Generalizing quantum Hall ferromagnetism to fractional Chern bands

We study the interplay between quantum Hall ordering and spontaneous sublattice symmetry breaking in multiple-Chern-number bands at fractional fillings. Primarily, we study fermions with repulsive interactions near half filling in a family of square lattice models with flat C=2 bands and a wide band gap. By perturbing about the particularly transparent limit of two decoupled C=1 bands and by exact diagonalization studies of small systems in the more general case, we show that the system generically breaks sublattice symmetry with a transition temperature Tc>0 and additionally exhibits a quantized Hall conductance of e2/h as T→0. We note the close analogy to quantum Hall ferromagnetism in the multicomponent problem and the connection to topological Mott insulators. We also discuss generalizations to other fillings and higher Chern numbers.