Understanding Magnetic Dichroism and Hybridization Gaps: Band Symmetry Question

[fk08]

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

 

[kanato]

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.