Weak dimensionality dependence and dominant role of ionic fluctuations in the charge-density-wave transition of NbSe2

Contradictory experiments have been reported about the dimensionality effect on the charge-density-wave transition in 2H NbSe2. While scanning tunneling experiments on single layers grown by molecular beam epitaxy measure a charge-density-wave transition temperature in the monolayer similar to the bulk, around 33 K, Raman experiments on exfoliated samples observe a large enhancement of the transition temperature up to 145 K. By employing a nonperturbative approach to deal with anharmonicity, we calculate from first principles the temperature dependence of the phonon spectra both for bulk and monolayer. In both cases, the charge-density-wave transition temperature is estimated as the temperature at which the phonon energy of the mode driving the structural instability vanishes. The obtained transition temperature in the bulk is around 59 K, in rather good agreement with experiments, and it is just slightly increased in the single-layer limit to 73 K, showing the weak dependence of the transition on dimensionality. Environmental factors could motivate the disagreement between the transition temperatures reported by experiments. Our analysis also demonstrates the predominance of ionic fluctuations over electronic ones in the melting of the charge-density-wave order.I. E. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (Grant No. FIS2016-76617-P). M. C. acknowledges support from Agence Nationale de la Recherche, Grant No. ANR-19-CE24-0028. L. M., M. C., and F. M. acknowledge support from the Graphene Flagship. F. M. and L. M. acknowledge support by the MIUR PRIN-2017 program, Project No. 2017Z8TS5B. Calculations were performed at the Joliot Curie-AMD supercomputer under the Partnership for Advanced Computing in Europe Project No. RA4956 and at the supercomputers of the Donostia International Physics Center (DIPC).Peer reviewe