Extended Data Fig. 8: ARPES simulation for charge density waves.
From: Dark states of electrons in a quantum system with two pairs of sublattices
a,b, Crystal structure of monoatomic chains running along x in normal (a) and CDW (b) states. The two sublattices formed by dimerization are labelled A and B in b. c,d, Band structure of monoatomic chains in normal (c) and CDW (d) states calculated by tight-binding models and plotted along kx. e, ϕAB of the lower energy band in d obtained from tight-binding models and shown along kx. f,g, ARPES simulations for normal (f) and CDW (g) states based on the model of sublattice interference. With the scattering plane of xz, Mk can be written in the form of \(1+{e}^{i{\phi }_{\text{AB}}}\) arising from integration over the scattering plane. This is independent of light polarisation because no parity conversion is expected across this scattering plane. The Fermi energy is assumed to be at the grey horizontal dotted lines. h, Magnified view of ARPES simulations marked by the red box in g, which shows typical spectral features that gradually diminish in the vicinity of energy gaps or along backfolding of the main band. This can be explained by incomplete phase polarisations near ±π/2a indicated by red arrows in e as a natural consequence of the two sublattices located slightly off the half-translation positions in b. Those centred at ±π/a with ϕAB ≈ ±π cannot be detected by ARPES, because they are nearly the dark states.
