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Question on band symmetry

  1. Sep 13, 2009 #1
    hello,

    i am trying to get familiar with magnetic dichroism, first question on that is, why bands of same symmetry are not allowd to cross each other and why as a consequence hybridization gaps are formed.

    thanks for help
     
  2. jcsd
  3. Sep 14, 2009 #2
    It's easier to answer the question of why bands with different symmetry can cross. If two basis states |a> and |b> are of different symmetry, then H|b> will modify |b> somehow but it does not change the symmetry. Then the product <a|H|b> will be zero, because states of different symmetry will integrate to zero.

    If two bands have the same symmetry, the Hamiltonian can and will mix them. That is, the product <a|H|b> will be non-zero if a and b have the same symmetry, so there will be an off diagonal element in the Hamiltonian. At the value of k where <a|H|a> = <b|H|b> there will be off diagonal elements, so when diagonalized the energies will be different, and this will result in the hybridization gap.
     
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