CDW-SDW
Charge density wave dynamics
2000–03 Ph.D. at the Centre de Recherche sur les Très Basses Températures (CNRS), University of Joseph Fourier in Grenoble, France
Supervisor: P. Monceau and R. Currat
Referees: T. Giamarchi, T. Klein and S. Ravy
Subject: Dynamics and structure of a charge density wave
This study follows a theme common in many physical systems: how elastic systems behave when interacting with disorder. I have studied how a charge density waves in one-dimensional materials interact with disorder when it is set in motion and how two charge density waves interact with each other. Most of the results of my thesis have been published (see list of publications). Manuscript (in french) available here [15]
- Motional ordering of a CDW
In the early thirty’s, Peierls has demonstrated in quasi-one-dimensional metal, that it exists an electron-phonon coupling which makes unstable the metallic state at low temperature [1]. Peierls considers the quasi-one-dimensional metal such as a chain of equally spaced atoms. Under a critical temperature T_{c}, the most stable state is a distortion of the atomic lattice associated with an electronic density modulation with the same periodicity: this is the CDW state. The electronic modulation has a wave vector Q equal to two time the Fermi wave vector. Like superconductivity, the modulation is caused by an instability of the Fermi surface due to electron-phonon interaction. Dimerization of the atomic position appears, a gap is opened: the increase of the elastic energy due to the nearness of the atoms (proportional to u^{2}) is compensated by the decrease of the electronic energy (proportional to u^{2}lnu). That’s why ground state at low temperature of the one dimensional system is a modulated lattice. Peierls transition is a metal-insulator transition. At rest the CDW is pinned by randomly distributed impurities. Above a threshold electric field, depinning occurs and the CDW slides with respect to the lattice, thus contributing to the electronic charge transport [2]. CDWs are representative of a general class of dynamical systems exhibiting elastic and plastic properties in the presence of quenched disorder (other examples: moving vortex lattices [3], Wigner crystals formed by a 2D electron gas in a magnetic field [4], solid friction interfaces [5], etc.). Current problems concern the nature of the transient and moving steady states. With this aspect, the correlation lengths of NbSe_{3} at rest and in motion have been measured, with and without additional RF excitation (in the mode-locked state), using x-ray synchrotron diffraction (measurements done at the European Synchrotron Radiation Facility [16]). The longitudinal correlation length is increased indicating a better CDW order when the CDW moves.
[1] R. E. Peierls, Quantum theory of solids, (Oxford University Press, 1955).
[2] G. Grüner, Rev. Mod. Phys. 60, 1129 (1988).
[3] G. Blatter, M. V. Feigelman, V. B. Geishkenbein, A. I. Larkin, and V. M. Vinokur, Rev. Mod. Phys. 66, 1145 (1994).
[4] E. Y. Andrei, G. Deville, D. C. Glattli, F. I. B. Williams, E. Paris, and B. Etienne, Phys. Rev. Lett. 60, 2765 (1988).
[5] D. Cule and T. Hwa, Phys. Rev. Lett. 77, 278 (1996).
- Dynamical decoupling of two CDW's
NbSe_{3} is a quasi-1D material which undergoes two successive Peierls transitions at T_{C1} = 145 K and T_{C2} = 59 K, with modulation wave vectors Q_{1} (0, 0.241, 0) and Q_{2} (0.5, 0.260, 0.5), respectively. These two modulation wave vectors nearly satisfy the relation: 2(Q_{1} + Q_{2})= (1 1 1) which suggests the possibility of a joint commensurability between the lattice and the two CDWs, effect known as a phase-locking and predicted theoretically [1]. However, no experimental evidences where found on Q_{1} in the vicinity of T_{C2} [2] and no phase-locking or sign of interaction between the two CDWs were observed previously in the static or the sliding regime. In these experiments. an antagonistic behavior of the two satellite peaks was detected at a much higher current value than the measured threshold. By combining transport, noise and X-ray diffraction measurement, this effect was identified as a sliding induced decoupling by charge transfer between the two CDWs. Finally, these results demonstrate that the switching effects [3] measured by transport measurements 30 K below T_{C2} are not linked to a possible phase-locking effect.
[1] R. Bruinsma and S. E. Trullinger, Phys. Rev. B 22, 4543 (1980).
[2] A. H. Moudden, J. D. Axe, P. Monceau, and F. Levy, Phys. Rev. Lett. 65, 223 (1990).
[3] Y. Li, D.Y. Noh, J. H. Price, K. L. Ringland, J. D. Brock, S.G. Lemay, K. Cicak, R. E. Thorne, and M. Sutton, Phys. Rev. B 63, 041103(R) (2001).
- Spin density wave in quasi-1D organic materials by neutron diffraction
During my PhD, I also studied by neutron diffraction the spin density wave transition (SDW) of two quasi-1D organic deuterated compounds d-(TMTSF) _{2} AsF _{6} and d-(TMTSF) _{2} PF _{6} . Despite several experiments, we haven't been able to detect this transition, certainly due to the small sizes of our crystals. Sometimes things don't work as you wish... These experiments were performed in the Institut Laue Langevin [17]. The quest of the SDW peak remains a serious challenge. For more details see Annexe B of my thesis (this part is in english) [18]
Related publications:
- A. Ayari, R. Danneau, H. Requardt, L. Ortega, J.E. Lorenzo, P. Monceau, R. Currat, S. Brazovskii and G. Grübel
Switching effects and sliding-induced charge transfer between the coexisting Q_{1} and Q_{2} charge density waves in NbSe_{3}
J. Phys. IV 131, 125 (2005)
- A. Ayari, R. Danneau, H. Requardt, L. Ortega, J.E. Lorenzo, P. Monceau, R. Currat, S. Brazovskii and G. Grübel
Sliding-induced decoupling and charge transfer between the coexisting Q_{1} and Q_{2} charge density waves in NbSe_{3}
Phys. Rev. Lett. 93, 106404 (2004) [19]
- R. Danneau, A. Ayari, D. Rideau, H. Requardt, J.E. Lorenzo, L. Ortega, P. Monceau, R. Currat and G. Grübel
Reply to Comment on Motional ordering of a charge density wave in the sliding state
Phys. Rev. Lett. 91, 049704 (2003) [20]
- R. Danneau, A. Ayari, D. Rideau, H. Requardt, J.E. Lorenzo, L. Ortega, P. Monceau, R. Currat and G. Grübel
Motional ordering of a charge density wave in the sliding state
Phys. Rev. Lett. 89, 106404 (2002) [21]
- R. Danneau, A. Ayari, D. Rideau, H. Requardt, J.E. Lorenzo, L. Ortega, P. Monceau, R. Currat, and G. Grübel
Increase of the charge density wave phase coherence in the sliding and the mode-locked state
J. Phys. IV 12, Pr9-177 (2002)
- H. Requardt, D. Rideau, R. Danneau, A. Ayari, F. Ya Nad, J.E. Lorenzo, P. Monceau, R. Currat, C. Detlefs, D. Smilgies and G. Grübel
X-ray diffraction study of the transient structure of sliding charge density waves in NbSe_{3}
J. Phys. IV 12, Pr9-181 (2002)
- H. Requardt, J.E. Lorenzo, R. Danneau, R. Currat and P. Monceau
Studies of the dynamics in charge density wave systems using inelastic X-ray scattering with meV-energy-resolution
J. Phys. IV 12, Pr9-39 (2002)