Geometric and Asymptotic Properties of Brillouin Zones in Lattices |
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Authors: | Jones Gareth A. |
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Affiliation: | Department of Mathematics, University of Southampton Southampton SO9 5NH |
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Abstract: | Each lattice in Rd determines a sequence of Brillouin zonesBn, fundamental regions for bounded by Bragg hyperplanes; forexample B1 is the Dirichlet region. Basic geometric and topologicalproperties of these zones are established, and we obtain asymptoticestimates (valid for almost all ) for (n) = , where L(n) is the number of connected componentsof the interior of Bn (called Landsberg subzones). Fermi surfacesare also briefly described. |
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