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Charge density wave
A charge density wave (CDW) is a periodic modulation of the electronic charge density - a standing wave in the electronic wave functions created by combining electron states moving in opposite directions. This is accompanied by a periodic distortion of the atomic lattice in a quasi-1-D or quasi-2-D layered metallic crystal. Its existence was first predicted in the 1930s by Rudolf Peierls. He argued that a 1-D metal would be unstable to the formation of energy gaps at the Fermi wavevectors ±''kF'', which reduce the energies of the filled electronic states at ±''kF'' as compared to their original Fermi energy ''EF''. The temperature below which such gaps form is known as the Peierls transition temperature, ''TP''. A spin density wave (SDW) can be viewed as two CDWs for the spin-up and spin-down subbands, whose charge modulations are 180° out-of-phase.
== Fröhlich model of superconductivity ==
In 1954, Herbert Fröhlich proposed a microscopic theory, in which energy gaps at ±''kF'' would form below a transition temperature as a result of the interaction between the electrons and phonons of wavevector ''Q''=2''kF''. Conduction at high temperatures is metallic in a quasi-1-D conductor, whose Fermi surface consists of fairly flat sheets perpendicular to the chain direction at ±''kF''. The electrons near the Fermi surface couple strongly with the phonons of 'nesting' wave number ''Q'' = 2''kF''. The 2''kF'' mode thus becomes softened as a result of the electron-phonon interaction. The 2''kF'' phonon mode frequency decreases with decreasing temperature, and finally goes to zero at the Peierls transition temperature. Since phonons are bosons, this mode becomes macroscopically occupied at lower temperatures, and is manifested by a static periodic lattice distortion. At the same time, an electronic CDW forms, and the Peierls gap opens up at ±''kF''. Below the Peierls transition temperature, a complete Peierls gap leads to thermally activated behavior in the conductivity due to normal uncondensed electrons. However,a CDW whose wavelength is incommensurate with the underlying atomic lattice would have no preferred position, or phase ''φ'', in its charge modulation ''ρ0'' + ''ρ1''cos(- φ'' ). Fröhlich thus proposed that the CDW could move and, moreover, that the Peierls gaps would be displaced in momentum space along with the entire Fermi sea, leading to an electric current proportional to ''dφ/dt''. However, as discussed subsequent sections, even an incommensurate CDW cannot move freely, but is pinned by impurities. Moreover, interaction with normal carriers leads to dissipative transport, unlike a superconductor.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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