What are charge density waves

A Charge density wave (Englishcharge density wave, CDW) is a ground state in certain quasi-one-dimensional conductors, which is characterized by collective conduction properties. It has been discussed theoretically since the 1930s (Rudolf Peierls[1] 1930 in the one-dimensional case) and experimentally proven in the 1970s.


In CDW, both the density of the conduction electrons and the position of the lattice atoms are periodically modulated with a wavelength

with the Fermi wave vector,

corresponding to a wave vector.

The modes of the atomic lattice and electrons are coupled. The amplitude of the deflections is relatively small (less than one percent of the distance between the lattice atoms and also only a few percent with respect to the density of the conduction electrons).

As Peierls showed, there is a band gap in the CDW , the Peierls gap, through which the energy of the conduction electrons is lowered near the Fermi surface. In one-dimensional systems, this compensates for the energy required for the associated lattice oscillation at low temperatures. The CDW mode is therefore the preferred ground state in these systems if the temperature is low enough (at a higher temperature the metallic state is stable due to thermal excitations). As the temperature falls, there is a Peierls transition[2] from the metallic to the CDW state takes place, a phase transition of the second order.

CDW show collective charge transport when an electric field is applied[3], but that depends on the underlying grid. Usually the wave vectors of the CDW are incommensurable with the lattice periods[4], and the CDW is "nailed down" in imperfections. Only from a certain applied electric field strength collective conduction occurs (the CDW then “glides” over the faults). The line behavior is strongly non-linear. CDW materials are characterized by very large values ​​of the dielectric constant. In the metallic state they are strongly anisotropic. They show a rich dynamic behavior (such as hysteresis and memory effects, coherent alternating current components in the CDW current[5], Mode locking of the CDW current with alternating current applied Shapiro levels in the current-voltage characteristic). These dynamic effects are primarily due to the interaction with the impurities that hold the CDW.

CDW were first published in 1977 by Nai-Phuan Ong and Pierre Monceau in niobium triselenide (NbSe3) discovered[6] and has since been observed in a number of other inorganic and organic materials, most of which are characterized by one-dimensional (chain-like) structures at the atomic level. The transition takes place in NbSe3 takes place at 145 K, but can also take place above room temperature, e.g. B. with niobium trisulfide (NbS3) at 340 K. It is usually in the range 50 to 200 K.

CDW are related to spin density waves, which can be understood as being composed of two CDW, each for opposite spin.

CDW serve theorists as an exemplary study object of the interaction of a collective excitation with randomly distributed interferences. A frequently used model is the FLR model for CDW, named after Hidetoshi Fukuyama, Patrick A. Lee and T. Maurice Rice.[7][8]


  • P. Monceau (Editor): Electronic properties of quasi one dimensional materials, Reidel, Dordrecht 1985.
  • George Green: Density waves in solids. Addison-Wesley, Frontiers in Physics, 1994.
  • G. Grüner: The dynamics of charge-density waves. In: Reviews of Modern Physics. Volume 60, No. 4, October 1, 1988, pp.1129-1181, doi: 10.1103 / RevModPhys.60.1129.
  • G. Grüner, A. Zettl: Charge density wave conduction: A novel collective transport phenomenon in solids. In: Physics Reports. Volume 119, No. 3, March 1985, pp.117-232, doi: 10.1016 / 0370-1573 (85) 90073-0.
  • Lew Gorkow, G. Grüner (editor): Charge density waves in solids. North Holland 1989.
  • Robert E. Thorne: Charge Density Wave Conductors. In: Physics Today. Volume 49, No. 5, 1996, pp. 42-47, doi: 10.1063 / 1.881498.
  • Wolfgang Tremel, E. Wolfgang Finckh: Charge density waves: electrical conductivity. In: Chemistry in our time. Volume 38, No. 5, 2004, pp. 326–339, doi: 10.1002 / ciuz.200400221.
  • Onno Cornelis Mantel: Mesoscopic Charge Density Wires. 1999 (PDF - Dissertation, TU Delft).

Individual evidence

  1. ↑ R. Peierls: On the theory of the electrical and thermal conductivity of metals. In: Annals of Physics. Volume 396, No. 2, 1930, pp. 121-148, doi: 10.1002 / andp.19303960202.
  2. ↑ Michael Fowler: Peierl's transition. February 28, 2007, accessed November 3, 2012.
  3. ↑ They therefore played a role in outdated theories for superconductors in the 1950s, for example by Herbert Fröhlich
  4. ↑ The ratio of the wavelength of the CDW (which is only determined by the Fermi wave vector) and the grid spacing is irrational
  5. ↑ This means that when a direct voltage is applied, alternating current occurs (typically from 1 to 100 MHz), Coherent current oscillations, Narrow band noise
  6. ↑ P. Monçeau, N. P. Ong, A. M. Portis, A. Meerschaut, J. Rouxel: Electric Field Breakdown of Charge-Density-Wave — Induced Anomalies in NbSe3. In: Physical Review Letters. Volume 37, No. 10, September 6, 1976, pp. 602-606, doi: 10.1103 / PhysRevLett.37.602.
  7. ↑ Hidetoshi Fukuyama, Patrick A. Lee: Pinning and conductivity of two-dimensional charge-density waves in magnetic fields. In: Physical Review B.. Volume 18, No. 11, December 1, 1978, pp. 6245-6252, doi: 10.1103 / PhysRevB.18.6245.
  8. ↑ P. A. Lee, T. M. Rice: Electric field depinning of charge density waves. In: Physical Review B.. Volume 19, No. 8, April 15, 1979, pp. 3970-3980, doi: 10.1103 / PhysRevB.19.3970.