Complex wave vectors in the energy gap find an expression for the imaginary part of the wave vector in the energy gap at the boundary of the first Brillouin zone, in the approximation that led to Eq. (46). Give the result for the Im (k) at the center of the energy gap. The result for small Im (k) is (h²/2m)[Im(k)]² ? 2mU²/h²G². The form as plotted in Fig. 12 is of importance in the theory of Zener tunneling from one band to another in the presence of a strong electric field.

E in units of hG/2m 0.27 0.26 0.25 0.24 T T I 0.23 0.48 Energy gap 0.49 0.005 0.01 Imaginary part of k/G 0 0.50 Real part of k/G 0.51 0.52