Physics – Condensed Matter – Materials Science
Scientific paper
2011-07-07
Physics
Condensed Matter
Materials Science
Submitted to J. Appl. Phys
Scientific paper
We derive closed-form expressions for 6x6 valence-band and 8x8 Kane Hamiltonians for wurtzite and zinc-blende semiconductor heterostructures in cylindrical coordinates, which provide a transparent and computationally efficient band formalism for low-dimensional semiconductor systems with the cylindrical symmetry. We use a specific combination of the Brillouin zone center Bloch functions as a new basis allowing to treat the envelope functions themselves as eigenstates of the operator of projection of total angular momentum on the symmetry axis, while the effective Hamiltonians parametrically depend on an eigenvalue of the operator. As an application, the developed method is used to map the ground and several excited hole states in an isolated wurtzite GaN quantum wire of the hexagonal cross-section to the states in an equivalent quantum wire of the circular cross-section.
Melnik Roderick V. N.
Takhtamirov Eduard
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