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Control of Spin Helix Symmetry in Semiconductor Quantum Wells by Crystal Orientation

Michael Kammermeier, Paul Wenk, and John Schliemann
Phys. Rev. Lett. 117, 236801 – Published 30 November 2016
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Abstract

We investigate the possibility of spin-preserving symmetries due to the interplay of Rashba and Dresselhaus spin-orbit coupling in n-doped zinc-blende semiconductor quantum wells of general crystal orientation. It is shown that a conserved spin operator can be realized if and only if at least two growth direction Miller indices agree in modulus. The according spin-orbit field has in general both in-plane and out-of-plane components and is always perpendicular to the shift vector of the corresponding persistent spin helix. We also analyze higher-order effects arising from the Dresselhaus term, and the impact of our results on weak (anti)localization corrections.

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  • Received 28 June 2016

DOI:https://doi.org/10.1103/PhysRevLett.117.236801

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Michael Kammermeier*, Paul Wenk, and John Schliemann

  • Institute for Theoretical Physics, University of Regensburg, 93040 Regensburg, Germany

  • *michael1.kammermeier@ur.de

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Issue

Vol. 117, Iss. 23 — 2 December 2016

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Images

  • Figure 1
    Figure 1

    (a) Global minimum λmin (in terms of Qso=4mβ(1)/2) of the spectrum of the spin diffusion operator Λsd for the optimal ratio of Rashba and Dresselhaus coefficients α/β(1) for different growth directions [n˜x,n˜y,5] (n˜x,n˜yZ). The white lines emphasize the vanishing minima. (b) Ratio between the global minimum λmin and the minimum 1/(Deτ^s,min(0)) found by considering the spectrum at q=0 solely, which corresponds to the D’yakonov Perel’ spin-relaxation tensor, Eq. (4). Along the white lines, both minima vanish exactly due to the SU(2) symmetry.

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  • Figure 2
    Figure 2

    Characteristic parameters in case of a persistent spin helix symmetry in dependence of the growth direction. Notice the degeneracy for α/β(1) in the [001] direction.

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  • Figure 3
    Figure 3

    2DEG grown along [113] for ce/cϕ=103 and ce=1 with α/β(1) close to the SU(2) symmetry point. (a) Relative MC ΔσR(B)=Δσ(B)Δσ(0) for different values of ε. For compactness, we restrict the plots for ε<0(ε>0) to negative(positive) magnetic fields. The colored lines correspond to exact numerical calculations, the black dotted lines to the approximate expression, Eq. (11). Gray dashed lines show the trend of the minima Δσ(Bmin) in dependence of ε. (b) The respective MC minimum as a function of ε. Red solid lines correspond to exact numerical calculations, black dotted and green dashed lines to approximate formulas.

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