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Sliding Charge Density Wave Induces Electron Transport P Sliding Charge Density Wave Induces Electron Transport P. Monceau and M. Renard, Grenoble (Centre de Recherches sur les Très Basses Températures) Over the past fifteen years, intensive ions. The local electron charge density is experimental and theoretical work has partially neutralized by a concomitant Fig. 1 — Charge density waves on a surface been undertaken to understand the phy­ displacement of each ion to a new equili­ of 1T-TaS2 below the Peierls transition detec­ sical properties of systems with restric­ brium position, the displacement of the ted by a tunnelling microscope. The spacing ted dimensionality. A low-dimensional nth ion, initially at nro, being between the mounds which form a hexa­ conductor has an electrical conductivity un = u0 sin (nqro + Φ) (2) gonal array is the CDW wavelength (from re­ that is strongly anisotropic with respect Since a gap, A, is opened at the Fermi ference 2). to the crystal structure — a specimen level, the CDW state has an energy lower made up of infinite parallel chains for than the metallic state. example, will exhibit a high conductivity CDW formation has also been obser­ Very recently the use of a scanning tun­ only in the chain direction. Interest in ved in two-dimensional layered com­ nelling microscope on a cleaved surface this type of phenomenon has been pounds, namely transition metal dichal- of the two-dimensional 1TTaS2 CDW greatly stimulated by the recently-acqui­ cogenides, the Fermi surface of which compound has revealed that the real red possibilities of synthesizing new approximates to a cylinder with nearly space CDW structure is formed by hex­ families of inorganic as well as organic parallel faces. Thus a large fraction of agonal arrays of mounds with the CDW low-dimensional conductors. In a great states on the Fermi surface are con­ wavelength spacing 2) (Fig. 1). number of these compounds the inter­ nected by the same vector q = 2kF (the The opening of a gap below the Peierls action between ions and electrons, the nesting condition). Nevertheless, the transition temperature is reminiscent of so-called electron-phonon interaction, low-temperature ground state remains semiconductors, but the essential fea­ can cause a modulated collective defor­ metallic. In contrast, for a strictly one­ ture of a CDW is that its wavelength, mation of the electronic charge density dimensional conductor, the Fermi sur­ λcdw = 2π/2kF, is controlled by the to give a lower energy state at low tem­ face consists of two parallel planes, so Fermi surface dimensions and is gene­ perature, as was first pointed out by that all states are connected by the rally unrelated to the undistorted lattice Peierls 1). same q. The energy gap removes the periodicities, i.e. the CDW is incommen­ whole Fermi surface, and the low tempe­ surate with the lattice. Consequently Peierls Transition and Fröhlich Conduc­ rature ground state is insulating. the crystal no longer has a translation tivity In the strictly one-dimensional case group and in contrast to semiconduc­ As is well known from band theory, no long range order can be established tors, the phase, Φ, of the lattice distor­ every Brillouin zone constitutes a locus because of fluctuations and there is no tion is not fixed relative to the lattice but of discontinuity for the electronic ener­ phase transition at any temperature. In is able to slide along q. This phenome­ gy. If, in a one-dimensional electronic practice, however, with pseudo one­ non is easy to understand if we reco­ system with a Fermi vector of kF, a pe­ dimensional conductors, we can iden­ gnize that if the lattice is regular, no posi­ riodic lattice distortion of wave-vector tify a characteristic temperature, called tion is energetically favoured and no 2kF is introduced, the band structure the Peierls transition temperature below locking results. In more theoretical will be modified because of the new which a lattice distortion occurs and the terms: if we think of the CDW as resul­ periodicity. A new Brillouin zone appears condensed state can be described by an ting from an electronic interaction via at | kf | and so, each occupied electronic order parameter. The latter can be defin­ the lattice phonons, this interaction is energy for|k| < kF decreases, giving rise ed either in terms of the electron density the same in every galilean frame, provi­ to a new ground state of the system modulation as pq exp (iΦ) (see equation ded that the frame velocity is small com­ characterized by a charge density wave 1) or in terms of the lattice distortion pared with the sound velocity (in which (CDW) with wave vector q = 2kF. The which is proportional to pq. case the interaction would be strongly occupied electronic states are Bloch Modulation of the ion positions can be modified). CDW condensation may thus wave functions with the superlattice pe­ detected by X-ray, neutron or electron arise in any set of galilean frames with riodicity: diffraction measurements: superlattice uniform velocity, v, giving in the labora­ ψk = exp(ikr) E Vk n exp (i n q r) spots appear near the main Bragg spots tory frame an electronic current density, and consequently the electronic density that correspond to the unmodulated J = - noev (3) has Fourier components with wave-vec­ structure. Measurements of the inverse where no is of the order of the electron tors ± nq, especially for the fundamen­ separation of these superlattice spots number density condensed in the band tal ones ± q: give the CDW wave length. In real space, below the CDW gap. Pel = P0 + 2pq cos (qr + Φ) + ... (1) images of CDWs have been obtained This model of a sliding CDW was pro­ where po is the uniform electron density using high resolution electronic diffrac­ posed by Fröhlich in 1954 3) as a mecha­ and 2pq the charge modulation ampli­ tion. This method is very well suited to nism which could lead to a supercon­ tude. The phase, Φ, specifies the posi­ study defects in the CDW lattice indu­ ducting state. This Fröhlich mode is a tion of the CDW relative to the lattice ced, for instance, by electron irradiation. direct consequence of translation inva- 99 riance. In practice, as shown by Lee, Rice and Anderson 4) this translation inva­ riance is broken because the phase, Φ, can in fact be pinned to the lattice, for example by impurities or by a long- period commensurability between the CDW wavelength and the lattice. Oscil­ lations of the pinned CDW are expected to produce a large low-frequency AC conductivity and a large dielectric cons­ tant. An applied DC electric field, how­ Fig. 2 — Variation of the non­ ever, can supply the CDW with an ener­ linear electrical conductivity gy sufficient to overcome the pinning, so (normaliZed to the Ohmic value) that above a threshold field, the CDW as a function of the reduced can slide and carry a current. Damping electric field for an orthorhom­ prevents superconductivity. This extra bic TaS3 sample. The insert conductivity associated with the collec­ shows the V(l) characteristics. tive CDW motion, called Fröhlich con­ ductivity, has recently been observed 5). follows: tends to the value σa + σbb which is of — The DC electrical conductivity in­ the order of the metallic conductivity creases above a threshold field ET. extrapolated from above the critical tem­ Materials — The conductivity is strongly frequen­ perature. ET is also observed to increase Up to now three families of inorganic cy-dependent in the range of 100 MHz - significantly when the crystals are compounds have been found to exhibit few GHz. doped with impurities. non-linear transport properties at tem­ — Above the threshold field, a time- The low-field AC conductivity shows peratures below the Peierls transition, dependent voltage is generated in the a strong increase in the range of 100 namely: the transition metal trichalco- crystal which can be analysed as the MHz-1 GHz and then saturates at a value genides such as NbSe3, NbS3, TaS3 combination of a periodic component close to the DC infinite field limit. This with monoclinic or orthorhombic struc­ and a broad band noise following a 1/f behaviour can be described in terms of a tures; the molybdenum oxides variation. harmonic oscillator response of the K030MoO3 and Rb030MoO3 called blue — Interference effects occur between pinned CDW mode. For NbSe3 and TaS3 bronzes and halogened transition metal the AC voltage generated in the crystal the response is overdamped. Recent tetrachalcogenides such as (NbSe4)2l, in the non-linear state and an external RF measurements in the range of 10-100 (NbSe4)10I3, (TaSe4)2l. Without going field. GHz have revealed an inertial term that into detail, the structure of these com­ — Hysteresis and memory effects are has led to an estimation being made of pounds can be described as comprising : observed, principally at low tempera­ the CDW effective mass, the pinning fre­ chains of trigonal prisms stacked on top ture. quency and the damping constant. of each other with a cross-section close However at low temperatures the single to an isosceles triangle in the case of Fig. 2 shows the typical variation of oscillator description fails and a distribu­ NbSe3, layers in the case of K03MoO3, the electrical conductivity σ (normalized tion of pinning frequencies must be and parallel (TaSe4) chains with iodine to the ohmic value) as a function of elec­ taken into account. atoms lying between them in the case of tric field. The corresponding V(l) charac­ When E is above ET, a time-dependent (TaSe4)2l. Whilst NbSe3 remains metal­ teristic is drawn in the inset; a deviation voltage is generated in the crystal which lic at low temperature, all the other com­ from Ohm's law is observed above a can be studied with a spectrum analy­ pounds exhibit a semiconducting beha­ critical current IT which leads to a thres­ ser.
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