Generating and detecting topological phases with higher Chern number

TL;DR

This paper demonstrates how to engineer and detect topological phases with higher Chern numbers in ultracold atomic gases by leveraging spin-orbit coupling symmetries and provides experimental schemes for realization and measurement.

Contribution

It introduces minimal two-band Hamiltonians with higher Chern numbers and links Chern number to spin polarization, enabling experimental realization and detection.

Findings

Higher Chern number phases arise from specific spin and spatial symmetries.

Constructed minimal Hamiltonians exhibit |C|=2,3 phases.

Proposed experimental schemes for ultracold gases to realize and measure these phases.

Abstract

Topological phases with broken time-reversal symmetry and Chern number |C|>=2 are of fundamental interest, but it remains unclear how to engineer the desired topological Hamiltonian within the paradigm of spin-orbit-coupled particles hopping only between nearest neighbours of a static lattice. 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.