Article | Published:

Direct determination of spin–orbit interaction coefficients and realization of the persistent spin helix symmetry

Nature Nanotechnology volume 9, pages 703709 (2014) | Download Citation

Subjects

Abstract

The spin–orbit interaction plays a crucial role in diverse fields of condensed matter, including the investigation of Majorana fermions, topological insulators, quantum information and spintronics. In III–V zinc-blende semiconductor heterostructures, two types of spin–orbit interaction—Rashba and Dresselhaus—act on the electron spin as effective magnetic fields with different directions. They are characterized by coefficients α and β, respectively. When α is equal to β, the so-called persistent spin helix symmetry is realized. In this condition, invariance with respect to spin rotations is achieved even in the presence of the spin–orbit interaction, implying strongly enhanced spin lifetimes for spatially periodic spin modes. Existing methods to evaluate α/β require fitting analyses that often include ambiguity in the parameters used. Here, we experimentally demonstrate a simple and fitting parameter-free technique to determine α/β and to deduce the absolute values of α and β. The method is based on the detection of the effective magnetic field direction and the strength induced by the two spin–orbit interactions. Moreover, we observe the persistent spin helix symmetry by gate tuning.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    et al. Signatures of majorana fermions in hybrid superconductor–semiconductor nanowire devices. Science 336, 1003–1007 (2012).

  2. 2.

    et al. Experimental realization of a three-dimensional topological insulator, Bi2Te3. Science 325, 178–181 (2009).

  3. 3.

    & Electronic analog of the electro-optic modulator. Appl. Phys. Lett. 56, 655–657 (1990).

  4. 4.

    , , & Gate control of spin–orbit interaction in an inverted In0.53Ga0.47As/In0.52Al0.48As heterostructure. Phys. Rev. Lett. 78, 1335–1338 (1997).

  5. 5.

    , , & Experimental and theoretical approach to spin splitting in modulation-doped InxGa1−xAs/InP quantum wells for B → 0. Phys. Rev. B 55, R1958–R1961 (1997).

  6. 6.

    et al. Spin–orbit induced electronic spin separation in semiconductor nanostructures. Nature Commun. 3, 1038 (2012).

  7. 7.

    et al. Direct observation of the Aharonov–Casher phase. Phys. Rev. Lett. 96, 076804 (2006).

  8. 8.

    , & Experimental realization of a ballistic spin interferometer based on the Rashba effect using a nanolithographically induced square loop array. Phys. Rev. B 74, 041302(R) (2006).

  9. 9.

    , , & Experimental demonstration of the time reversal Aharonov–Casher effect. Phys. Rev. Lett. 97, 196803 (2006).

  10. 10.

    , , & Coherent control of a single electron spin with electric fields. Science 318, 1430–1433 (2007).

  11. 11.

    et al. Ballistic spin resonance. Nature 458, 868–871 (2009).

  12. 12.

    et al. Manipulation of mobile spin coherence using magnetic-field-free electron spin resonance. Nature Phys. 9, 280–283 (2013).

  13. 13.

    et al. Evidence for the ballistic intrinsic spin Hall effect in HgTe nanostructures Nature Phys. 6, 448–454 (2010).

  14. 14.

    & Spin relaxation of conduction electrons in noncentrosymmetric semiconductors. Sov. Phys. Solid State 13, 3023–3026 (1971).

  15. 15.

    Properties of semiconductors with an extremum loop. Sov. Phys. Solid State 2, 1224–1238 (1960).

  16. 16.

    Spin–orbit coupling effects in zinc blende structures. Phys. Rev. 100, 580–586 (1955).

  17. 17.

    & Anisotropic transport in a two-dimensional electron gas in the presence of spin–orbit coupling. Phys. Rev. B. 68, 165311 (2003).

  18. 18.

    , & Exact SU(2) symmetry and persistent spin helix in a spin–orbit coupled system. Phys. Rev. Lett. 97, 236601 (2006).

  19. 19.

    et al. Emergence of the persistent spin helix in semiconductor quantum wells. Nature 458, 610–613 (2009).

  20. 20.

    , , & Direct mapping of the formation of a persistent spin helix. Nature Phys. 8, 757–762 (2012).

  21. 21.

    et al. Gate-controlled persistent spin helix state in (In,Ga)As quantum wells. Phys. Rev. B 86, 081306(R) (2012).

  22. 22.

    , & A resonant spin lifetime transistor. Appl. Phys. Lett. 83, 1462–1464 (2003).

  23. 23.

    , & Nonballistic spin-field-effect transistor. Phys. Rev. Lett. 90, 146801 (2003).

  24. 24.

    et al. Proposal of spin complementary field effect transistor. Appl. Phys. Lett. 100, 113502 (2012).

  25. 25.

    et al. Gate-controlled spin–orbit quantum interference effects in lateral transport. Phys. Rev. Lett. 90, 076807 (2003).

  26. 26.

    et al. Experimental separation of Rashba and Dresselhaus spin splittings in semiconductor quantum wells. Phys. Rev. Lett. 92, 256601 (2004).

  27. 27.

    et al. Measurement of Rashba and Dresselhaus spin–orbit magnetic fields. Nature Phys. 3, 650–654 (2007).

  28. 28.

    , , , & Gate-controlled spin–orbit interaction in a parabolic GaAs/AlGaAs quantum well. Phys. Rev. Lett. 103, 027201 (2009).

  29. 29.

    , & Direct imaging of gate-controlled persistent spin helix state in a modulation-doped GaAs/AlGaAs quantum well. Appl. Phys. Exp. 7, 013001 (2014).

  30. 30.

    , , & Universal spin-induced time reversal symmetry breaking in two-dimensional electron gases with Rashba spin–orbit interaction. Phys. Rev. Lett. 94, 186805 (2005).

  31. 31.

    , , , & All-electrical detection of the relative strength of Rashba and Dresselhaus spin–orbit interaction. Phys. Rev. Lett. 101, 266401 (2008).

  32. 32.

    Dimensional control of antilocalization and spin relaxation in quantum wires. Phys. Rev. Lett. 98, 176808 (2007).

  33. 33.

    & Waveguide diffusion modes and slowdown of D'yakonov–Perel' spin relaxation in narrow two-dimensional semiconductor channels. Phys. Rev. B 61, R2413–R2416 (2000).

  34. 34.

    et al. Suppression of weak antilocalization in GaxIn1–xAs/InP narrow quantum wires. Phys. Rev. B 74, 081301(R) (2006).

  35. 35.

    , & Enhancement of spin lifetime in gate-fitted InGaAs narrow wires. Phys. Rev. Lett. 102, 226601 (2009).

  36. 36.

    & Optimal block-tridiagonalization of matrices for coherent charge transport. J. Comput. Phys. 228, 8548–8565 (2009).

  37. 37.

    , , & Anisotropic universal conductance fluctuation in disordered quantum wires with Rashba and Dresselhaus spin–orbit interaction and applied in-plane magnetic field. Semicond. Sci. Technol. 24, 064005 (2009).

Download references

Acknowledgements

The authors acknowledge support from the Strategic Japanese–German Joint Research Program. K.R. thanks the DFG for support within Research Unit FOR 1483. T.D. acknowledges support by the DFG within research project SFB 689. This work was financially supported by Grants-in-Aid from the Japan Society for the Promotion of Science (JSPS; no. 22226001).

Author information

Author notes

    • Y. Kunihashi

    Present address: NTT Basic Research Laboratories, NTT Corporation, 3-1 Morinosato-Wakamiya, Atsugi, Kanagawa 243-0198, Japan

Affiliations

  1. Graduate school of Engineering, Tohoku University, 6-6-02 Aramaki-Aza Aoba, Aoba-ku, Sendai 980-8579, Japan

    • A. Sasaki
    • , S. Nonaka
    • , Y. Kunihashi
    • , M. Kohda
    •  & J. Nitta
  2. Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany

    • T. Bauernfeind
    • , T. Dollinger
    •  & K. Richter

Authors

  1. Search for A. Sasaki in:

  2. Search for S. Nonaka in:

  3. Search for Y. Kunihashi in:

  4. Search for M. Kohda in:

  5. Search for T. Bauernfeind in:

  6. Search for T. Dollinger in:

  7. Search for K. Richter in:

  8. Search for J. Nitta in:

Contributions

A.S., S.N. and Y.K. performed device fabrication and measurements. T.B., T.D. and K.R. performed numerical calculations. A.S. and M.K. wrote the main part of the manuscript. T.D. and K.R. wrote the theoretical part. All authors discussed the results and worked on the manuscript at all stages. M.K., K.R. and J.N. planned the project. J.N. directed the research.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to J. Nitta.

Supplementary information

PDF files

  1. 1.

    Supplementary information

    Supplementary Information

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nnano.2014.128

Further reading