Fig. 1: Probing of charge-density-wave order in 2H-TaSe₂.

a Schematic dispersion (black solid lines) of an acoustic phonon with a soft mode at q_CDW ≈ (1/3,0,0) for energy-loss (positive energies) and energy-gain (negative energies). The red dot indicates the position of the corresponding superlattice peak in the ordered phase. Thick vertical (green) and horizontal (blue) arrows illustrate the scans done on the HERIX spectrometer to investigate the phonon softening and superlattice peak formation in 2H-TaSe₂. Labels b–d refer to the following panels showing typical results for the corresponding scans in more detail. Insets in (a) show the crystal structure of 2H-TaSe₂ (\(P{6}_{3}/{mmc}\), a = b = 3.44 Å, c = 12.7 Å, #194) and the layout of the Brillouin zone with high symmetry points labeled. b Energy scan at q ≠ q_CDW. For a realistic picture we convoluted a damped harmonic oscillator function with the pseudo-voigt-like experimental resolution (ΔE_FWHM = 1.5 meV). c Energy scan at q = q_CDW. The signal from the superlattice peak is approximated by the resolution function whereas the damped phonon is represented by a damped harmonic oscillator function convoluted with the resolution function. The scattering contributions from the superlattice peak [thick (red) solid line] are easily distinguished from the phonon contribution [thick (blue) dashed line]. d Momentum scan at zero energy transfer, E = 0, across the CDW superlattice peak (red dot in (a)). Because of the finite energy resolution and the broad phonon lineshapes, it is not clear how strongly soft phonon mode and superlattice peak contribute to the scattering at zero energy transfer.