Transition-metal dichalcogenides (TMDC) have attracted a tremendous interest in the last few years as they exhibit many interesting properties, such as the coexistence of two competing electronic orders: superconductivity and charge-density wave (CDW) as well as optical valley control and valleytronics in MoS2 monolayers.

In particular, an intense debate has developed around the origin of CDW order and its impact on the spectroscopic properties of these materials. The dynamic density response is a key quantity that could help us to disentangle CDW and superconductivity order. It is quantified by the loss function, or equivalently the dynamic structure factor S(q,ω). Its investigation has been the subject of a very recent EELS study that has reported a negative plasmon dispersion for in-plane momentum transfers of the loss function of 2H-NbSe2 [1]. This result was different from the expectations derived from the homogeneous electron gas, where the plasmon dispersion is positive. The negative plasmon dispersion was ascribed to correlation effects arising from the incipient CDW [1].

In an earlier publication [2], we presented the results of an extensive ab initio theoretical analysis of the loss functions of two prototypical TMDC materials, namely 2H-NbSe2 and 2H-Cu0.2NbS2, which respectively do and do not exhibit a CDW ordered phase. We found a negative plasmon dispersion in both materials and proposed a very general and simple interpretation of the in-plane negative plasmon behaviour. Our interpretation links the peculiar anisotropic band structure of those systems with narrow d-symmetry bands crossing the Fermi level.

Comparison between experimental (bold line) and theoretical (thin line) spectra of Cu0.2NbS2

Fig. 8: Comparison between experimental (bold line) and theoretical (thin line) spectra of Cu0.2NbS2 (a) and NbSe2 (b) at different values of momentum transfer Q (in multiple of 2π/c) normal to the plane of the layers. A broadening of 1.0 eV was used in the calculations.

Our study was conducted at ID20 using nonresonant inelastic X-ray scattering (IXS) spectroscopy. The results represent an important step towards the understanding of neutral excitations in this class of materials. In fact, at variance with the previous theoretical and experimental work that mainly focused on the low energy plasmon, we investigated the dynamic density response at higher energy up to 50 eV for momentum transfer normal to the plane of the layers. The dynamic range in energy and momentum required by this study is only accessible to IXS. Our results are summarised in Figure 8 where we compare the measured loss function obtained by IXS with state-of-the-art time-dependent density functional theory (TDDFT) calculations performed in adiabatic local density approximation (ALDA). The agreement between theory and experiment is good enough to show that TDDFT-ALDA is able to capture the physics of the collective excitations in this class of materials. At the same time, we found that the spectra of 2H-NbSe2 and 2H-Cu0.2NbS2 are similar not only at low energy and for in plane momentum transfer, as shown in [2], but also at higher energy and large momentum transfer normal to the plane. This result further validates our interpretation of the in-plane negative dispersion of the low energy plasmon reported in the previous work.


Principal publication and authors
P. Cudazzo (a,b), K.O. Ruotsalainen (c), C.J. Sahle (c), A. Al-Zein (d),  H. Berger (e), E. Navarro-Moratalla (f),  S. Huotari (c), M. Gatti (b,g,h) and  A. Rubio (a,b), Physical Review B 90, 125125 (2014).
(a) Nano-Bio Spectroscopy Group, Departamento Física de Materiales, Universidad del País Vasco, Centro de Física de Materiales CSIC-UPV/EHU-MPC and DIPC, San Sebastián (Spain)
(b) European Theoretical Spectroscopy Facility (ETSF)
(c) Department of Physics, University of Helsinki (Finland)
(d) ESRF
(e) École Polytechnique Fédérale de Lausanne (EPFL), Institut de Physique des Nanostructures (Switzerland)
(f) Instituto de Ciencia Molecular (ICMol), Universidad Valencia (Spain)
(g) Laboratoire des Solides Irradiés, École Polytechnique, CNRS-CEA/DSM, Palaiseau (France)
(h) Synchrotron SOLEIL, Saint Aubin (France)

[1] J. van Wezel et al., Phys. Rev. Lett. 107, 176404 (2011).
[2] P. Cudazzo, M. Gatti, A. Rubio, Phys. Rev. B 86, 075121(2012).