Set of supplementary notes.

10.4. FERMI LIQUIDS AT THE LIMIT: HEAVY FERMIONS 155
Figure 10.9: Inverse of the magnetic susceptibility χ of UPt 3 plotted versus temperature T . At
high temperature, χ −1 ∝ T , suggesting local-moment behaviour.
The Sommerfeld coefficient of the heat capacity is linked to the electronic density of states
at the Fermi level, g(E F ), which in turn is inversely proportional to the Fermi velocity v F . This
is because v F = 1 |∇ h¯ kE|, and the density of states is obtained by integrating dk/dE over the
Fermi surface: g(E F ) ∝ ∫ dA 1
|∇ k
. On the other hand, the momentum of quasiparticles at the
E|
Fermi surface is h¯k F , but can also be written as m ∗ v F . As the conduction electron density in
CeCu 6 is not expected to be very different from that in Cu, we can expect k F to be similar in
both metals. In fact, k F is of order 0.5-1.0 Å −1 in many metals. This value is not affected by
the strength of electronic interactions, because the size of the Fermi surface is essentially fixed
only by the number of electrons, not by their interactions. We find, then, that the effective
quasiparticle mass m ∗ ∝ g(E F ). All else being equal, the quasiparticles in CeCu 6 would appear
to have a 150 times higher effective mass than those in Cu.
Note, also, that the high value for C/T is in CeCu 6 is only reached at the lowest temperatures.
Such a strong upturn of C/T at low T is observed in many cases. It suggests that the
heavy fermion state develops fully only at low temperature.
10.4.2 High T: “local moments”, low T: Fermi liquid
While the behaviour of CeCu 6 and other heavy fermion materials at low temperatures is consistent
with the key results of Fermi liquid theory, the picture changes dramatically at high
temperature (Fig. 10.9).
Recall that an isolated magnetic moment will display a strongly temperature dependent
susceptibility χ ∝ 1/T according to the Curie-law. A similar form is observed in many heavy
fermion materials at high temperature, often with a slope that is consistent with the Curie constant
expected from the electronic configuration of the corresponding magnetic ions (Uranium,
Cerium or Ytterbium, typically). This suggests that the partially filled f-orbitals act as local