Ab Initio Construction of Symmetry-adapted k·p Hamiltonians for the Electronic Structure of Semiconductors
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Date
2020-08-26
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Journal Title
Physical Review B
Volume Title
102
Article Title
085121
Publisher
American Physical Society (APS)
Abstract
While k·p Hamiltonians are frequently used for the description of electronic states in quantum nanostructures, a method is lacking to obtain them in their symmetrized form directly from ab initio band structure calculations of bulk material. We developed a method for obtaining the parameters and the symmetry-adapted form of the k·p Hamiltonian from the output of an ab initio band structure calculation. The method consists of (i) evaluation of momentum matrix elements between the wave functions obtained from band structure calculation; (ii) identification of the unitary transformation that transforms these wave functions to the symmetry-adapted basis; (iii) transformation of the k·p Hamiltonian to the symmetry-adapted basis. We illustrate the methodology by obtaining k·p Hamiltonians that describe the band structure of zinc-blende CdSe and then we use the Hamiltonians obtained to calculate the electronic states in CdSe quantum wells. Excellent agreement between density functional theory and k·p is obtained for the electronic structure, even for quite thin wells.