Set of supplementary notes.

154 CHAPTER 10. FERMI LIQUID THEORY
850 mJ/(mol K 2 )
CeCu 6
7x0.7mJ/(mol K 2 )
“Cu 7
” = Cu x 7
Figure 10.8: Low temperature heat capacity of CeCu 6 and of Cu. The molar heat capacity of
pure Cu has been multiplied by 7 to allow direct comparison of the heat capacity per atom.
10.4 Fermi liquids at the limit: heavy fermions
10.4.1 What are heavy fermions
A key result from Fermi liquid theory is the realisation that the effective mass of the quasiparticles
in an interacting system can be very different from the band mass, which is determined
solely from the band structure of the non-interacting system. Strong interactions can in principle
cause high effective masses. Heavy fermion materials have very high Sommerfeld coefficient
of the heat capacity C/T ∼ 1 J/(molK), and high, weakly temperature-dependent magnetic
susceptibility. This suggests they follow Fermi liquid theory, but the effective quasiparticle
masses are strongly enhanced: in some cases up to 1000 times m e . Usually, heavy fermion
materials contain Cerium, Ytterbium or Uranium, which contribute partially filled f-orbitals
to the band structure. These highly localised states are important, because in a lattice, they
lead to very narrow bands. The strong Coulomb repulsion prevents double occupancy of these
states. There are hundreds of heavy fermion materials. Examples include CeCu 2 Si 2 , CeCu 6 ,
CeCoIn 5 , YbCu 2 Si 2 , UPt 3 .
Fig. 10.8 shows the Sommerfeld coefficient of the heat capacity, C/T for the typical heavy
fermion material CeCu 6 . Note that in the low temperature limit, C/T approaches 850 mJ/(molK 2 ).
If we compare this value to that expected from pure Cu, we find that the heat capacity per
atom is boosted by a factor of 150. In other words, if we replace 14% of the copper atoms in a
sample of pure Cu by Ce, we increase the low temperature heat capacity 150-fold!