High-Temperature Fractional Quantum Hall State in Floquet-Kagome Flat Band

Fractional quantum Hall effect (FQHE) has been predicted in topological flat band (FB) by single-particle band structure combined with phenomenological theory or solution of many-body lattice Hamiltonian with fuzzy parameters. A long-standing roadblock towards realization of FB-FQHE is lacking the many-body solution of specific materials under realistic conditions. Here, we demonstrate a combined study of single-particle Floquet band theory with exact diagonalization (ED) of many-body Hamiltonian. We show that a time-periodic circularly polarized laser inverts the sign of second-nearest-neighbor hopping in a Kagome lattice and enhances spin-orbit coupling in one spin channel, to produce a Floquet FB with a high flatness ratio of bandwidth over band gap, as exemplified in monolayer Pt₃C₃₆S₁₂H₁₂. The ED of the resultant Floquet-Kagome lattice Hamiltonian gives a one-third-filling ground state with a laser-dependent excitation gap of FQH state, up to an estimated temperature above 70 K. Our findings pave the way to explore the alluding high-temperature FB-FQHE.