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Charge density waves (CDW) have been studied at the surface of a cleaved TTF-TCNQ single crystal using a low temperature scanning tunneling microscope (STM) under ultra high vacuum (UHV) conditions, between 300K and 33K with molecular resolution. All CDW phase transitions of TTF-TCNQ have been identified. The measurement of the modulation wave vector along the a direction provides the first evidence for the existence of domains comprising single plane wave modulated structures in the temperature regime where the transverse wave vector of the CDW is temperature dependent, as hinted by the theory more than 20 years ago.

It is shown that, for transition-metal trichalcogenides NbSe3, for TaS3 both with a monoclinic and an orthorhombic unit cell, and for transition-metal tetrachalcogenide (TaSe4)2I, compounds which exhibit transport properties associated with charge-density-wave motion, the linear relationship between the current carried by the charge-density wave and the fundamental frequency of the ac voltage detected in the nonlinear state leads to a pinning potential periodicity which is half the charge-density-wave wavelength in agreement with the recent theory of Josephson oscillations of Barnes and Zawadowski.After NbSe3, ' nonlinear transport properties measured at temperatures below a Peierls transition have been measured in many other compounds such as TaS3 both with the orthorhombic" and monoclinic' unit cell, in NbS3, ' in blue bronze K030Mo03, and very recently in a transitionmetal tetrachalcogenide (TaSe4)2I. ' The extra conductivity observed was explained by a current-carrying chargedensity-wave (CDW) state as proposed by Frohlichg in 1954. The translation invariance of the phase of the CDW in real systems is broken by commensurability pinning or impurity pinning.A finite electric field must be applied in order to dislodge the CDW from the pinning centers. ' Above this threshold electric field, a periodic signal is measured through the voltage leads of the sample. " This ac signal was interpreted as the motion of the CDW in the anharmonic periodic pinning potential created by the impurities. "As all the lattice distortions of the compounds exhibiting CDW depinning were weakly incommensurate with the lattice, it was supposed that the pinning periodicity was the CDW wavelength. However, if the CDW is commensurate, the pinning periodicity would be the lattice constant along the chains. ' Very recently, Barnes and Zawadowski' studied the interaction of a moving CDW with impurities. They show that the CDW can be considered as the superposition of two macroscopic quantum states which are split by the motion of the CDW. Each state is composed of electron-hole pairs with, respectively, total momentum +Q. A second-order perturbation theory takes into account two impurity scatterings which transfer an electron-hole pair with momentum g to an electron-hole pair with momentumg. The result is an energy density periodic in space with a periodicity co/2w.The first-order perturbation theory leads to an energy density also periodic in space with the periodicity Xcpw as assumed in classical models. "" If in k space the Fermi distribution moves at the velocity u, the current in the sample is Jcpw where ne is the total electron concentration in the bands affected by the CDW. The CDW velocity can be written as the product of the fundamental frequency measured in the ac voltage and the pinning periodicity. Therefore JCOw/v = )le)i pinning ne can be calculated by simple band calculations: the Fermi level is at q =2kF =2'/scow and, in absence of any Peierls transition, there are two electrons in the band filled up to b'=27r/b, where b is th...

The experimental STM images for the CDW phase of the blue bronze Rb0.3MoO3 have been successfully explained on the basis of first-principles DFT calculations. Although the density of states near the Fermi level strongly concentrates in two of the three types of Mo atoms (MoII and MoIII), the STM measurement mostly probes the contribution of the uppermost O atoms of the surface, associated with the MoIO6 octahedra. In addition, it is found that the surface concentration of Rb atoms plays a key role in determining the surface nesting vector and hence the periodicity of the CDW modulation. Significant experimental inhomogeneities of the b * surface component of the wavevector of the modulation, probed by STM, are reported. The calculated changes in the surface nesting vector are consistent with the observed experimental inhomogeneities.

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