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Hole - Nuclear Spin Interaction in Quantum Dots

We have measured the carrier spin dynamics in p-doped InAs/GaAs quantum dots by pump-probe photo-induced circular dichroism and time-resolved photoluminescence experiments. We show that the hole spin dephasing is controlled by the hyperfine interaction between hole and nuclear spins. In the absence of external magnetic field, we find a characteristic hole spin dephasing time of 15 ns, in close agreement with our calculations based on dipole-dipole coupling between the hole and the quantum dot nuclei. Finally we demonstrate that a small external magnetic field, typically 10 mT instead of 200 mT for the case of electrons, quenches the hyperfine hole spin dephasing.


Chamarro
(1) (1)  We show that the hole spin dephasing is controlled by the hyperfine interaction between hole and nuclear spins. In the absence of external magnetic field, we find a characteristic hole spin dephasing time of 15  An individual spin in a solid confined to a nanometer scale represents an ultimate quantum memory and is thus a potential candidate for the realization of spintronic and quantum information processing devices [1,2,3]. Compared to bulk materials, the strong spatial confinement of carriers in semiconductor quantum dots (QDs) efficiently quenches the main spin relaxation mechanisms such as the D'Yakonov-Perel one [4] while enhancing mechanisms based on carrier exchange and hyperfine interaction. The hyperfine interaction of an electron with the nuclei, based on the Fermi contact term, has recently been identified as the primary obstacle to quantum computation applications as it yields efficient electron spin dephasing [5,6,7,8]. For a hole, this Fermi contact coupling, is expected to be much weaker because of the p-symmetry of the valence band states [4,9]. Indeed pioneer experimental work performed in silicon, fifty years ago, has shown that the nuclear spin relaxation time due to the interaction with free carriers was about one order of magnitude smaller in p-doped than in n-doped bulk material [10].
However the corresponding hole spin relaxation or dephasing induced by nuclear spins were not evidenced before in semiconductors because the hole spin dynamics in bulk or quantum well structures is governed by the very rapid spin relaxation mechanisms induced by the strong heavy-and light-hole mixing in the valence bands [4,11,12,13]. These spin-orbit related effects are strongly inhibited in QDs due to their fully quantized electronic structure.
Recently, a lower limit of tens of nanoseconds in zero external magnetic field was estimated for hole spin relaxation times in CdSe or InAs QDs, but these measurements were limited by the radiative recombination of the photo-created complexes [14,15]. In the presence of high external magnetic fields (1-12 T), which screen the effects related to nuclear spins, it has been demonstrated that a spin-orbit-mediated single-phonon scattering between Zeeman levels governs the hole spin relaxation processes [16,17,18]. This mechanism leads to a decrease of the hole spin relaxation time when increasing the magnetic field.
In this letter, we measure the hole spin dynamics by time-resolved optical orientation experiments in an ensemble of p-doped InAs/GaAs QDs. We demonstrate that, in the absence of applied magnetic field, the hole spin dephasing is controlled by the hyperfine hole-nuclear spin interaction. We show that this effect relies on the dipole-dipole coupling combined with the mixing of heavy-and light-hole states in QDs. Finally we evidence that a small magnetic field of the order of 10 mT, instead of 200mT for the case of electrons, quenches the hole spin relaxation.
The QDs structures were grown by molecular beam epitaxy on a (001) GaAs substrate.
The sample presented here consists of 30 planes of self-assembled InAs QDs, separated by 38-nm thick GaAs spacer layers. The QD surface density is about 10 10 cm -2 . The structure was p-modulation doped with a Carbon delta-doping layer (nominal density ~2x10 11 cm -2 ) located below each QD layer.
To probe the resident hole spin polarization, we measured the photo-induced circular dichroism (PCD) in the QD sample. A picosecond Ti:sapphire laser is split into pump and probe beams (the repetition frequency is 76 MHz). The pump beam polarization is σ+/σmodulated at 42 kHz with a photo-elastic modulator; the probe beam is linearly polarized.
After transmission through the sample, the probe beam is decomposed into its two circular components, and the difference in their intensities is measured with a balanced optical bridge.
To improve the signal-to-noise ratio, a double lock-in amplifier analysis of the signal is performed, the pump and probe beams being modulated with a mechanical chopper at two different frequencies. In the same sample, the electron spin dynamics has been measured by time-resolved photoluminescence (PL) experiments; 1.5 ps pulses generated by a Ti-Sapphire laser at a repetition frequency of 82 MHz were used as excitation light, and the PL signal was recorded by using a S1 photocathode streak camera with an overall time resolution of 20 ps.
In the PCD experiments, a circularly polarized pump beam propagating along the growth axis z is tuned to the energy of the lowest-allowed optical transition of InAs QDs, containing a single resident hole (E = 1.35 eV). This excitation creates a complex of three particles, called the positive trion (X + ), in its ground state. This transient complex consists of two holes with opposite spins forming a singlet (the photo-generated one and the resident one due to doping), and of a photo-generated electron with its spin pointing down or up depending on the σ + or σcircularly polarized excitation, respectively. For simplicity, we consider, for the optical orientation process, pure heavy-hole states [19]. Thus, the pump beam helicity selectively generates spin-polarized electrons. During the lifetime of these photo-generated electrons, the electron-nuclear hyperfine interaction leads to an efficient coherent coupling of the two electron spin states [5,7]. The spontaneous decay of the trion state by emission of a polarized photon leads to efficient hole spin cooling, as evidenced recently in cw single QD experiments [20] (see Fig. 1a). This process allows us to spin-polarize the resident holes in the QDs with a pulsed resonant excitation. . Thus the PCD signal simply writes: Fig. 1  To obtain a direct evidence of the hole-nuclear spin interaction, we have applied an external magnetic field ! r B parallel to the growth axis z of the sample. As for an electron [5,6],    26,27,28 . The modified hh states can be written as [28,29] ! ˜ " ±3 / 2 = 1 where ! " = " e i# is a coefficient taking into account the strain contribution. Then, the general dipole-dipole Hamiltonian [22] for a given hole can be written as follows in the basis The summation is over all the lattice nuclei with magnetic momentum CdTe QDs [26,27,28]. The dipole-dipole hyperfine constants j C can be obtained by using the dipole-dipole matrix elements derived in ref. [9], with symmetry rules applied to the hole Bloch function. As in ref. [9], the main contribution to the dipole-dipole interaction is due to the short-range contribution of the dipole-dipole coupling. This leads to The effective nuclear field ! r B N h experienced by a hole in a QD, through dipole-dipole interaction with the nuclei, is then written: where ! g h is the hole Landé factor, and ! r e x , r e y , r e z are the unit vectors along the x,y, z axes. The magnitude and direction of this field are randomly distributed from QD to another QD, and the randomness is described by an anisotropic gaussian probability distribution of where ! T " h is the ensemble dephasing time, arising from the random hole precession directions and frequencies in the randomly distributed frozen nuclear field. To obtain information about the electron-nuclear coupling strength in the same sample, we measured the photo-created electron spin dynamics in time-resolved photoluminescence (PL) experiments. Figure 3 displays the dynamics of the circular polarization ! P c = I + " I " I + + I " detected at the peak of the QD ground state PL (1.36 eV) after a circularly-polarized ! " + picosecond excitation (I + and Iare the luminescence intensities, copolarized and counter-polarized with the circularly polarized laser pulse). This curve allows us to measure the time evolution of the average X + spin, i.e. the photo-generated electron spin since the two holes in the trion form a spin singlet. As demonstrated before [7,8], the observed decay of the PL circular polarization directly reflects the spin dephasing of the photo-generated electrons due to their hyperfine interaction with nuclei. This interaction can be described as an effective nuclear field ! r B N e acting on a localized electron spin, which is frozen during the lifetime of the photo-generated electron [5]. The initial decay time of the average electron spin polarization, ! T " e , which characterizes the fluctuations of the hyperfine interaction can be estimated from Fig.3 to be ! T " e ~500 ps, which is comparable to previous results in similar systems. By using the contact hyperfine constants In conclusion, we have demonstrated that the hole spin dynamics in InAs semiconductor QDs is governed by the dipole-dipole interaction with randomly oriented nuclear spins due to the heavy-and light-hole mixing of the QD ground state. The effect of this hyperfine interaction on the hole spin relaxation time can be efficiently suppressed by an external magnetic field provided that it is larger than the fluctuations of the effective nuclear field acting on the hole spin. We have shown that this field is of the order of a few mT, which is one order of magnitude smaller than the magnetic field required to screen the interaction of an electron with the nuclear spins in the same dots. This nuclear induced hole spin dephasing, which has not been measured before in semiconductors, must be taken into account in future nanoscopic hole-spin-based quantum devices. Finally, studies to control and minimize the heavy-light hole mixing would be interesting in order to reduce or even cancel the hyperfine interaction of holes in QDs.