Dynamics in the charge-density-wave systemNbSe3using inelastic x-ray scattering with meV energy resolution

Abstract

We present a study of the ambient and low-temperature dynamics on a single-crystalline sample of NbSe 3 using meV-resolution inelastic x-ray scattering. Two phonon branches ͑LA, TA 1 ) propagating along the system's quasi-one-dimensional direction b ជ * have been determined. The low-temperature data indicate the absence of a Kohn anomaly, similar to the case of (TaSe 4 ) 2 I, but at variance with other quasi-one-dimensional charge-density-wave systems ͑KCP, K 0.3 MoO 3 ) investigated so far.Charge-density-wave ͑CDW͒ states in quasi-onedimensional ͑Q1D͒ metallic systems have been the object of intense studies over the last 25 years. However, detailed information about the systems' lattice and CDW dynamics is still quite scarce. To a large extent this is due to the generally very small size of monocrystalline samples of CDW compounds, often too small for techniques like inelastic neutron scattering. Only the dynamics of three CDW systems, available in cm 3 -sized single crystals, have been accessible so far: the platinum-chain compound KCP, 1,2 the blue bronze K 0.3 MoO 3 , 3,4 and (TaSe 4 ) 2 I. 5 The Peierls instability leading to the CDW state is characterized by the opening of an electronic gap at the Fermi level and by a strong softening ͑Kohn anomaly͒ in the lowenergy phonon spectrum at the CDW-modulation wave vector qϭ2k F , where k F is the Fermi wave vector. As shown by Lee et al., 6 below the Peierls transition temperature T P , this soft mode splits up into two branches corresponding to CDW-amplitude excitations ͑amplitudon͒ and CDW-phase excitations ͑phason͒. The latter is expected to stay at zero excitation energy at qϭ2k F or to take up very low, but finite energies related to CDW-pinning by impurities in the system.The Kohn anomaly (TϾT P ) and the CDW dynamics (T ϽT P ) have indeed been observed in KCP, 1,2 as well as in K 0.3 MoO 3 , 3,4 using inelastic neutron scattering ͓three-axis spectroscopy ͑TAS͔͒. Contrary to these results, a thorough TAS study on (TaSe 4 ) 2 I revealed only a very limited phonon softening upon cooling towards T P and no evidence of phason-amplitudon decoupling below T P . 5 Here we present inelastic x-ray scattering ͑IXS͒ measurements on the CDW system NbSe 3 . Monocrystals of NbSe 3 grow in the form of whiskers with only very small cross sections ͑typically less than 0.1 mmϫ5 m), which made NbSe 3 essentially inaccessible to studies of the lattice-and CDW-related dispersions by neutron scattering techniques. So far only one TAS study of the longitudinal acoustic ͑LA͒ branch propagating along the Q1D direction has been performed by Monceau et al. 7 on a bunchlike assembly of 10 4 -10 5 NbSe 3 crystals aligned along the Q1D direction.Additionally, a Raman study of room-temperature optical lattice excitations is reported by Wieting et al. 8 The monoclinic Q1D compound NbSe 3 ͑space group P2 1 /m) undergoes two successive Peierls transitions at T P1 ϭ145 K and T P2 ϭ59 K. Below T P1 it develops a CDW superstructure with a modulation wave vector q ជ 1 ϭ(0,0.241,0) to which is a...

Response of Acoustic Phonons to Charge and Orbital Order in the 50% Doped Bilayer ManganiteLaSr2Mn2O7

“…Some known CDW compounds do not follow this phenomenology exactly. For example, in NbSe 2 , phonons soften over a relatively large range of wave vectors around the ordering wave vector [39]; NbSe 3 , which is believed to be in the strong-coupling regime, shows not softening but line broadening at the CDW wave vector on approach to the transition [40]. But all CDW compounds exhibit some anomalous phonon behavior tied to the ordering wave vector.…”

Theory of subgap interchain tunneling in quasi 1D conductors

“…Here, ⌬ 0 Ϸ 50-75 meV = 600-900 K, 0 Ϸ 1.7 Thz, ប 0 = T 0 Ϸ 7 meVϷ 80 K, T c = 180 K, u =2ϫ 10 4 m / s, v F =2ϫ 10 5 m / s; then ␤ Ϸ 2.5. For NbSe 3 , the data on phonon modes are contradictory, 35 but can be estimated from the bare frequency as T 0 ഛ 8 meV Ϸ 90 K; then we expect, for the second CDW, a similar value ␤ = v F / 4u = ⌬ 0 / 2ប 0 Ϸ 3. These values of the exponent ␤ are quite high to provide a fast fall of the current within the pseudogap, in qualitative accordance with the experiment, but the price is that the temperature limitations pool the theory to the 3D ordered phase, where more studies of the combined effects of the temperature and the long range order are necessary to be developed, in particular, the prefactors need to be calculated.…”

Nature of the Peierls transition in charge density wave systems: Strong coupling versus weak coupling

“…This contribution is essentially based on the papers [11] and [13]. I acknowledge the co-authors of these works: H. Berger, R. Currat, B. Hennion, M. Krisch, F. Levy, J.E.…”

“…NbSe 3 undergoes two CDWs, an upper one at T P 1 = 145 K and a second one at T P 2 = 59 K. The inelastic X-ray scattering (IXS) is a powerful technique for the study of phonon dispersion on samples only available in very small quantities. Measurements have been performed on the IXS beamline ID28 at the ESRF (Grenoble, France) on a NbSe 3 whisker of length about 6 mm and with a cross section of about 150 µm × 3 µm (width × thickness) [13].…”