Generalizing Quantum Hall Ferromagnetism to Fractional Chern Bands

TL;DR

This paper explores how quantum Hall ferromagnetism extends to fractional Chern bands, revealing spontaneous symmetry breaking and quantized Hall conductance in lattice models with interactions.

Contribution

It demonstrates the emergence of sublattice symmetry breaking and quantized Hall conductance in fractional Chern bands, extending quantum Hall ferromagnetism concepts to lattice systems.

Findings

System breaks sublattice symmetry with T_c > 0

Exhibits quantized Hall conductance of e^2/h at low T

Analogy to quantum Hall ferromagnetism and topological Mott insulators

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 $T \rightarrow 0$. 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.