Charge density waves interaction between CDWs

In conducting solids, the conduction electron density is spatially modulated, forming charge density waves (CDW) the periodic distortion accompanying the CDW (due to interaction between the conduction electron and the lattice) is responsible for the incommensurate phase (Overhauser, 1962 Di Salvo Rice, 1979 Riste, 1977). The occurrence of CDW and the periodic distortion can be understood in terms of the model proposed by Peierls and Frdhlich for one-dimensional metals. Let us consider a row of uniformly spaced chain of ions (spacing = a) associated with conduction electrons of energy E k) and a wave vector k. At 0 K, all the states are filled up to the Fermi energy, = E(kp). If the electron density is sinusoidally modulated as in Fig. 4.15 such that... 

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