However, there are mechanisms by which a metal (defined more rigorously as a material having delocalized electron states at the Fermi level) can fail to conduct electricity, and the example that comes to mind is Anderson localization. In Anderson localization, scattering off impurities causes electron wavefunctions to interfere with one another in such a way that that the probability distribution cannot propagate (and propagation is necessary for metallic resistivity). According to this theory all 1-dimensional or 2-dimensional metals with disorder should not conduct electricity (at very low temperature)