Thursday, July 21, 2011

Thermoelectric power in strongly correlated Fermi liquids

Finding universal dimensionless ratios has proven key in understanding both elemental metals and strongly correlated Fermi liquids. Examples of important ratios include those associated with the names Sommerfeld-Wilson, Korringa,  Lorenz, and Kadowaki-Woods. Here is another one...

Today I read I nice article On the thermoelectricity of correlated electrons in the zero-temperature limit by Kamran Behnia, Didier Jaccard and Jacques Flouquet. The graph below shows evidence for a universal ratio for a wide range of materials. The ratio of the slope of the thermopower S(T) versus temperature to the specific heat coefficient gamma equals +/-1/eNA where NA is Avagadro's number and the sign depends on whether the charge transport is via electrons or holes.
Note the log-log scale which covers three decades.

This is the value of the ratio expected for a non-interacting fermion gas. It would be slightly different in Mott's formula for the thermopower with an energy dependent scattering rate [such subtleties are probably lost on the log-log scale]. 
A universal ratio for an Anderson impurity model was predicted by Houghton, Read, and Won [amongst others and discussed in Appendix E of Hewson's book on the Kondo effect].
A discussion of the temperature dependence of the thermopower for a DMFT (Dynamical-Mean-Field-Theory) treatment of the Hubbard model is here.

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