Emergent fractional quantum anomalous Hall effect in a second-order topological insulator

The fractional quantum anomalous Hall (FQAH) phase, featuring unique fractionally quantized states, has garnered substantial experimental progress in recent years. To unlock its full potential for applications in advanced electronics, integrating the FQAH phase with nontrivial higher-order topological states hosting fractional corner states is highly promising. Here, we establish a theoretical model on a generic $s{p}^{2}$ hybridized honeycomb lattice with a second-order topological insulating (SOTI) index that can give rise to the appealing FQAH state. Two topological flat bands carrying opposite nonzero Chern numbers emerge around the Fermi level, separated by an SOTI band gap. Exact-diagonalization calculations reveal that electron correlations drive the topological flat bands into rare FQAH states at fractional fillings of 1/3 and 2/5. These prominent fractional topological states persist across a wide parameter range, demonstrating exceptional resilience to variations in band dispersion and orbital composition. The coexistence of FQAH and SOTI states is anticipated to be realized in a practical silicene nanomesh material from first-principles calculations. Our work provides a different pathway for the fabrication of multifunctional and highly miniaturized topological quantum devices in pursuit of the topological quantum computing.