Theory of invariants‐based formulation of k·p Hamiltonians with application to strained zinc‐blende crystals

Group theoretical methods and k·p 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 appro...

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Bibliographic Details
Published in:Annalen der Physik 2017-06, Vol.529 (6), p.n/a
Main Authors: Wanner, Johannes, Eckern, Ulrich, Höck, Karl‐Heinz
Format: Article
Language:English
Subjects:
Conduction bands
Crystals
Effective Hamiltonian
group theoretical methods
Hamiltonian functions
Invariants
k·p theory
Splitting
strained crystals
Symmetry
Zincblende
zinc‐blende symmetry
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Summary:Group theoretical methods and k·p 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 k·p 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. An effective – low energy – description of electronic properties is crucial in many areas of solid state physics, in particular, for the development of semiconductor based devices. In this context, the standard model, the so called k·p theory, is re‐examined in order to determine the spin‐dependent contributions to the effective conduction band Hamiltonian. New contributions are found which describe strain‐dependent spin‐splitting.
ISSN:0003-3804
1521-3889
DOI:10.1002/andp.201600218