Electrons in metals 157
responsiblefor most oftheenhancementfactor. Theeffectis to coupletogether elec-
trons which can scatter (emit or absorb) phonons, i.e. those whose energies lie within
aboutkkkBθDofthe Fermienergy. (TheDebye temperatureθDis a scale temperature
for phonons, typicallyabout room temperaturefor manysolids, see section 9.3.2. It
is much less than the Fermi temperature for a metal.)
The resultofthis scattering, or mixing together, ofone-electron statesisillustrated
inFig. 14.1. Itisthe one-electron states close to the Fermienergy(just the ones we
are interested in!) which become mixed up with each other by the interaction with
thephonons. The resultisthat theeffectivedensityofstates atμisincreasedabove
Enhanced
Wavevector k
kkkF
kkkBD
Unenhanced
Unenhanced
Energy
Enhanced
Density of states gg ()
kkkF
kkkBD
Energy
(a)
(b)
Fig. 14. 1 (a) The dispersion relation and (b) the densityof states for a free electrongas (dashed curves)
and for an electrongas with interactions (full curves, ‘enhanced’).