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.

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