-symmetry breaking. The demonstration of FQAHE could lead to non-Abelian anyons that form the basis of topological quantum computation. So far, FQAHE has been observed only in twisted MoTe2 at a moiré filling factor v > 1/2. Graphene-based moiré superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility.

In this project, we observed integer and fractional QAH effects in a rhombohedral pentalayer graphene–hBN moiré superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance at v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moiré superlattice, respectively, accompanied by clear dips in the longitudinal resistance Rxx. Rxy equals 2ℎe2 at v = 1/2 and varies linearly with v, similar to the composite Fermi liquid in the half-filled lowest Landau level at high magnetic fields. By tuning the gate-displacement field D and v, we observed phase transitions from composite Fermi liquid and FQAH states to other correlated electron states. The system provides an ideal platform for exploring charge fractionalization and (non-Abelian) anyonic braiding at zero magnetic field, especially considering a lateral junction between FQAHE and superconducting regions in the same device.