Characterize order outside the moiré K-star diagnostics

Characterize possible charge order at reciprocal-space wavevectors other than the six moiré Brillouin-zone K points, including order that may be hidden by symmetry averaging in the measured structure factor.

Background

The structure-factor analysis focuses on the six primitive Brillouin-zone corners associated with three-sublattice order. The authors note that a state can retain crystalline correlations even when translation-related charge patterns cancel the mean-density Fourier component at the K star. Thus, the reported K-star observables do not resolve all possible ordering wavevectors or symmetry-hidden order.

References

These quantities probe the $K$ star and leave open possible order at other wavevectors or order hidden by symmetry averaging.

Learning Quantum Matter through Attention in Complex Space  (2609.11792 - Jing et al., 10 Sep 2026) in Appendix D, subsection “Structure-factor components”

The present scan does not establish that such averaging occurs in the high-field state.

Learning Quantum Matter through Attention in Complex Space  (2609.11792 - Jing et al., 10 Sep 2026) in Appendix D, subsection “Structure-factor components”