= Solution
A <charge density wave> is a spatial modulation of the electron <charge density>, often accompanied by a periodic lattice distortion. Write a weak modulation as $\rho(x)=\rho_0+\rho_1\cos(Qx+\varphi)$. In a one-dimensional metal, the <Peierls distortion> couples states near opposite <Fermi points> most strongly for $Q=2k_F$. Opening a gap near the <Fermi energy> lowers occupied electronic energies, while the lattice deformation has a positive elastic energy cost. Their competition can make a periodic state favorable below a transition temperature.
The modulation can be commensurate or incommensurate with the underlying <Bravais lattice>. Diffraction detects additional satellite peaks, while transport can show reduced low-energy carrier density. Impurities can pin its phase; above a depinning field a collectively sliding modulation can contribute nonlinear current. These effects distinguish collective density modulation from simply assigning independent static charges to isolated lattice sites.
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