Dartmouth Events

Abstract: Topological phases with broken time-reversal symmetry and Chern number |C| ≥ 2 are of fundamental interest, but their realization on all experimental platforms, including ultracold atoms in optical lattices, remains challenging. We show that phases with higher Chern number arise when the spin-orbit coupling satisfies a combination of spin and spatial rotation symmetries. We leverage this result both to construct minimal two-band tight binding Hamiltonians that exhibit |C| = 2, 3 phases, and to show that the Chern number of one of the energy bands can be inferred from the particle spin polarization at the high-symmetry crystal momenta in the Brillouin zone. Using these insights, we provide a detailed experimental scheme for the specific realization of a time-reversal-breaking topological phase with |C| = 2 for ultracold atomic gases on a triangular lattice subject to spin-orbit coupling. The Chern number can be directly measured using Zeeman spectroscopy; for fermions the spin amplitudes can be measured directly via time of flight, while for bosons this is preceded by a short Bloch oscillation. Our results provide a pathway to the realization and detection of novel topological phases with higher Chern number in ultracold atomic gases.