1. Spin-Orbit Interaction in nanowires
Daryoush Shiri, IQC, June 28-30, 2014
QIC 890/891, Module 7
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8. EXAMPLE:
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11. Bandstructure (dispersion) of a nanowire in presence of Spin-Orbit Interaction (SOI)
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14. Now we solve H Ψ = E Ψ
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18. Analytical solution for E(kx) ? More Simplifications
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21. Note that dispersions are asymmetric.
Eigen-spinors are eigenvectors corresponding to E+ and E-
Note that dispersions are asymmetric.
Eigen-spinors are kx dependent i.e. NONE of the levels (sub-bands) has a definite spin quantization direction.
If a mechanism scatters electrons (changes their kx), then spin will be affected by that mechanism as well.
Any application for these effects?
D. Shiri, IQC, July 2014

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24. This means that any electron scattering from red (black)
to red (black) sub-band does not cause any spin-flip.
Spin flip occurs by scattering from (Red to black) and vice versa.
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26. Introduction to Spintronics, Supriyo Bandyopadhyay & Marc Cahay
Summary
References:
Introduction to Spintronics,
Supriyo Bandyopadhyay & Marc Cahay
CRC Press, (2008).
Quantum Transport,
Supriyo Datta,
Cambridge University press, (2005).
Quantum Mechanics: Special Chapters
Walter Greiner,
Springer Verlag, (1998).
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27. Edge States
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28. 1- Show that [𝜎 .( 𝑝 +𝑒 𝐴 )] 2 = ( 𝑝 +𝑒 𝐴 ) 2 +2 𝑚 0 𝜇 𝐵 𝐵 . 𝜎
Exercise:
1- Show that [𝜎 .( 𝑝 +𝑒 𝐴 )] 2 = ( 𝑝 +𝑒 𝐴 ) 2 +2 𝑚 0 𝜇 𝐵 𝐵 . 𝜎
2- In the following nanowire Hamiltonian determine:
(a) which SOI effect (Rashba or Dresselhaus) causes a magnetic field in parallel with the external magnetic field?
(b) which one generates an effective magnetic field perpendicular to the external magnetic field?
and
propose an experiment with which you cam measure Rashba and Dresselhaus SOI strengths i.e. factors in a nanowire.
D. Shiri, IQC, July 2014