Drude weight and superconducting weight

The Drude weight D (also called charge stiffness) measures the effective electron density contributing to dc conductivity; it vanishes in insulators. It is a general concept, which applies to any metal, including cases with disorder and electron-electron interaction. We provide a thorough analysis of D and of its meaning, both in the general case and in the special case of band metals, where we also show that D has a close relationship to orbital magnetization. The superconducting weight D-s measures instead the superfluid density accounting for the Meissner effect. The two quantities D and D-s are the main criteria to discriminate between insulators, metals, and superconductors.