Element-sensitive measurement of the hole–nuclear spin interaction in quantum dots

Journal name:
Nature Physics
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Published online

It has been proposed that valence-band holes can form robust spin qubits1, 2, 3, 4 owing to their weaker hyperfine coupling compared with electrons5, 6. However, it was demonstrated recently7, 8, 9, 10, 11 that the hole hyperfine interaction is not negligible, although a consistent picture of the mechanism controlling its magnitude is still lacking. Here we address this problem by measuring the hole hyperfine constant independently for each chemical element in InGaAs/GaAs, InP/GaInP and GaAs/AlGaAs quantum dots. Contrary to existing models10, 11 we find that the hole hyperfine constant has opposite signs for cations and anions and ranges from −15% to +15% relative to that for electrons. We attribute such changes to the competing positive contributions of p-symmetry atomic orbitals and the negative contributions of d-orbitals. These findings yield information on the orbital composition of the valence band12 and enable a fundamentally new approach for verification of computed Bloch wavefunctions in semiconductor nanostructures13. Furthermore, we show that the contribution of cationic d-orbitals leads to a new mechanism of hole spin decoherence.

At a glance


  1. Optical techniques for isotope-selective measurement of the hole hyperfine constants.
    Figure 1: Optical techniques for isotope-selective measurement of the hole hyperfine constants.

    a, Photoluminescence spectra of a single neutral InGaAs/GaAs quantum dot in a magnetic field Bz8.0T. For low-power optical excitation, four photoluminescence lines are observed in each spectrum corresponding to all possible combinations of the electron spin states (↑,↓) and hole states ( ) forming two bright excitons ( , ) and two dark excitons ( , ) that have a small (<0.01) admixture of bright states making dark states visible in photoluminescence spectra9, 17. To demonstrate independent detection of electron and hole hyperfine shifts two spectra are shown corresponding to negative (open symbols) and positive (solid symbols) nuclear spin polarization left fenceIzright fenceinduced on the dot by pumping with σ+ and σ polarized light, respectively. b, Timing diagram of the pump–probe experiment used in the measurements of the hole hyperfine constants: nuclear spins are polarized by a high-power optical pump pulse. Following this, a radiofrequency oscillating magnetic field is switched on to achieve isotope-selective depolarization of nuclear spins. Finally, the sample is excited with a low-power probe laser pulse, during which the photoluminescence spectrum of both bright and dark excitons (similar to that in a) is measured. See further details of experimental techniques in Methods.

  2. Experimental results of the isotope-selective hole hyperfine measurements.
    Figure 2: Experimental results of the isotope-selective hole hyperfine measurements.

    a,b, Dependence of the hole hyperfine shift ΔEhkon the electron hyperfine shift ΔEek for different isotopes in GaAs quantum dot A1 (a) and InGaAs quantum dot B1 (b). Solid lines show fitting: the slopes correspond to the relative hole–nuclear hyperfine constants γk (see details in Methods). We find γGa−7.0%, γAs+15.0% for GaAs quantum dot A1 and γGa−6.5%, γAs+10.5% for InGaAs quantum dot B1. As the NMR resonances of 69Ga and 115 In in InGaAs cannot be resolved16, we measure the total hyperfine shifts ΔEeIn+69Ga and ΔEhIn+69Ga produced by these isotopes. Further analysis gives γIn−16.0% for quantum dot B1 (see Supplementary Section S3B). The dashed line in b is a guide to the eye.

  3. Model calculations of the hole hyperfine constants.
    Figure 3: Model calculations of the hole hyperfine constants.

    a, Schematic representations of p- and d-orbitals that transform according to the F2 representation of the Td point group of the crystal symmetry. b, Calculated dependence of the relative hole hyperfine constant γk of Ga and As as a function of d-shell contribution |αd|2 (lines). Horizontal bands show experimentally measured confidence intervals for γk for GaAs quantum dots (see Table 1). c, Dependence of integrals Ml(r0) (see equation (3)) on the upper integration limit r0 for 3d- and 4p-shells for both Ga and As. Values of Ml(r0) are normalized by their values at , and r0 is normalized by the distance between Ga and As nuclei rGa–As0.245nmin GaAs. The rapid saturation of the Ml(r0) variations shows that the major contribution to the hole hyperfine interaction (>95%) arises from a small volume with a radius of r00.15×rGa–As around the nucleus.


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Author information


  1. Department of Physics and Astronomy, University of Sheffield, Sheffield S3 7RH, UK

    • E. A. Chekhovich,
    • M. S. Skolnick &
    • A. I. Tartakovskii
  2. Ioffe Physical-Technical Institute of RAS, St Petersburg 194021, Russia

    • M. M. Glazov
  3. Spin Optics Laboratory, St Petersburg State University, St Petersburg 198504, Russia

    • M. M. Glazov
  4. Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield S1 3JD, UK

    • A. B. Krysa &
    • M. Hopkinson
  5. Laboratoire de Photonique et de Nanostructures, Route de Nozay, 91460 Marcoussis, France

    • P. Senellart &
    • A. Lemaître


A.B.K., M.H., P.S. and A.L. developed and grew the samples. E.A.C. and A.I.T. conceived the experiments. E.A.C. developed the techniques and carried out the experiments. E.A.C., M.M.G. and A.I.T. analysed the data. E.A.C., M.M.G., A.I.T. and M.S.S. wrote the manuscript with input from all authors.

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