The quasi-two-dimensional NbSe2 is a van der Waals layered material and a member of the remarkable transition metal dichalcogenide family. A metal at room temperature, NbSe2 undergoes a charge density wave (CDW) transition at about 33 K and a superconducting transition at about 5 K. This CDW transition is interesting on many fronts, not least as it is an incommensurate, continuous phase transition and the CDW phase remains incommensurate right down to the formation of the superconducting phase [1].

In the study of dynamics, a variety of techniques, including inelastic neutron scattering and He scattering, have either concentrated on the surface or the bulk properties. Inelastic X-ray scattering offers the unique possibility to study surface and bulk dynamics in a single experiment. This is achieved by setting the sample in grazing-incidence condition thus holding the incoming X-rays below the critical angle of total external reflection. In this case, the incident electromagnetic field displays an exponential decay in the sample bulk. In this geometry the scattering depth is about 4 nm [2], and the topmost four atomic layers contribute 50% to the scattered signal. By increasing the incidence angle beyond the critical angle one can penetrate deep into the sample bulk. This surface sensitive setup was realised on ID28 by inserting a deflector mirror in front of the sample. Thanks to the small vertical beam size at the sample position, the experiment could be conducted with an overall energy resolution of 3 meV, even in this flux-demanding geometry.

Fig. 2: (a) The scattering geometry for grazing-incidence inelastic scattering. (b) Spectra of NbSe2 collected in surface and bulk geometry at 2/3 of the Brillouin zone along the [00] direction. (Raw data: open circles with error bars. Dashed lines: individual elastic and inelastic contributions. Solid line: overall best fit result.

By varying the angle of incidence above and below the critical angle of total external reflection we have measured surface and bulk NbSe2 energy transfer spectra, from -20 to 35 meV, at a number of points in momentum space (see Figure 2). The predominantly longitudinal 1 1 and 1 2 modes are intense. In addition, small contributions from some of the 3 branches, predominantly of transverse nature, are also visible. We use a damped harmonic oscillator (DHO) model function to extract peak positions and so determine surface and bulk phonon dispersion curves shown in Figure 3. In both configurations the longitudinal 1 2 mode displays significant softening in energy at 2/3 of the reduced Brillouin zone. This points to a strong interaction between the phonons and the conduction electrons. The increased anomaly at the surface is evidence that some change is occurring in the topmost layers. One possibility is that the surface electronic state cuts the Fermi surface at a different position from that of the bulk Fermi wave vector, as predicted by Benedek et al. [3]. Another possibility would involve an increased electron-phonon interaction, which is consistent with the change of symmetry and coordination of the upper atomic layers with respect to that of the bulk.

Fig. 3: Room temperature surface () and bulk () phonon dispersion curve of 2H-NbSe2 here = 2 – h is in reciprocal space units. The ∑1 1, ∑1 2 modes are shown. A shift to lower energy is seen in the surface data at = 0.33 (lines are a guide to the eye).

In summary, we have measured the bulk and surface phonon dispersion relations for 2H-NbSe2 at 300 K, by selecting between surface- and bulk- sensitive geometry by means of grazing-incidence inelastic X-ray scattering, and varying depth sensitivity from 4 nm to 100 nm. Our results indicate that the anomaly for the surface mode occurs at a lower energy than that measured in bulk sensitive geometry in the same experiment, showing evidence of a modified behaviour in the uppermost layers. We demonstrate that inelastic X-ray scattering in grazing-incidence conditions provides a unique tool to selectively study either surface or bulk lattice dynamics in a single experiment.



[1] D. E. Moncton, J. D. Axe, and F. J. DiSalvo, Phys. Rev. B 16, 801 (1977).
[2] H. Dosch, Phys. Rev. B 35, 2137 (1987).
[3] G. Benedek, L. Miglio, and G. Seriani, in Helium Atom Scattering from surfaces, edited by E. Hulpke, Springer Series in Surface Science, 27, 208 (1992).

Principal Publication and Authors

B.M. Murphy (a, b), H. Requardt (c), J. Stettner (a), J. Serrano (c), M. Krisch (c), M. Müller (a), W. Press (a,d), Phys. Rev. Lett. 95, 256104 (2005).
(a) Institut für Experimentelle und Angewandte Physik, Christian-Albrechts-Universität, Kiel (Germany)
(b) CCLRC Daresbury Laboratory, Warrington (UK)
(c) ESRF
(d) ILL