The dispersion relation for electrons in an f.c.c. crystal is given, in the tight binding approximation, by
\(\varepsilon(k)=-4 \varepsilon_0\)\(\left[\cos \frac{k_x a}{2} \cos \frac{k_y a}{2}+\cos \frac{k_y a}{2} \right.\)\(\left. \cos \frac{k_z a}{2}+\cos \frac{k_z a}{2} \cos \frac{k_x a}{2}\right]\)
where a is the lattice constant and ε0 is a constant with the dimension of energy. The x - component of the velocity of the electron at \(\left(\frac{\pi}{a}, 0,0\right)\) is
1
\(\rm -2 \varepsilon_0 a / \hbar \)
2
\(\rm 2 \varepsilon_0 a / \hbar \)
3
\(\rm -4 \varepsilon_0 a / \hbar \)
4
\(\rm 4 \varepsilon_0 a / \hbar\)