Fig. 5: Charge-density-wave (CDW) phase diagram.

a Temperature–pressure phase diagram of 2H-TaSe₂ derived from x-ray diffraction experiments. Blue (red) dots indicate the (T,p) points at which XRD (elastic IXS) measurements were performed. The blue/gray solid lines are guides to the eye for the pressure dependence of the T_ICDW/T_CCDW crossover and pass between investigated temperature–pressure points (blue/red dots) for which we do or do not observe a superlattice peak (blue line) or do observe a commensurate or incommensurate CDW ordering wave vector q_CDW (gray line). In regions of the phase diagram, where ICDW-CCDW crossover is not precisely known due to the limited number of points we could investigate with XRD, we show the evolution of T_CCDW as gray-dashed line. The color-code reflects the deduced values of the incommensurability δ of the CDW ordering wave vector q_CDW = (1/3-δ,0,0) [wave vectors Q/q and δ are given in reciprocal lattice units (r.l.u.)]. Open circles represent the superconducting transition temperature T_sc reported in ref. ²³. b Energy of the CDW soft phonon mode deduced from our high-pressure IXS measurements at T = 4 K (see Supplementary Fig. 5 for details). Error bars are deduced from the peak fitting procedure outlined in Supplementary Fig. 5. c Calculated square phonon energy of the soft phonon mode in 2H-TaSe₂ based on density-functional-perturbation theory (DFPT, black symbols, left-hand scale). Pressure effects were included using the experimental lattice parameters observed in XRD at T = 40 K. The vertical dashed (blue) line indicates the pressure p_c,DFPT = 18.8 GPa, for which a linear fit of the square phonon energy (dashed line) crosses zero. Calculations including electron–phonon coupling for p > p_c,DFPT predict a superconducting T_sc,DFPT = 11.8 K just above p_c,DFPT, which decreases for higher pressures (green symbols, right-hand scale).