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BOUND STATES IN ELECTRON SYSTEMS INDUCED BY THE SPIN-ORBIT INTERACTION

BOUND STATES IN ELECTRON SYSTEMS INDUCED BY THE SPIN-ORBIT INTERACTION. Magarill L.I. in collaboration with Chaplic A.V. A shallow and narrow potential well.  =. 3D: No bound states 2D, axially symmetric well: one bound s-state,. 1D, symmetric potential:

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BOUND STATES IN ELECTRON SYSTEMS INDUCED BY THE SPIN-ORBIT INTERACTION

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  1. BOUND STATES IN ELECTRON SYSTEMS INDUCED BY THE SPIN-ORBIT INTERACTION Magarill L.I. in collaboration with Chaplic A.V.

  2. A shallow and narrow potential well  = 3D: No bound states 2D, axially symmetric well: one bound s-state, 1D, symmetric potential: one bound state, Valid with SOI neglected

  3. Hamiltonian of 2D electrons with SOI in the Bychkov-Rashba form interacting with an axially symmetric potential well

  4. Dispersion relation for 2D with SOI p0 p0=mea loop of extrema

  5. The lower branch of the dispersion law of 2D electrons has a form and corresponds to a 1D particle at least in the sense of density of states. Formally the particle has anisotropic effective mass: radial component is me , azimuthal component = (the dispersion law is independent of the angle in the p-plane).

  6. p-representation of the Schrodinger equation: Cylindrical harmonics of the spinor wave functions:

  7. For m-th harmonic:

  8. s-state x=2meU0R2

  9. p-state No bound states for zero SOI at x < xc =x12; J0(x1)=0 j=1/2 j=3/2

  10. Effect of the magnetic field ground state (s-level) Direct Zeemann contribution neglected (g=0), only SOI induced effect ^ Splitting

  11. 2 Liquid He-4 Roton dispersion relation: fold degeneracy 2 l

  12. y U(x) x 2D electrons with B-R SOI in 1D short-range potential

  13. a=0.5U0 a=U0 a=0.5U0 a=U0 a=0.5U0 a=U0 There exists pcand at|py| >pc «+»-statebecomes delocalized.

  14. py =0.5 meU0 py =1.5 meU0

  15. z Narrow quantum well and 3D electrons U=-U0d(z) Dresselhaus SOI VSO=g[(sypy-sxpx)pz2+sz(px2-py2)pz+pxpy(sxpy-sypx)]

  16. Localization or delocalization of an electron in z-direction depends on the orientation of longitudinal momentum p||: [110] - lower subband: localization for all p|| upper subband: termination point [100] – both subbands for all values of p|| relate to the localized states

  17. Small longitudinal momenta Two independent equations for two components of the wave function:

  18. U1 U2 Asymmetric well GaxAl1-xAs/A3B5/GayAl1-yAs

  19. Two identical wells a For m=-1 two localized states, for m=1 only one. U0 U0

  20. Conclusion We have shown that 2D electrons interact with impurities in a very special way if one takes into account SO coupling: because of the loop of extrema, the system behaves as a 1D one for negative energies close to the bottom of continuum. This results in the infinite number of bound states even for a short-range potential. 1D potential well in 2DEG and 3DEG for proper values of characteristic parameters form bound states for only one spin state of electrons. The ground state in a short-range 2D potential well possesses the anomalously large effective g-factor.

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