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We present an ab initio approach for the calculation of phonon self-energiesand their fluctuation diagnostics, which allows us to identify the electronicprocesses behind phonon anomalies. Application to thetransition-metal-dichalcogenide monolayer 1H-TaS$_2$ reveals that couplingbetween the longitudinal-acoustic phonons and the electrons from an isolatedlow-energy metallic band is entirely responsible for phonon anomalies such asthe mode softening and associated charge-density waves observed in thismaterial. Our analysis allows us to distinguish between differentmode-softening mechanisms including matrix-element effects, Fermi-surfacenesting, and Van Hove scenarios. We find that matrix-element effectsoriginating from a peculiar type of Dirac pseudospin textures control thecharge-density-wave physics in 1H-TaS$_2$ and similar transition metaldichalcogenides.

physical review. b./physical review. b

Ab initio phonon self-energies and fluctuation diagnostics of phonon  anomalies: Lattice instabilities from Dirac pseudospin physics in transition  metal dichalcogenides