Fractional Quantum Anomalous Hall Effect in a Graphene Moire Superlattice

Abstract: The fractional quantum anomalous Hall effect (FQAHE), the analog 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 which form the basis of topological quantum computation. So far, FQAHE has been observed only in twisted MoTe2 (t-MoTe2) at moire filling factor v > 1/2. Graphene-based moire superlattices are believed to host FQAHE with the potential advantage of superior material quality and higher electron mobility. Here we report the observation of integer and fractional QAH effects in a rhombohedral pentalayer graphene/hBN moire superlattice. At zero magnetic field, we observed plateaus of quantized Hall resistance Rxy = h/(ve^2) at filling factors v = 1, 2/3, 3/5, 4/7, 4/9, 3/7 and 2/5 of the moire superlattice respectively. These features are accompanied by clear dips in the longitudinal resistance Rxx. In addition, at zero magnetic field, Rxy equals 2h/e^2 at v = 1/2 and varies linearly with the filling factor-similar to the composite Fermi liquid (CFL) 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 CFL and FQAH states to other correlated electron states. Our graphene 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.

Fractional Quantum Anomalous Hall Effect in Multilayer Graphene

This paper investigates the occurrence of the fractional quantum anomalous Hall effect (FQAHE) within multilayer graphene systems, specifically examining pentalayer rhombohedral graphene (RG) in conjunction with hexagonal boron nitride (hBN) to form a moiré superlattice. The research explores the observation of both integer and fractional quantum anomalous Hall (QAH) effects in this newly developed graphene moiré system at zero magnetic field. The implications of these findings have substantial relevance for advancing both the theoretical understanding and practical applications of quantum materials.

The study distinguishes itself by achieving the observation of FQAHE in a graphene-based moiré superlattice, filling a notable gap in the existing literature where previous observations were limited to more defective Materials like twisted transition metal dichalcogenides (TMDs). The specific focus on pentalayer RG expands upon existing studies that have mostly examined trilayer configurations. Significantly, the research presents quantized Hall resistance at various filling factors (notably $v = 1, 2/3, 3/5, 4/7, 4/9, 3/7, 2/5$), showcasing the potential for graphene moiré superlattices to exhibit complex fractional quantum states due to their higher material quality and superior electron mobility compared to other TMD systems.

Numerically, the work highlights quantized resistance plateaus and the clear dips in longitudinal resistance at these filling factors, reinforcing the observed FQAHE in the system. It provides a phase diagram that maps the transitions from composite Fermi liquid (CFL) and FQAHE states to other correlated electron states, emphasizing the ability to manipulate these phase states via gate displacement field and filling factor tuning. Such tunability adds a layer of control in exploring and manipulating quantum phases, making the RG/hBN superlattice a promising platform for future research into exotic states of matter such as non-Abelian anyons.

The experimental setup demonstrates that the electron density corresponding to these fractional filling factors is drastically lower compared to analogous states in TMD systems, offering a fundamental insight into the lower carrier density regime in graphene-based moiré superlattices. The hysteresis observed in the resistance with respect to a swept magnetic field further supports the robustness of the state, highlighting strong electron correlations and topology effects at work.

From a theoretical and practical standpoint, these observations mark an important advancement in understanding the zero-field FQAHE within high-Chern-number flat bands, paving the way for potential applications in quantum computing through the use of non-Abelian anyons in topological quantum computation. Moreover, the coexistence of various states, including superconductivity within the same graphene setup, underscores the potential for graphene systems to act as a versatile testbed for realizing synthetic non-Abelian anyonic braiding mechanisms.

Future directions in the field as suggested by this research could involve expanded experimental investigations into the unexplored regime of varied layer numbers and twist angles in graphene-based moiré systems, alongside potential theoretical work to create robust predictions for these configurations. The insights presented form a foundation for exploring more exotic fractional quantum states, enhancing the applicability of these findings in advanced electronics and quantum information sciences.