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This book discusses group theory investigations of zincblende and
wurtzite semiconductors under symmetry-breaking conditions. The
text presents the group theory elements required to develop a
multitude of symmetry-breaking problems, giving scientists a fast
track to bypass the need for recalculating electronic states. The
text is not only a valuable resource for speeding up calculations
but also illustrates the construction of effective Hamiltonians for
a chosen set of electronic states in crystalline semiconductors.
Since Hamiltonians have to be invariant under the transformations
of the point group, the crystal symmetry determines the multiplet
structure of these states in the presence of spin-orbit,
crystal-field, or exchange interactions. Symmetry-breaking leads to
additional coupling of the states, resulting in shifts and/or
splittings of the multiplets. Such interactions may be intrinsic,
as in the case of the quasi-particle dispersion, or extrinsic,
induced by magnetic, electric, or strain fields. Using a power
expansion of the perturbations these interaction terms can be
determined in their parameterized form in a unique way. The
hierarchic structure of this invariant development allows to
estimate the importance of particular symmetry-breaking effects in
the Hamiltonian. A number of selected experimental curves are
included to illustrate the symmetry-based discussions, which are
especially important in optical spectroscopy. This text is written
for graduate students and researchers who want to understand and
simulate experimental findings reflecting the fine structure of
electronic or excitonic states in crystalline semiconductors.
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