Generalizing Quantum Hall Ferromagnetism to Fractional Chern Bands

Abstract

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 $T_c>0$ and additionally exhibits a quantized Hall conductance of $e^2/h$ as $T\to 0$. We note the close analogy to quantum Hall ferromagnetism in the multi-component problem and the connection to topological Mott insulators. We also discuss generalizations to other fillings and higher Chern numbers.

References in corpus (6)

• Fractional quantum Hall states at zero magnetic field
• Nearly-flat bands with nontrivial topology
• Topological Mott Insulators
• Fractional quantum Hall effect in the absence of Landau levels
• Nematic Valley Ordering in Quantum Hall Systems
• Evidence for a finite temperature phase transition in a bilayer quantum Hall system

Cited by in corpus (3)

• Topological Flat Bands and Correlated States in Twisted Monolayer-Bilayer Graphene
• Two-component quantum Hall effects in topological flat bands
• Quantum Hall effects of exciton condensate in topological flat bands