How Does Spin-Orbit Interaction Influence Effective Mass in Semiconductors?

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SUMMARY

The discussion centers on the effective mass model for electrons in the conduction band of semiconductors and the role of spin-orbit interaction (SO). Participants assert that while the effective mass model is commonly used, it is essential to consider the full k·p equation with spin-orbit included for a more accurate representation. The consensus is that spin-orbit interaction and external magnetic fields do not affect the effective mass in the k·p framework. The Hamiltonian formulation presented, H = p²/2m* + SO + MAGNETIC FIELD, is confirmed to be equivalent to applying second-order perturbation theory in the context of deriving the effective mass Hamiltonian.

PREREQUISITES
  • Understanding of effective mass models in semiconductor physics
  • Familiarity with k·p perturbation theory
  • Knowledge of spin-orbit coupling in quantum mechanics
  • Basic principles of Hamiltonian mechanics
NEXT STEPS
  • Study the full k·p equation with spin-orbit interaction included
  • Explore advanced perturbation theory techniques in quantum mechanics
  • Research the implications of external magnetic fields on semiconductor properties
  • Examine case studies of effective mass variations in different semiconductor materials
USEFUL FOR

Physicists, semiconductor researchers, and graduate students specializing in condensed matter physics or materials science will benefit from this discussion.

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Often I see people using an effective mass model to describe electrons in the bottom of the conduction band.
Spin orbit is then included as a perturbation in this effective mass model. But what is the justification for using this sort of model?
Would the correct way not be to start from the full k dot p equation with spin orbit included and then derive an effective mass model from this? My concern is due to the fact that I would expect the effective mass to be dependent on the spin orbit interaction, but maybe that is not true.
Also, what about external magnetic fields. Do these affect the effective mass?
 
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no and no, spin orbit and the magnetic field do not affect the effective mass in \vec{k}\cdot\vec{p}
 
Okay so when I write a Hamiltonian on the form:

H = p2/2m* + SO + MAGNETIC FIELD

Is this equivalent to starting from the k dot p method and applying second order perturbation theory? (as you do in the case where you want to derive the effective mass hamiltonian without the SO and magnetic field terms).
 

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