High-Temperature fractional quantum Hall state in the Floquet kagome flat band

A fractional quantum Hall effect (FQHE) has been predicted in a topological flat band (FB) by a single-particle band structure combined with phenomenological theory or solution of a many-body lattice Hamiltonian with fuzzy parameters. A long-standing roadblock toward the realization of a FB-FQHE is lacking the many-body solution of specific materials under realistic conditions. We demonstrate a combined study of single-particle Floquet band theory with exact diagonalization (ED) of a 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 a FQH state, up to an estimated temperature above 70 K. Our findings pave the way for exploring the alluding high-Temperature FB-FQHE.