Disordered elastic systems and electronic crystals

Electrons can crystallize to form a Wigner crystal. This crystallization is particularly effective in two dimensions. The effect of disorder on such electronic crystals can be taken into account using the same techniques and concepts, in particular the notion of Bragg glass phase, than the one developed to tackle classical disordered elastic systems. We analyze the properties of such a disordered Wigner crystal and discuss the physical consequences, both for the thermodynamics (compressibility etc.) and for the transport properties. This approach allows a good description of the optical conductivity and in particular to obtain correctly the density and field dependence of the pinning frequency. Relevance to experimental systems is discussed