Dimensionless ratios for metals

When the quantum theory of metals was formulated in the 1920's and 1930's significant insight was obtained by considering several dimensionless ratios which show that different physical quantities are related to each other purely in terms of fundamental constants. Furthermore, using quantum many-body theory and Landau's Fermi liquid theory it has been possible to show that even in strongly correlated electron materials such as heavy fermion compounds many of these ratios have the same value that they do for a non-interacting fermion gas. This is surprising because some of the quantities can be orders of magnitude larger than for a non-interacting system. Important examples include the Sommerfeld-Wilson ratio (ratio of the magnetic susceptibility to the linear temperature coefficient of the specific heat capacity), Lorentz ratio (associated with the Weidemann-Franz law), Korringa ratio, and the Kadowaki-Woods ratio. These ratios are useful because they

• demonstrate universality
• tell us that the same electrons are reponsible for the two quantities that form the ratio
• provide significant constraints on theories
• can be used as a criteria for non-Fermi liquid theory

In a series of posts I plan to illustrate just how robust these ratios are, using recent research from UQ.