Optical phonons and the soft mode in 2H-NbSe2

Abstract

We present an investigation of the lattice dynamics of the charge-density-wave compound 2H-NbSe 2 . We analyze the precise nature of the wave vector dependent electron-phonon coupling (EPC) and derive the bare dispersion of the charge-density-wave (CDW) soft phonon mode using inelastic x-ray scattering combined with ab-initio calculations. Experimentally, phonon modes along the Γ -M line, i.e. q = (h, 0, 0) with 0 ≤ h ≤ 0.5, with the same longitudinal symmetry (Σ 1 ) as the CDW soft mode were investigated up to 32 meV. In agreement with our calculations we observe significant EPC in the optic modes at h ≤ 0.2. We analyze the EPC in the optic as well as acoustic modes and show that the q dependences stem from scattering processes between two bands at the Fermi surface both having Nb 4d character. Finally, we demonstrate that the soft mode dispersion at T = 33 K (= T CDW ) can be well described on the basis of a strongly q dependent EPC matrix element and an acoustic-like bare phonon dispersion in agreement with observations near room temperature.

Charge order from orbital-dependent coupling evidenced by NbSe2

“…In the interaction of equation (1) we restrict attention to the longitudinal component of g, since only the longitudinal acoustic phonons are observed to soften in inelastic neutron and X-ray scattering experiments 19 .…”

“…First, it was observed in X-ray scattering experiments that at the transition temperature a broad momentum-range of phonons simultaneously softens towards zero energy 7,19 . This is in stark contrast to the sharp Kohn anomaly expected in a Peierls-like transition 13 and may be understood to be an effect of the importance of the entropy carried by phonon fluctuations in the strongly coupled scenario [20][21][22] .…”

Charge order inNbSe2

“…The 1Q CDW phases found in locally-strained regions by recent scanning tunneling microscopy (STM) experiments have a slightly modified wave number of Q CDW = (1 − δ) mechanisms underlying the CDW formation, including nested saddle-points in the electronic dispersion 21 , local field effects 22 , or a combination of weak nesting with strongly momentum-dependent electron-phonon coupling 18,23 . The latter claim found some support in the observation that inelastic X-ray scattering indicates that the longitudinal acoustic phonons in NbSe 2 are softened over a broad range of momenta around the CDW wave vector 23,24 . This is in contrast to the sharp Kohn anomaly characteristic of one-dimensional and well-nested CDW materials.…”

“…3, and the vector nature of g accounts for its coupling to atomic displacements in three real-space directions. The CDW in NbSe 2 is known from X-ray diffraction experiments to correspond to the softening of a longitudinal acoustic phonon, with negligible softening of the transverse modes 23,24 . Henceforth we consider only the longitudinal part of the electron-phonon coupling.…”

Wave-vector-dependent electron-phonon coupling and the charge-density-wave transition inTbTe3

“…Quantitatively, DFPT underestimates Γ by a factor of about 20. Indeed, we found in several studies that DFPT underestimates the experimental line widths for soft phonon modes in the CDW compounds NbSe 2 [5,20] and TiSe 2 [21] but also in the superconductor YNi 2 B 2 C [22]. However, DFPT predictions were typically a factor of only two below the observed values in these compounds, and were assigned to anharmonic contributions disregarded in DFPT.…”