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Luttinger parameter

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In semiconductors, valence bands are well characterized by 3 Luttinger parameters. At the Г-point in the band structure, and orbitals form valence bands. But spin–orbit coupling splits sixfold degeneracy into high energy 4-fold and lower energy 2-fold bands. Again 4-fold degeneracy is lifted into heavy- and light hole bands by phenomenological Hamiltonian by J. M. Luttinger.

Three valence band state

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In the presence of spin–orbit interaction, total angular momentum should take part in. From the three valence band, l=1 and s=1/2 state generate six state of as

The spin–orbit interaction from the relativistic quantum mechanics, lowers the energy of states down.

Phenomenological Hamiltonian for the j=3/2 states

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Phenomenological Hamiltonian in spherical approximation is written as[1]

Phenomenological Luttinger parameters are defined as

and

If we take as , the Hamiltonian is diagonalized for states.

Two degenerated resulting eigenenergies are

for

for

() indicates heav-(light-) hole band energy. If we regard the electrons as nearly free electrons, the Luttinger parameters describe effective mass of electron in each bands.

Example: GaAs

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In gallium arsenide,

References

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  1. ^ Haug, Hartmut; Koch, Stephan W (2004). Quantum Theory of the Optical and Electronic Properties of Semiconductors (4th ed.). World Scientific. p. 46. doi:10.1142/5394. ISBN 978-981-238-609-0.

Further reading

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