Patterns and driving forces of dimensionality-dependent charge density waves in 2H-type transition metal dichalcogenides

Abstract

Charge density wave (CDW) is a startling quantum phenomenon, distorting a metallic lattice into an insulating state with a periodically modulated charge distribution. Astonishingly, such modulations appear in various patterns even within the same family of materials. Moreover, this phenomenon features a puzzling diversity in its dimensional evolution. Here, we propose a general framework, unifying distinct trends of CDW ordering in an isoelectronic group of materials, 2H-MX 2 (M = Nb, Ta and X = S, Se). We show that while NbSe 2 exhibits a strongly enhanced CDW order in two dimensions, TaSe 2 and TaS 2 behave oppositely, with CDW being absent in NbS 2 entirely. Such a disparity is demonstrated to arise from a competition of ionic charge transfer, electron-phonon coupling, and electron correlation. Despite its simplicity, our approach can, in principle, explain dimensional dependence of CDW in any material, thereby shedding new light on this intriguing quantum phenomenon and its underlying mechanisms.

Weak Dimensionality Dependence and Dominant Role of Ionic Fluctuations in the Charge-Density-Wave Transition of NbSe2

“…Moreover, we show that, in spite of interlayer interaction, the CDW transition temperature and spatial modulation weakly depend on thickness. Our result supports the STM measurements on single layers grown by MBE [37], but it questions the Raman results on exfoliated samples that estimate a large enhancement of T CDW in the monolayer [35,36]. It is to be seen whether the enhanced T CDW observed in Raman experiments is a consequence of the sample deterioration, e.g., oxidation, during the exfoliation process or if it is affected by the substrate.…”

“…In other TMDs as well, the phonon frequency of the mode that drives the CDW is strongly reduced by cooling and eventually vanishes at T CDW [33,34]. The CDW transition temperature in the NbSe 2 monolayer has been determined by Raman measurements in exfoliated samples on sapphire substrates [35,36], as well as by scanning tunneling microscopy (STM) in single layers grown by molecular beam epitaxy (MBE) on bilayer graphene, which confirmed that the CDW order remains 3 × 3 [37]. The problem is that while the Raman experiments on exfoliated samples estimate a huge enhancement of T CDW up to 145 K [35,36], STM experiments determine that dimensionality does not affect T CDW as the CDW occurs between 25 and 45 K [37].…”

Computational Methods for Charge Density Waves in 2D Materials

“…Lastly, a general framework for dimensionality dependent CDWs in both TaS 2 and TaSe 2 was proposed by Lin et al [ 168 ]. They focused on 2 H MX 2 (M = Nb, Ta and X = S, Se).…”

“…In terms of vibrational properties, the IC-CDW phase more pronounced in TaSe 2 more greatly affects Raman mode observations between room temperature and temperatures corresponding to the C-CDW phase transition. In terms of dimensionality, a key point is that both materials differ significantly on their calculated electron–phonon coupling constant [ 168 ], and since such coupling is tied to superconductivity, it follows that observations of the latter would also be substantially altered.…”

“…( c ) Schematic illustration of the possible phase diagram describing the CDW response in a layered material in terms of ionic charge transfer (ΔQ I ), electron–phonon coupling constant (λ), and the spatial extension of electronic wave functions (1/<r 2 >). Reference [ 168 ] is an open-access article distributed under the terms of the Creative Commons CC BY license (Available online: (accessed on 14 December 2021)), which permits unrestricted use, distribution, and reproduction in any medium.…”