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Contradictory experiments have been reported about the dimensionality effecton the charge-density-wave transition in 2H NbSe$_2$. While scanning tunnellingexperiments on single layers grown by molecular beam epitaxy measure acharge-density-wave transition temperature in the monolayer similar to thebulk, around 33 K, Raman experiments on exfoliated samples observe a largeenhancement of the transition temperature up to 145 K. By employing anon-perturbative approach to deal with anharmonicity, we calculate from firstprinciples the temperature dependence of the phonon spectra both for bulk andmonolayer. In both cases, the charge-density-wave transition temperature isestimated as the temperature at which the phonon energy of the mode driving thestructural instability vanishes. The obtained transition temperature in thebulk is around 59 K, in rather good agreement with experiments, and it is justslightly increased in the single-layer limit to 73 K, showing the weakdependence of the transition on dimensionality. Environmental factors couldmotivate the disagreement between the transition temperatures reported byexperiments. Our analysis also demonstrates the predominance of ionicfluctuations over electronic ones in the melting of the charge-density-waveorder.

Weak Dimensionality Dependence and Dominant Role of Ionic Fluctuations in the Charge-Density-Wave Transition of NbSe$_2$