High-temperature fractional quantum Hall states.

We show that a suitable combination of geometric frustration, ferromagnetism, and spin-orbit interactions can give rise to nearly flatbands with a large band gap and nonzero Chern number. Partial filling of the flatband can give rise to fractional quantum Hall states at high temperatures (maybe even room temperature). While the identification of material candidates with suitable parameters remains open, our work indicates intriguing directions for exploration and synthesis.