Empty lattice approximation: Difference between revisions

Revision as of 11:47, 24 April 2014

Revision as of 16:41, 13 May 2014

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:<math>E_n(\bold{k}) = \frac{\hbar^2 (\bold{k} + \bold{G_n})^2}{2m}</math>

The <math>\bold{G}_n</math> are the [[reciprocal lattice]] vectors to which the bands <math>E_n(\bold{k})</math> belong. Electrons with wave vectors outside the first [[Brillouin zone]] are scattered by the lattice and mapped back into the first Brillouin zone by a so-called [[Umklapp scattering|Umklapp process]].

The figure on the right shows the dispersion relation for three periods in reciprocal space of a one-dimensional lattice with lattice cells of length ''a''.