Electrons in Periodic Media. The Role of Magnetic Field

  • Eleftherios N. EconomouEmail author
Part of the Graduate Texts in Physics book series (GTP)


We examine the conditions under which a periodic Hamiltonian can be approximated by a free electron Hamiltonian with an appropriately defined effective mass; under certain approximations, the center k of a wavepacket of Bloch functions follows a trajectory obeying the Newtonian equation \( \hbar \dot{k} = F\) add, where F add is an additional nonperiodic force due to external fields and/or impurities, etc. From the trajectory in k space, we find the trajectory in real space using the relation, \( dr/dt = {\upsilon_{nk}} = \partial {E_n} (k) / \hbar \partial k \). We demonstrate how this scheme achieves agreement with the experimental data in calculating the cyclotron resonances, the de Haas–van Alphen effect, the Hall effect, and the magnetoresistance succeeding where the JM failed very badly.


Fermi Surface Real Space Periodic Medium Constant Energy Bloch Function 
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Further Reading

  1. See Ashcroft and Mermin, [SS75], pp. 229–239 and 262–281.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.Foundation for Research and Technology-Hellas (FORTH) Department of PhysicsUniversity of CreteHeraklionGreece

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