Theory of invariants‐based formulation of Hamiltonians with application to strained zinc‐blende crystals |
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| Authors: | Johannes Wanner Ulrich Eckern Karl‐Heinz Höck |
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| Affiliation: | Universit?t Augsburg, Institut für Physik, Augsburg, Germany |
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| Abstract: | Group theoretical methods and  theory are combined to determine spin‐dependent contributions to the effective conduction band Hamiltonian. To obtain the constants in the effective Hamiltonian, in general all invariants of the Hamiltonian have to be determined. Hence, we present a systematic approach to keep track of all possible invariants and apply it to the  Hamiltonian of crystals with zinc‐blende symmetry, in order to find all possible contributions to effective quantities such as effective mass, g‐factor and Dresselhaus constant. Additional spin‐dependent contributions to the effective Hamiltonian arise in the presence of strain. In particular, with regard to the constants C3 and D which describe spin‐splitting linear in the components of k and ε , considering all possible terms allowed by symmetry is crucial. |
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| Keywords: | Effective Hamiltonian zinc‐blende symmetry group theoretical methods theory strained crystals |
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theory are combined to determine spin‐dependent contributions to the effective conduction band Hamiltonian. To obtain the constants in the effective Hamiltonian, in general all invariants of the Hamiltonian have to be determined. Hence, we present a systematic approach to keep track of all possible invariants and apply it to the 
Hamiltonian of crystals with zinc‐blende symmetry, in order to find all possible contributions to effective quantities such as effective mass, g‐factor and Dresselhaus constant. Additional spin‐dependent contributions to the effective Hamiltonian arise in the presence of strain. In particular, with regard to the constants C3 and D which describe spin‐splitting linear in the components of k and ε , considering all possible terms allowed by symmetry is crucial.