Biophysics & Soft Matter Physics, London (ON)

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Charge Density Wave dynamics

What are charge-density waves?

Due to the reduced phase space, fluctuations, impurities and interactions have a strong effect on low dimensional systems. Systems that exhibit CDWs are typically quasi one-dimensional metals. They become insulators at the phase transition to the CDW state.  Almost 40 years ago  R. Peierls and H. Frohlich independently suggested that a coupling of the electron and phonon systems in a one dimensional metal is unstable with respect to a  static lattice deformation of wavevector Q=2kF.

Due to the periodicity of the lattice deformation, the electron density will also become  periodically modulated. This is illustrated in Figure 1. As a result of the modulation, a gap opens up in the single-particle excitation spectrum at the Fermi level, and a spatially periodic charge density modulation is formed with wavevector 2kF. The deformation is limited by the corresponding increase in elastic energy. This can be seen by writing down the energies for the lattice distortion and electrons; the CDW state has an energy that is lower by a logarithmic factor as compared to the uniform state.

Figure 1. The upper figures show the single particle energy band a) in the case when the electron and the phonon systems are not coupled. In that case the ions are equally spaced and the charge density - represented by the red line - is uniform. b) When the electron and phonon systems are allowed to interact, the competition between the elastic and electronic energies leads to a static lattice deformation and periodically modulated charge density. This is called the Peierls instability, and it referes to the zero temperature case. In real quasi-1D systems, this transition takes place at a finite temparature TP called the Peierls temperature. 

Why should we study charge-density waves?

Besides the industrial potential (switches, capacitors, detectors, etc.), CDWs provide one of the very few systems where it is possible to study the effects of quenced randomness on a periodic medium both theoretically and experimentally. In general, these systems display very intriguing physics and rise questions about the nature of the depinning transition, the effect of disorder on structural properties, and the possibility of the existence of nonequilibrium analogs of solids and liquids. Examples of related systems are flux line lattices in type-II superconductors, and magnetic bubble arrays. In addition to the above, rather macroscopic, aspects, the electronic properties of CDWs, or low-dimensional, systems are a separate and very active field of study. We are, however, interested in the more macrscopic properties, in particluar the interplay between elasticity, disorder and external driving forces.

MPEG movies of sliding charge-density waves:

  • Impurities distributed randomly (from a Gaussian distribution; weak pinning limit)
    • A small driving force is applied.The driving force is below the depinning threshold. While there are areas that have depinned, the is no net current flowing through the system. However, at the boundaries of moving and stationary areas dislocations are generated dynamically.
    • Same as the previous one but with a higher driving force. The systems is very close to the depinning thershold. There is a small net current flowing through the system. However, there are still large areas that remain pinnined. A lot of dislocations are generated at the boundaries of the moving and stationary areas leading to an increase of disorder in the system.
    • Higher driving force. The systems has depinned, but there are areas moving with different velocities.
    • Very far above the depinning threshold the system becomes again more disordered.
A couple of snapshots from the simulations:
     
    Figure 1:The CDW is pinned  by impurities. There is a finite number of dislocations (or topological defects) present even when the driving force is zero.  Figure 2:A small driving force is applied leading to proliferation of dislocations, i.e., to a more disordered structure. Figure 3:When the driving force is further increased, the dislocations move and annihilate, and the structure becomes more ordered.
CDW References:
    A quick introduction to CDWs:

  1. S. Brown and G. Grüner, Charge and Spin Density Waves, Scientific American, April 1994, p. 50.
  2. R. E. Thorne, Charge-Density-Wave Conductors, Physics Today, May 1996, p. 42. (Note: highly recommended, an excellent introduction to the many aspects related to CDWs)

    Reviews: 

  3. G. Grüner and A. Zettl, Charge Density Wave Conduction: 
          A Novel Collective Transport Phenomenon in Solids, Phys. Rep., vol. 119, p. 117 (1985)
  4. P. Monceau (ed.), Electronic properties of inorganic quasi-one-dimensional compounds 
          (Part I: Theoretical, Part II: Experimental), D. Reidel Publishing Company, 1985.
  5. G. Grüner, The Dynamics of Charge-Density Waves, Rev. Mod. Phys., vol. 60, p. 1129 (1988)
  6. L.P. Gor'kov and G. Grüner (eds.), Charge Density Waves in Solids, Elsevier Publishers, 1989.
  7. G. Grüner, Density waves in solids, Addison-Wesley (Reading, MA), 1994.
     

Our publications related to charge-density wave dynamics

  • Defects, Order, and Hysteresis in Driven Charge-Density Waves, Mikko Karttunen, Mikko Haataja, K. R. Elder, and Martin Grant,
    Phys. Rev. Lett., vol. 83, pp. 3518-3521 (1999)
    [Online] [preprint]

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Last modified Sunday October 23, 2011