Set of supplementary notes.

156 CHAPTER 10. FERMI LIQUID THEORY
renormalised f-band
pinned to Fermi level
(0)
k F
E F
k F
Hybridisation
between broad
s, p, d-band and
f-band causes
large Fermi
surface
broad band from
s, p, d orbitals
k
Figure 10.10: Schematic band structure for heavy fermion materials
moments at high temperatures, as if the formation of band states could be ignored.
On the other hand, the Curie form of the susceptibility does not extend all the way to zero
temperature, but rather it crosses over the to a constant value in the low temperature limit, just
as the Sommerfeld coefficient of the heat capacity did. This suggests that at low temperatures,
a local moment picture of these materials is not appropriate, and we must instead consider
them as heavy Fermi liquids. It is difficult to reconcile these two ways of thinking about the
same material.
10.4.3 Renormalised band picture for heavy fermion systems
A qualitative understanding of the origin of the heavy fermion state can be obtained by considering
the hybridisation between the bands associated with the more extended s,p, and d-orbitals
on the atoms and the bands which arise from the very tightly localised atomic f-orbitals.
Because a partially filled f-orbital will always lie inside filled s, p and even d orbitals with
a higher major quantum number, there is negligible hybridisation between f-orbitals on neighbouring
atoms – they are just too far apart. This results in a very flat band from the atomic
f-states.
If we consider single-electron states naively, then we find that the f-band formed from
the atomic f-orbitals is well below the chemical potential, and should therefore be completely
full. In such a scheme there would be no local moments at high temperature and no heavy
fermion behaviour at low temperature. The scheme fails, because it ignores the strong Coulomb
repulsion between electrons sharing the same f-state.
Instead, once a single electron has occupied an f-orbital, the energy cost for a second electron
hopping onto the same orbital is very high, almost prohibitive. We can modify our single
particle picture to ensure that the f-orbitals have an average occupancy of one, by renormalising