Overhauser Shift Research Articles

First-principles hyperfine tensors for electrons and holes in GaAs and silicon

Understanding (and controlling) hyperfine interactions in semiconductor nanostructures is important for fundamental studies of material properties as well as for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles density-functional theory (DFT) and $\mathbf{k}\cdot\mathbf{p}$ theory, we have calculated hyperfine tensors for electrons and holes in GaAs and crystalline silicon. Accounting for relativistic effects near the nuclear core, we find contact hyperfine interactions for electrons in GaAs that are consistent with Knight-shift measurements performed on GaAs quantum wells and are roughly consistent with prior estimates extrapolated from measurements on InSb. We find that a combination of DFT and $\mathbf{k}\cdot\mathbf{p}$ theory is necessary to accurately determine the contact hyperfine interaction for electrons at a conduction-band minimum in silicon that is consistent with bulk Knight-shift measurements. For hole spins in GaAs, the overall magnitude of the hyperfine couplings we find from DFT is consistent with previous theory based on free-atom properties, and with heavy-hole Overhauser shifts measured in GaAs (and InGaAs) quantum dots. In addition, we theoretically predict that the heavy-hole hyperfine coupling to the As nuclear spins is stronger and almost purely Ising-like, while the (weaker) coupling to the Ga nuclear spins has significant non-Ising corrections. In the case of hole spins in silicon, we find (surprisingly) that the strength of the hyperfine interaction in the valence band is comparable to that in the conduction band and that the hyperfine tensors are highly anisotropic (Ising-like) in the heavy-hole subspace. These results suggest that the hyperfine coupling cannot be ruled out as a limiting mechanism for coherence ($T_2^{\ast}$) times recently measured for heavy holes in silicon quantum dots.

Nuclear spin dynamics in [001] AlAs quantum well in the regime of integer and fractional quantum Hall effect

Relaxation of nuclear spins located in the vicinity of 2D electron system confined in a 16 nm [001] AlAs/AlGaAs quantum well was studied with the aid of electron spin resonance (ESR) in the regime of integer and fractional quantum Hall effect. Nuclear spin-lattice relaxation time τ was measured from the time decay of the Overhauser shift near different filling factors of the electron system. The resultant dependence of τ on filling factor turned out to be nontrivial. At the temperature 1.5 K τ reached its maximal value at the exact filling ν = 1 and decreased when ν was altered, yet this maximum vanished when the system was cooled down to 0.5 K. The fractional quantum Hall effect state at the filling of 2∕3 was formed at the temperature of 0.5 K, and the development of this state was accompanied by the slowing of the nuclear spin relaxation. This observation suggests the enhancement of energy gap in the spin excitation spectrum of two-dimensional electrons at 2/3 state.

Electrical Initialization of Electron and Nuclear Spins in a Single Quantum Dot at Zero Magnetic Field.

The emission of circularly polarized light from a single quantum dot relies on the injection of carriers with well-defined spin polarization. Here we demonstrate single dot electroluminescence (EL) with a circular polarization degree up to 35% at zero applied magnetic field. The injection of spin-polarized electrons is achieved by combining ultrathin CoFeB electrodes on top of a spin-LED device with p-type InGaAs quantum dots in the active region. We measure an Overhauser shift of several microelectronvolts at zero magnetic field for the positively charged exciton (trion X+) EL emission, which changes sign as we reverse the injected electron spin orientation. This is a signature of dynamic polarization of the nuclear spins in the quantum dot induced by the hyperfine interaction with the electrically injected electron spin. This study paves the way for electrical control of nuclear spin polarization in a single quantum dot without any external magnetic field.

Double resonance calibration of g factor standards: Carbon fibers as a high precision standard

The g factor of paramagnetic defects in commercial high performance carbon fibers was determined by a double resonance experiment based on the Overhauser shift due to hyperfine coupled protons. Our carbon fibers exhibit a single, narrow and perfectly Lorentzian shaped ESR line and a g factor slightly higher than gfree with g=2.002644=gfree·(1+162ppm) with a relative uncertainty of 15ppm. This precisely known g factor and their inertness qualify them as a high precision g factor standard for general purposes. The double resonance experiment for calibration is applicable to other potential standards with a hyperfine interaction averaged by a process with very short correlation time.

ν=2/3 fractional quantum Hall state in an AlAs quantum well probed by electron spin resonance

The electron spin resonance (ESR) of two-dimensional electrons confined in a high-quality, 16-nm AlAs quantum well was investigated near the filling factor $\ensuremath{\nu}=2/3$ of the fractional quantum Hall effect (FQHE). The spin resonance was robust in the vicinity of the fractional filling $\ensuremath{\nu}=2/3$, indicating that the $\ensuremath{\nu}=2/3$ state is at least partially spin polarized. The formation of the $2/3$ FQHE state did not result in any modifications of the ESR linewidth and, hence, of the electron spin relaxation rate. Yet the nuclear spin-lattice relaxation rate extracted from the time decay of the ESR Overhauser shift demonstrated a strong nonmonotonic dependence on the electron filling factor with a minimum near $\ensuremath{\nu}=2/3$. This observation suggests the enhancement of the energy gap in the spin excitation spectrum of two-dimensional electrons at the $\ensuremath{\nu}=2/3$ state.

Nuclear magnetic resonance and nuclear spin relaxation in AlAs quantum well probed by ESR

The study of nuclear magnetic resonance and nuclear spin-lattice relaxation was conducted in an asymmetrically doped to $n\sim1.8\times10^{11}$ cm$^{-2}$ 16 nm AlAs quantum well grown in the $[001]$-direction. Dynamic polarization of nuclear spins due to the hyperfine interaction resulted in the so-called Overhauser shift of the two-dimensional conduction electron spin resonance. The maximum shifts achieved in the experiments are several orders of magnitude smaller than in GaAs-based heterostructures indicating that hyperfine interaction is weak. The nuclear spin-lattice relaxation time extracted from the decay of Overhauser shift over time turned out to depend on the filling factor of the two-dimensional electron system. This observation indicates that nuclear spin-lattice relaxation is mostly due to the interaction between electron and nuclear spins. Overhauser shift diminishes resonantly when the RF-radiation of certain frequencies was applied to the sample. This effect served as an indirect, yet powerful method for nuclear magnetic resonance detection: NMR quadrupole splitting of $^{75}$As nuclei was clearly resolved. Theoretical calculations performed describe well these experimental findings.

Electron paramagnetic resonance study of the nuclear spin dynamics in an AlAs quantum well

The nuclear spin dynamics in an asymmetrically doped 16-nm AlAs quantum well grown along the [001] direction has been studied experimentally using the time decay of the Overhauser shift of paramagnetic resonance of conduction electrons. The nonzero spin polarization of nuclei causing the initial observed Overhauser shift is due the relaxation of the nonequilibrium spin polarization of electrons into the nuclear subsystem near electron paramagnetic resonance owing to the hyperfine interaction. The measured relaxation time of nuclear spins near the unity filling factor is (530 ± 30) min at the temperature T = 0.5 K. This value exceeds the characteristic spin relaxation times of nuclei in GaAs/AlGaAs heterostructures by more than an order of magnitude. This fact indicates the decrease in the strength of the hyperfine interaction in the AlAs quantum well in comparison with GaAs/AlGaAs heterostructures.

Hyperfine coupling of hole and nuclear spins in symmetric (111)-grown GaAs quantum dots

In self assembled III-V semiconductor quantum dots, valence holes have longer spin coherence times than the conduction electrons, due to their weaker coupling to nuclear spin bath fluctuations. Prolonging hole spin stability relies on a better understanding of the hole to nuclear spin hyperfine coupling which we address both in experiment and theory in the symmetric (111) GaAs/AlGaAs droplet dots. In magnetic fields applied along the growth axis, we create a strong nuclear spin polarization detected through the positively charged trion X$^+$ Zeeman and Overhauser splittings. The observation of four clearly resolved photoluminescence lines - a unique property of the (111) nanosystems - allows us to measure separately the electron and hole contribution to the Overhauser shift. The hyperfine interaction for holes is found to be about five times weaker than that for electrons. Our theory shows that this ratio depends not only on intrinsic material properties but also on the dot shape and carrier confinement through the heavy-hole mixing, an opportunity for engineering the hole-nuclear spin interaction by tuning dot size and shape.

P-shell carrier assisted dynamic nuclear spin polarization in single quantum dots at zero external magnetic field

Repeated injection of spin polarized carriers in a quantum dot leads to the polarization of nuclear spins, a process known as dynamic nuclear spin polarization (DNP). Here, we report the first observation of p-shell carrier assisted DNP in single QDs at zero external magnetic field. The nuclear field - measured by using the Overhauser shift of the singly charged exciton state of the QDs - continues to increase, even after the carrier population in the s-shell saturates. This is also accompanied by an abrupt increase in nuclear spin buildup time as p-shell emission overtakes that of the s-shell. We attribute the observation to p-shell electrons strongly altering the nuclear spin dynamics in the QD, supported by numerical simulation results based on a rate equation model of coupling between electron and nuclear spin system. DNP with p-shell carriers could open up avenues for further control to increase the degree of nuclear spin polarization in QDs.

Nuclear spin polarization in the electron spin-flip Raman scattering of singly charged (In,Ga)As/GaAs quantum dots

Through an examination of the dynamic nuclear spin polarization and resonant spin-flip Raman scattering, the authors directly measure the optical-induced Overhauser shift in singly charged (In,Ga)As/GaAs quantum dots. Using a two-color laser excitation scheme, they observe the time evolution of the Overhauser shift, which demonstrates the nuclear spin depolarization over a few seconds. Furthermore, it is shown that this depolarization is strongly dependent on temperature.

Interplay of Electron and Nuclear Spin Noise in n-Type GaAs.

We present spin-noise spectroscopy measurements on an ensemble of donor-bound electrons in ultrapure GaAs:Si covering temporal dynamics over 6 orders of magnitude from milliseconds to nanoseconds. The spin-noise spectra detected at the donor-bound exciton transition show the multifaceted dynamical regime of the ubiquitous mutual electron and nuclear spin interaction typical for III-V-based semiconductor systems. The experiment distinctly reveals the finite Overhauser shift of an electron spin precession at zero external magnetic field and a second contribution around zero frequency stemming from the electron spin components parallel to the nuclear spin fluctuations. Moreover, at very low frequencies, features related with time-dependent nuclear spin fluctuations are clearly resolved making it possible to study the intricate nuclear spin dynamics at zero and low magnetic fields. The findings are in agreement with the developed model of electron and nuclear spin noise.

Dynamic nuclear polarization in InGaAs/GaAs and GaAs/AlGaAs quantum dots under nonresonant ultralow-power optical excitation

We study experimentally the dependence of dynamic nuclear spin polarization on the power of nonresonant optical excitation in two types of individual neutral semiconductor quantum dots: InGaAs/GaAs and GaAs/AlGaAs. We show that the mechanism of nuclear spin pumping via second-order recombination of optically forbidden (``dark'') exciton states recently reported in InP/GaInP quantum dots [E. A. Chekhovich et al., Phys. Rev. B 83, 125318 (2011)] is relevant for material systems considered in this work. In the InGaAs/GaAs dots this nuclear spin polarization mechanism is particularly pronounced, resulting in Overhauser shifts up to $\ensuremath{\sim}$80 $\ensuremath{\mu}$eV achieved at ultralow optical excitation power, $\ensuremath{\sim}$1000 times smaller than the power required to saturate ground state excitons. The Overhauser shifts observed at ultralow power pumping in the interface GaAs/AlGaAs dots are generally found to be smaller (up to $\ensuremath{\sim}$40 $\ensuremath{\mu}$eV). Furthermore in GaAs/AlGaAs we observe dot-to-dot variation and even sign reversal of the Overhauser shift which is attributed to the dark-bright exciton mixing originating from electron-hole exchange interaction in dots with reduced symmetry. Nuclear spin polarization degrees reported in this work under ultralow-power optical pumping are comparable to those achieved by techniques such as resonant optical pumping or above-gap pumping with high-power circularly polarized light. Dynamic nuclear polarization via second-order recombination of ``dark'' excitons may become a useful tool in single quantum dot applications, where manipulation of the nuclear spin environment or electron spin is required.

The photon-assisted dynamic nuclear polarization effect in a double quantum dot

We report on the Overhauser shift (OHS) of electric dipole spin resonance peaks in the reverse direction to that previously reported. Measuring electric dipole spin resonance in a double quantum dot, we observe two resonance peaks reflecting a Zeeman energy difference between the two quantum dots, and find that the dependence of the peak position on microwave power is different for each dot. The perturbation theory for hybridizing the flip-flop and photon-assisted tunneling mechanisms is discussed and is found to successfully explain the power dependence. This theory can also consistently explain the OHS in both directions, explaining the experimental results previously reported. Our results reveal the bidirectionality of OHSs and this is expected to play an important part in the development of effective nuclear spin squeezing techniques.

Nuclear spin depolarization via slow spin diffusion in single InAlAs quantum dots observed by using erase-pump-probe technique

Nuclear spin diffusion in single self-assembled InAlAs quantum dots was studied by using erase-pump-probe technique. As a measure of nuclear spin polarization, transients of the Overhauser shift (OHS) of positive trion were probed in the respective pulse region. The achieved stable OHS was relaxed with a long depolarization time as long as a few tens of seconds and a diffusion constant of ∼5 × 10−15 cm2/s was estimated. The slow transfer of the spin energy is considered to be due to the dipole-dipole interaction of the nuclei. In addition, through the magnetic field dependence of OHS, the stability of the nuclear spin polarization was briefly discussed, and the saturated maximum values of OHS were investigated experimentally.

Direct observation of nuclear field fluctuations in single quantum dots

The spin interaction between an electron and nuclei was investigated optically in a single self-assembled InAlAs quantum dot (QD). In spin dynamics at the initial stage, the fluctuation of nuclear field and the resulting electron spin relaxation time play a crucial role. We examined a positively charged exciton in a QD to evaluate the key physical quantities directly via the temporal evolution measurements of the Overhauser shift and the degree of circular polarization. In addition, the validity of our used spin dynamics model was discussed in the context of the experimentally obtained key parameters.

Nuclear spin polarization in single self-assembled In0.3Ga0.7As quantum dots by electrical spin injection

For a single In${}_{0.3}$Ga${}_{0.7}$As quantum dot in a spin light-emitting diode, we compare the nuclear spin polarization created by a spin polarized electrical current with the nuclear spin polarization originating from optically generated spin polarized carriers. As detection method we employ high-resolution optical spectroscopy of the Overhauser shift. We find that optically and electrically generated electron spin populations in the quantum dot result in a nuclear spin polarization of comparable magnitude, provided the injected electrons have the same spin polarization degree in both excitation modes. An asymmetric dependence of nuclear spin polarization on electron spin polarization is observed, consistent with the theoretical treatment. The results imply that nuclear spin polarization degrees of $\ensuremath{\sim}$58% can be achieved by purely electrical means in self-assembled quantum dots.

Nuclear spin‐polarization in single InGaAs quantum dots through electrical and optical spin‐injection in spin‐LEDs

AbstractWe investigate nuclear spin polarization in a single InGaAs quantum dot via electrical injection of spinpolarized electrons in a spin‐injection light‐emitting diode. The Overhauser shift in the single‐dot electroluminescence is compared with results obtained for optical spin injection in the same structure.The results clearly demonstrate the possibility of efficient nuclear spin polarization by purely electrical means which might be useful for future spintronic applications. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Measurement of a Heavy-Hole Hyperfine Interaction in InGaAs Quantum Dots Using Resonance Fluorescence

We measure the strength and the sign of hyperfine interaction of a heavy hole with nuclear spins in single self-assembled quantum dots. Our experiments utilize the locking of a quantum dot resonance to an incident laser frequency to generate nuclear spin polarization. By monitoring the resulting Overhauser shift of optical transitions that are split either by electron or exciton Zeeman energy with respect to the locked transition using resonance fluorescence, we find that the ratio of the heavy-hole and electron hyperfine interactions is -0.09 ± 0.02 in three quantum dots. Since hyperfine interactions constitute the principal decoherence source for spin qubits, we expect our results to be important for efforts aimed at using heavy-hole spins in quantum information processing.

Dynamic Nuclear Polarization in III–V Semiconductors

We report on electron spin resonance, nuclear magnetic resonance and Overhauser shift experiments on two of the most commonly used III–V semiconductors, GaAs and InP. Localized electron centers in these semiconductors have extended wavefunctions and exhibit strong electron–nuclear hyperfine coupling with the nuclei in their vicinity. These interactions not only play a critical role in electron and nuclear spin relaxation mechanisms, but also result in transfer of spin polarization from the electron spin system to the nuclear spin system. This transfer of polarization, known as dynamic nuclear polarization (DNP), may result in an enhancement of the nuclear spin polarization by several orders of magnitude under suitable conditions. We determine the critical range of doping concentration and temperature conducive to DNP effects by studying these semiconductors with varying doping concentration in a wide temperature range. We show that the electron spin system in undoped InP exhibits electric current-induced spin polarization. This is consistent with model predictions in zinc-blende semiconductors with strong spin–orbit effects.

Spin polarization of the neutral exciton in a single quantum dot

While efficient nuclear polarization has earlier been reported for the charged exciton in InAs/GaAs quantum dots at zero external magnetic field, we report here on a surprisingly high degree of circular polarization, up to ≈ 60 % , for the neutral exciton emission in individual InAs/GaAs dots. This high degree of polarization is explained in terms of the appearance of an effective nuclear magnetic field which stabilizes the electron spin. The nuclear polarization is manifested in experiments as a detectable Overhauser shift. In turn, the nuclei located inside the dot are exposed to an effective electron magnetic field, the Knight field. This nuclear polarization is understood as being due to the dynamical nuclear polarization by an electron localized in the QD. The high degree of polarization for the neutral exciton is also suggested to be due to separate in-time capture of electrons and holes into the QD.