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

It has been proposed that valence-band holes can form robust spin qubits1–4 owing to their weaker hyperfine coupling compared with electrons5,6. However, it was demonstrated recently7–11 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. Owing to the s-type character of the Bloch wavefunction, the hyperfine interaction of the conduction band electrons is isotropic (the Fermi contact interaction) and is described by a single hyperfine constant A, positive (A > 0) for most III–V semiconductors and proportional to the electron density at the nucleus. In contrast, for valence-band holes the contact interaction vanishes owing to the symmetry properties of the wavefunction, and the non-local dipole–dipole interaction dominates10,11,13–15. As a result, the sign, magnitude and anisotropy of the hyperfine interaction depend on the actual form of the valence-band Bloch wavefunction, which is usually not available with sufficient precision. Thus, predicting the properties of the hole hyperfine coupling using first-principle calculations remains a difficult task. In this work we perform direct measurements of the hyperfine constants that describe the hole hyperfine interaction with nuclear spins polarized along the growth axis of the structure (that is, the diagonal elements of the hole hyperfine Hamiltonian). This is achieved by simultaneous and independent detection of the electron and hole Overhauser shifts using high-resolution photoluminescence spectroscopy of neutral quantum dots. In contrast to previous work9, we now also apply excitation with a radiofrequency oscillating magnetic field, which allows isotopeselective probing of the valence-band hole hyperfine interaction16. Using this technique we find that in all studied materials, cations