A tight-binding band has and spacing

PHYSICS · Multi-part · Fermi University Physics · Condensed Matter, Materials & Soft Matter · Free electrons, energy bands and electronic structure · Free electrons, energy bands and electronic structure

Condensed Matter Physics, Ch Tight binding, band filling and the three kinds of solid

Problem

A tight-binding band has

t = 0.55\ \mathrm{eV}

and spacing

a = 2.95\ \mathrm{\mathring{A}}

, and holds only a small fraction of an electron per atom, so its Fermi surface sits close to the band bottom. ((a)) Using

v = \hbar^{-1}\,\mathrm{d}E/\mathrm{d}k

(Chapter 4), find the group velocity of an electron at

k = \pi/(4a)

. ((b)) Find the effective mass at the bottom of the band, in units of

m

. ((c)) A free-electron gas of the same density has an electronic heat capacity coefficient

\gamma_{\rm free}

(Chapter 8), and

\gamma

scales with the effective mass at the Fermi surface. Without calculating a number, say whether the observed

\gamma

for this band should be larger or smaller than

\gamma_{\rm free}

, and how that compares with copper's case in this chapter.

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