Spin-Orbit Interaction in nanowires

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Presentation transcript:

Spin-Orbit Interaction in nanowires Daryoush Shiri, IQC, June 28-30, 2014 QIC 890/891, Module 7 D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

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D. Shiri, IQC, July 2014

EXAMPLE: D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

Bandstructure (dispersion) of a nanowire in presence of Spin-Orbit Interaction (SOI) D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

Now we solve H Ψ = E Ψ D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

Analytical solution for E(kx) ? More Simplifications D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

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

D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

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. D. Shiri, IQC, July 2014

D. Shiri, IQC, July 2014

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). D. Shiri, IQC, July 2014

Edge States D. Shiri, IQC, July 2014

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