Statistical Physics, Second Revised and Enlarged Edition

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’).