Physics – Condensed Matter – Materials Science
Scientific paper
2011-07-18
Physics
Condensed Matter
Materials Science
Scientific paper
Recent work by Elder, Ward and Zhang [Phys. Rev. B 83. 165210 (2011)] has shown need for correction and modification of current implementation of the k.p method and operator ordering scheme using the interaction parameters defined under double group consideration. This manuscript examines the treatment of spin-orbit interaction under the single group formulation. We show that the restriction to the adapted double group bases is not appropriate. In addition, the unitary transformation employed to diagonalise the spin orbit interaction in the valence band of semiconductors with diamond lattice is not the correct one. Under the double group consideration, spin-orbit interaction affects all the states and offers a mechanism for changing the relative positions of various zone centre states in the conduction band. This can lead to inversion in materials such as {\alpha}-tin. The re- arrangement of conduction band zone centre states leads to a negative {\gamma}2 in most materials. Experimental data suggest that silicon, like diamond, has positive {\gamma}2. A form of the Hamiltonian generally used in the literature is obtained from the results of EWZ using a unitary transformation of the valence band basis and re-definition of some of the Luttinger invariants. The form of this Hamiltonian, obtained historically using the incorrect diagonalisation matrix while introducing spin orbit interaction in the single group formulation, is correct pro- vided the underling unitary transformation is recognised. Such a unitary transformation enables explanation of optical transition selection rules for this form of Hamiltonian and has the effect of inverting the signs of {\gamma}2 in the valence band. The coupling by k2 - 3kz2 perturbation remains between the |3/2, \pm 3/2> of valence band and |1/2, \mp 1/2> of the spin split off band independent of sign of {\gamma}2...
Elder Warren J.
Zhang Jing
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