# Charge density wave

A charge density wave ( english charge density wave , CDW) is a basic state in certain quasi- one-dimensional conductors , characterized by collective line characteristics. It has been discussed theoretically since the 1930s ( Rudolf Peierls 1930 in the one-dimensional case) and demonstrated experimentally in the 1970s.

## description

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

${\ displaystyle \ lambda _ {c} = {\ frac {\ pi} {k_ {F}}}}$

with the Fermi wave vector , ${\ displaystyle k_ {F}}$

corresponding to a wave vector . ${\ displaystyle 2 \ cdot k_ {F}}$

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).

In the CDW, as Peierls showed, a band gap forms at , 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 higher temperatures the metallic state is stable due to thermal excitations). As the temperature falls, there is a Peierls transition from the metallic to the CDW state, a second order phase transition . ${\ displaystyle | k | = k_ {F}}$

CDW show collective charge transport when an electric field is applied, but this depends on the underlying lattice. Most are the wave vectors of the CDW incommensurable with the lattice periods, and the CDW is in impurities "nailed". Collective conduction only occurs from a certain applied electric field strength (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, mode locking of the CDW current with applied alternating current with Shapiro steps in the current-voltage characteristic ). These dynamic effects are mainly due to the interaction with the impurities that hold the CDW. ${\ displaystyle E_ {T}}$

CDW were first discovered in 1977 by Nai-Phuan Ong and Pierre Monceau due to their unusual conductivity properties in niobium  triselenide (NbSe 3 ) and have since been observed in a number of other inorganic and organic materials, which are mostly characterized by one-dimensional (chain-like) structures at the atomic level. In the case of NbSe 3, the transition takes place at 145  K , but can also take place above room temperature , e.g. B. for niobium trisulfide  (NbS 3 ) 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.

## literature

• P. Monceau (editor): Electronic properties of quasi one dimensional materials , Reidel, Dordrecht 1985.
• George Grüner: Density waves in solids . Addison-Wesley, Frontiers in Physics, 1994.
• G. Grüner: The dynamics of charge-density waves . In: Reviews of Modern Physics . tape 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 . tape 119 , no. 3 , March 1985, p. 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 . tape 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 . tape 38 , no. 5 , 2004, p. 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 . tape 396 , no. 2 , 1930, p. 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, NP Ong, AM Portis, A. Meerschaut, J. Rouxel: Electric Field Breakdown of Charge-Density-Wave — Induced Anomalies in NbSe 3 . In: Physical Review Letters . tape 37 , no. 10 , September 6, 1976, p. 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 . tape 18 , no. 11 , December 1, 1978, pp. 6245-6252 , doi : 10.1103 / PhysRevB.18.6245 .
8. ^ PA Lee, TM Rice: Electric field depinning of charge density waves . In: Physical Review B . tape 19 , no. 8 , April 15, 1979, pp. 3970-3980 , doi : 10.1103 / PhysRevB.19.3970 .