Not all densities are equal

One of the great challenges of describing and understanding strongly correlated metals is that the notion of "charge carrier density" becomes ambiguous. In a simple Fermi liquid metal all the different densities listed below are essentially identical (modulo some factors involving fundamental constants).

• Number of charge carriers (from simple chemical counting).
• The conduction band filling.
• Volume (area) of the Fermi surface
• Drude weight in the optical conductivity
• Hall coefficient (or number)
• Superfluid density of superconducting state

Some of these issues are explored in this PRB by Haerter and Shastry.