Commensurability of the 3/8 instability wavevector

Determine whether the true instability wavevector in CsV₃Sb₅ is commensurate at δ = 3/8 or slightly incommensurate, using methods capable of resolving wavevectors beyond the supercell sizes accessible to current calculations.

Background

The paper identifies the R₃ phonon mode near Q = (3/8, 0, 1/2) as the leading harmonic instability of CsV₃Sb₅ and studies it primarily at the commensurate value δ = 3/8 because that wavevector is directly accessible on the employed 8 × 8 × 4 reciprocal-space grid. Fourier interpolation instead places the most unstable wavevector near δ ≈ 0.39, but the authors state that available supercell sizes cannot resolve whether the experimentally relevant ordering is exactly commensurate or slightly incommensurate.