Electron and Nuclear Spin Interactions in the Optical Spectra of Single GaAs Quantum Dots

Abstract

Fine and hyperfine splittings arising from electron, hole, and nuclear spin interactions in the magnetooptical spectra of individual localized excitons are studied. We explain the magnetic field dependence of the energy splitting through competition between Zeeman, exchange, and hyperfine interactions. An unexpectedly small hyperfine contribution to the splitting close to zero applied field is described well by the interplay between fluctuations of the hyperfine field experienced by the nuclear spin and nuclear dipole/dipole interactions. DOI: 10.1103/PhysRevLett.86.5176 PACS numbers: 78.67.Hc, 71.70.Ej The spin of an electron in a 10 nm GaAs quantum dot (QD) interacts with ϳ10 5 nuclear spins. This hyperfine interaction, though relatively weak, may ultimately limit spin coherence of localized electrons in QDs or shallow impurities -a concern that strongly influences developing visions of information technologies based on spin [1][2][3]. Nevertheless, there may be ways around even this intrinsic scattering process; for example, by optically polarizing all nuclear spin and thereby dramatically reducing phase space [1]. Furthermore, one could imagine using the nuclear spin for information storage or to control the electronic spin [4]. However, it is necessary to develop a more precise understanding of spin interactions in nanostructures in the presence of external magnetic and optical fields before such creative ideas can be explored.In this Letter, we present and analyze spectroscopic signatures of spin via fine and hyperfine structure splittings in the magneto-optical spectra of individual GaAs QDs under polarized and nearly resonant laser excitation. We find it necessary to consider the interaction of the electron spin with an external magnetic field (Zeeman interaction), exchange Coulomb interactions between the electron and hole, and hyperfine interactions between the electronic spin and the spins of the nuclei. Because of the hyperfine interaction, it is necessary to consider also the nuclear spin system. We are led then to consider, for the nuclei, the Zeeman interaction, dipole-dipole interactions between neighboring nuclear spins [5], and the hyperfine interaction. We quantify in experiment and theory how interactions manifest themselves in the spectral fine structure of a single exciton, discovering and explaining a remarkably complex dependence on magnetic field arising from competition between these various spin interactions.We have studied QDs formed by monolayer-high interface islands in a 4.2 nm GaAs quantum well with 25 nm Al 0.3 Ga 0.7 As barriers. The quantum wells were grown using molecular beam epitaxy with two-minute growth interrupts at the interfaces to allow large interface islands to develop. Individual QDs were excited and detected through 1 2 micron diameter apertures in an aluminum shadow mask patterned on the sample surface. A split-coil superconducting magnet was used in backscattering Faraday geometry. Previous studies have demonstrated that optical pumping could lead to large nu...

Electron Spin as a Spectrometer of Nuclear-Spin Noise and Other Fluctuations

“…This approximation clearly does not hold at low magnetic fields, and the problem becomes considerably more complicated. The study of electron spin evolution subject to the full isotropic hyperfine interaction has attracted a great deal of attention lately [26,27,25,28], particularly because of a series of free induction decay experiments probing electron spin dynamics in quantum dots in the low magnetic field regime [29]. In the author's opinion the most successful theoretical approach so far in the description of these experiments is to treat the collective nuclear spin field classically by taking averages over its direction and magnitude [26].…”

“…This shows that the threshold field for neglecting the non-secular isotropic hyperfine interaction in the Hahn echo is given by the inhomogeneously broadened linewidth, B th = j A 2 j /γ e ∼ 10 − 100 G (for a donor impurity in silicon, B th is ≈ 1 G for natural samples and ≈ 10 G for 29 Si enriched samples).…”

“…with the Si conduction band minimum at k 0 = (0.85)2π/a Si , gyromagnetic ratios for 29 Si nuclear spins γ n = 5.31 × 10 3 (sG) −1 , and the free electron γ e0 = 1. …”

“…Here T ′ 2 was interpreted as arising from a combination of spin-flip processes and the instantaneous diffusion mechanism, due to the finite concentration of donors. Tyryshkin et al 29 Si] Experiment Theory Fig. 8.…”

“…The electron spin of a donor impurity in silicon is sensitive to the magnetic noise produced by nuclear spins within its wave function. When two 29 Si isotopes are close to each other, their nuclear spin states may flip-flop due to their mutual dipolar interaction. These flip flop events produce time dependent fluctuations in the electron's hyperfine field, leading to phase relaxation and spin echo decay.…”