Hole–spin dephasing time associated with hyperfine interaction in quantum dots

Abstract

The spin interaction of a hole confined in a quantum dot with the surrounding nuclei is described in terms of an effective magnetic field. We show that, in contrast to the Fermi contact hyperfine interaction for conduction electrons, the dipole-dipole hyperfine interaction is anisotropic for a hole, for both pure or mixed hole states. We evaluate the coupling constants of the hole-nuclear interaction and demonstrate that they are only one order of magnitude smaller than the coupling constants of the electron-nuclear interaction. We also study, theoretically, the hole spin dephasing of an ensemble of quantum dots via the hyperfine interaction in the framework of frozen fluctuations of the nuclear field, in absence or in presence of an applied magnetic field. We also discuss experiments which could evidence the dipole-dipole hyperfine interaction and give information on hole mixing. 2 I -INTRODUCTIONThe spin of an individual electron, confined in a quantum dot (QD), is currently considered as a potential candidate for the realization of spintronic and quantum information processing in solid-state-based devices [1][2][3]. While in bulk or quantum wells, the electronic spin is efficiently relaxed by processes related to spin-orbit coupling, such as the D'YakonovPerel mechanism [4], the spatial confinement of carriers in semiconductor QDs significantly reduces the relaxation and decoherence processes. Recently, the hyperfine coupling with the spins of the lattice nuclei has been identified as the ultimate limit, at low temperature, to the electron spin relaxation or decoherence in QDs.For conduction electrons, the hyperfine interaction has a Fermi contact character, and is at the origin of ensemble dephasing times of the order of one nanosecond in III-V QDs [5][6][7][8][9].For holes, the Fermi contact coupling is massively suppressed because of the p-symmetry of the valence band states. The hyperfine interaction is then induced by the weaker long-range dipole-dipole coupling [10], so that much longer relaxation and decoherence times are expected [11].Recent progresses in the preparation and reading of an ensemble of hole spins [12] or of a single hole spin, confined in QD, offer the opportunity to study their dynamics. By inserting single QDs in n-i-Schottky diode structures, D. Heiss et al. [13] and A.J. Ramsay et al.[14] have evidenced the possibility to initialize and store hole spins, as previously done with conduction electrons [15], while measuring the time dependence of their polarization.In the present work, we show that, while being weaker than the electron Fermi contact interaction, the long-range dipole-dipole coupling between holes and nuclei can be an efficient decoherence mechanism, and leads to ensemble dephasing times of the order of ten nanoseconds in III-V QDs.The paper is organized as follows: In section II, the hyperfine dipole-dipole coupling between nuclear spins and the spin of a hole is written in terms of an effective nuclear magnetic field acting on the hole spin. In this section, differe...

Hole-spin initialization and relaxation times in InAs/GaAs quantum dots

“…25 for the C and T h 0 definitions) and has to be compared to the electron spin time at the same scale, T e N ≈hN /A with A the electron hf constant. 18 At low temperature and in the absence of an applied magnetic field, Cheng et al 11 have obtained in interface-fluctuation GaAs QDs T e N = 34 μs, and Pal et al 43 in InP QDs have measured T e N = 1 μs.…”

“…23 Experimental evidences of heavy-hole and light-hole mixing have been reported, before our works, and associated to the in-plane anisotropy and strain in InAs, CdSe, and CdTe self-assembled QDs (see Ref. [25][26][27]). In the caption of Fig.…”

“…At the carrier-precession timescale, due to the small variations of the nuclear effective field, it can be considered as frozen, but its dot-to-dot fluctuations induce a carrier spin dephasing and a partial relaxation of the ensemble spin carriers characterized by a dephasing time T e,h . 18,25 A longer relaxation time scale in the carrier spin dynamics also arises from the inhomogeneity of the carrier wave function, which makes the nuclear field change in time-the contribution of an individual nucleus to the nuclear field being proportional to the square of the carrier wave function at its place. Then, the slow carrier spin relaxation is related to this slow frozen field variation, which induces a carrier spin relaxation at a timescale T e,h N longer than the ensemble dephasing time T e,h (T e,h N ≈ √ NT e,h ).…”

“…Unlike electrons for which the contact term is the predominant contribution of the hf interaction, holes couple more weakly to nuclear spins via the anisotropic dipoledipole term of the hf interaction. 24,25 Recently, the relative strength of the electron-nuclear coupling to the hole-nuclear coupling has been measured to be of the order of ten. [26][27][28] Meanwhile, when the effect of the nuclear dipole-dipole interaction is neglected, 29 theoretical works predict for both carriers two-time scales in the spin dynamics imposed by the hf interaction.…”

“…The hf interaction has been identified as the dominant electron-and hole-spin dephasing source at weak or zero magnetic field and low temperature in QDs, [18][19][20][21][22][23][24][25] leading to a dephasing time in the order of nanoseconds or tens of nanoseconds. Unlike electrons for which the contact term is the predominant contribution of the hf interaction, holes couple more weakly to nuclear spins via the anisotropic dipoledipole term of the hf interaction.…”