Nuclear-spin-induced oscillatory current in spin-blockaded quantum dots

Exploring nonlinear dynamics in periodically driven time crystal from synchronization to chaotic motion

The coupled electron-nuclear spin system in an InGaAs semiconductor as testbed of nonlinear dynamics can develop auto-oscillations, resembling time-crystalline behavior, when continuously excited by a circularly polarized laser. We expose this system to deviations from continuous driving by periodic modulation of the excitation polarization, revealing a plethora of nonlinear phenomena that depend on modulation frequency and depth. We find ranges in which the system's oscillations are entrained with the modulation frequency. The width of these ranges depends on the polarization modulation depth, resulting in an Arnold tongue pattern. Outside the tongue, the system shows a variety of fractional subharmonic responses connected through bifurcation jets when varying the modulation frequency. Here, each branch in the frequency spectrum forms a devil's staircase. When an entrainment range is approached by going through an increasing order of bifurcations, chaotic behavior emerges. These findings can be described by an advanced model of the periodically pumped electron-nuclear spin system. We discuss the connection of the obtained results to different phases of time matter.

Wigner-molecularization-enabled dynamic nuclear polarization

Multielectron semiconductor quantum dots (QDs) provide a novel platform to study the Coulomb interaction-driven, spatially localized electron states of Wigner molecules (WMs). Although Wigner-molecularization has been confirmed by real-space imaging and coherent spectroscopy, the open system dynamics of the strongly correlated states with the environment are not yet well understood. Here, we demonstrate efficient control of spin transfer between an artificial three-electron WM and the nuclear environment in a GaAs double QD. A Landau-Zener sweep-based polarization sequence and low-lying anticrossings of spin multiplet states enabled by Wigner-molecularization are utilized. Combined with coherent control of spin states, we achieve control of magnitude, polarity, and site dependence of the nuclear field. We demonstrate that the same level of control cannot be achieved in the non-interacting regime. Thus, we confirm the spin structure of a WM, paving the way for active control of correlated electron states for application in mesoscopic environment engineering.

Preparing Multipartite Entangled Spin Qubits via Pauli Spin Blockade

Preparing large-scale multi-partite entangled states of quantum bits in each physical form such as photons, atoms or electrons for each specific application area is a fundamental issue in quantum science and technologies. Here, we propose a setup based on Pauli spin blockade (PSB) for the preparation of large-scale W states of electrons in a double quantum dot (DQD). Within the proposed scheme, two W states of n and m electrons respectively can be fused by allowing each W state to transfer a single electron to each quantum dot. The presence or absence of PSB then determines whether the two states have fused or not, leading to the creation of a W state of n + m - 2 electrons in the successful case. Contrary to previous works based on quantum dots or nitrogen-vacancy centers in diamond, our proposal does not require any photon assistance. Therefore the 'complex' integration and tuning of an optical cavity is not a necessary prerequisite. We also show how to improve the success rate in our setup. Because requirements are based on currently available technology and well-known sensing techniques, our scheme can directly contribute to the advances in quantum technologies and, in particular in solid state systems.

Signatures of Hyperfine, Spin-Orbit, and Decoherence Effects in a Pauli Spin Blockade

We detect in real time interdot tunneling events in a weakly coupled two-electron double quantum dot in GaAs. At finite magnetic fields, we observe two characteristic tunneling times T_{d} and T_{b}, belonging to, respectively, a direct and a blocked (spin-flip-assisted) tunneling. The latter corresponds to the lifting of a Pauli spin blockade, and the tunneling times ratio η=T_{b}/T_{d} characterizes the blockade efficiency. We find pronounced changes in the behavior of η upon increasing the magnetic field, with η increasing, saturating, and increasing again. We explain this behavior as due to the crossover of the dominant blockade-lifting mechanism from the hyperfine to spin-orbit interactions and due to a change in the contribution of the charge decoherence.

Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet

In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back locally, modifying the local electronic Zeeman energy. Here we report a nonlocal effect arising from the interplay between nuclear polarization and the spatial structure of electronic domains in a ν=2/3 fractional quantum Hall state. In our experiments, we use a quantum point contact to locally control and probe the domain structure of different spin configurations emerging at the spin phase transition. Feedback between nuclear and electronic degrees of freedom gives rise to memristive behavior, where electronic transport through the quantum point contact depends on the history of current flow. We propose a model for this effect which suggests a novel route to studying edge states in fractional quantum Hall systems and may account for so-far unexplained oscillatory electronic-transport features observed in previous studies.

Critical Behavior of Alternately Pumped Nuclear Spins in Quantum Dots

Nuclear spins in a spin-blocked quantum dot can be pumped and eventually polarized in either of two opposite directions that are selected by applying two different source-drain voltages. Applying a square pulse train as the source-drain voltage can continuously switch the pumping direction alternately. We propose and demonstrate a critical behavior in the polarization after alternate pumping, where the final polarization is sensitive to the initial polarization and pulse conditions. This sensitivity leads to stochastic behavior in the final polarization under nominally the same pumping conditions.

Exchange-Induced Spin Blockade in a Two-Electron Double Quantum Dot

We have experimentally identified the exchange-induced spin blockade in a GaAs double quantum dot. The transport is suppressed only when the eigenstates are well-defined singlet and triplet states, and thus sensitive to dynamic nuclear-spin polarization that causes singlet-triplet mixing. This gives rise to unusual current spectra, such as a sharp current dip and an asymmetric current profile near the triplet resonance of a double quantum dot. Numerical simulations suggest that the current dip is a signature of identical nuclear-spin polarization in the two dots, which is attractive for coherent spin manipulations in a material with nuclear spins.

Proposal for a Domain Wall Nano-Oscillator driven by Non-uniform Spin Currents

We propose a new mechanism and a related device concept for a robust, magnetic field tunable radio-frequency (rf) oscillator using the self oscillation of a magnetic domain wall subject to a uniform static magnetic field and a spatially non-uniform vertical dc spin current. The self oscillation of the domain wall is created as it translates periodically between two unstable positions, one being in the region where both the dc spin current and the magnetic field are present, and the other, being where only the magnetic field is present. The vertical dc spin current pushes it away from one unstable position while the magnetic field pushes it away from the other. We show that such oscillations are stable under noise and can exhibit a quality factor of over 1000. A domain wall under dynamic translation, not only being a source for rich physics, is also a promising candidate for advancements in nanoelectronics with the actively researched racetrack memory architecture, digital and analog switching paradigms as candidate examples. Devising a stable rf oscillator using a domain wall is hence another step towards the realization of an all domain wall logic scheme.

Quenching of dynamic nuclear polarization by spin-orbit coupling in GaAs quantum dots

The central-spin problem is a widely studied model of quantum decoherence. Dynamic nuclear polarization occurs in central-spin systems when electronic angular momentum is transferred to nuclear spins and is exploited in quantum information processing for coherent spin manipulation. However, the mechanisms limiting this process remain only partially understood. Here we show that spin–orbit coupling can quench dynamic nuclear polarization in a GaAs quantum dot, because spin conservation is violated in the electron–nuclear system, despite weak spin–orbit coupling in GaAs. Using Landau–Zener sweeps to measure static and dynamic properties of the electron spin–flip probability, we observe that the size of the spin–orbit and hyperfine interactions depends on the magnitude and direction of applied magnetic field. We find that dynamic nuclear polarization is quenched when the spin–orbit contribution exceeds the hyperfine, in agreement with a theoretical model. Our results shed light on the surprisingly strong effect of spin–orbit coupling in central-spin systems.

Dynamic nuclear polarization is the transfer of electronic angular momentum to nuclear spins and is a potential route for coherently manipulating spin in quantum information. Here, the authors show that spin–orbit coupling can quench dynamic nuclear polarization in a gallium arsenide quantum dot.

Role of dual nuclear baths on spin blockade leakage current bistabilities

Spin-blockaded electronic transport across a double quantum dot (DQD) system represents an important advancement in the area of spin-based quantum information. The basic mechanism underlying the blockade is the formation of a blocking triplet state. The bistability of the leakage current as a function of the applied magnetic field in this regime is believed to arise from the effect of nuclear Overhauser fields on spin-flip transitions between the blocking triplet and the conducting singlet states. The objective of this paper is to present the nuances of considering a two bath model on the experimentally observed current bistability by employing a self consistent simulation of the nuclear spin dynamics coupled with the electronic transport of the DQD set up. In doing so, we first discuss the important subtleties involved in the microscopic derivation of the hyperfine mediated spin flip rates. We then give insights as to how the differences between the two nuclear baths and the resulting difference Overhauser field affect the two-electron states of the DQD and their connection with the experimentally observed current hysteresis curve.

Spin-current Seebeck effect in quantum dot systems

We first bring up the concept of the spin-current Seebeck effect based on a recent experiment (Vera-Marun et al 2012 Nature Phys. 8 313), and investigate the spin-current Seebeck effect in quantum dot (QD) systems. Our results show that the spin-current Seebeck coefficient S is sensitive to different polarization states of the QD, and therefore can be used to detect the polarization state of the QD and monitor the transitions between different polarization states of the QD. The intradot Coulomb interaction can greatly enhance S due to the stronger polarization of the QD. By using the parameters for a typical QD whose intradot Coulomb interaction U is one order of magnitude larger than the linewidth Γ, we demonstrate that the maximum value of S can be enhanced by a factor of 80. On the other hand, for a QD whose Coulomb interaction is negligible, we show that one can still obtain a large S by applying an external magnetic field.

Steady-state entanglement in the nuclear spin dynamics of a double quantum dot

We propose a scheme for the deterministic generation of steady-state entanglement between the two nuclear spin ensembles in an electrically defined double quantum dot. Because of quantum interference in the collective coupling to the electronic degrees of freedom, the nuclear system is actively driven into a two-mode squeezedlike target state. The entanglement buildup is accompanied by a self-polarization of the nuclear spins towards large Overhauser field gradients. Moreover, the feedback between the electronic and nuclear dynamics leads to multistability and criticality in the steady-state solutions.

Nuclear spin effects in semiconductor quantum dots

The interaction of an electronic spin with its nuclear environment, an issue known as the central spin problem, has been the subject of considerable attention due to its relevance for spin-based quantum computation using semiconductor quantum dots. Independent control of the nuclear spin bath using nuclear magnetic resonance techniques and dynamic nuclear polarization using the central spin itself offer unique possibilities for manipulating the nuclear bath with significant consequences for the coherence and controlled manipulation of the central spin. Here we review some of the recent optical and transport experiments that have explored this central spin problem using semiconductor quantum dots. We focus on the interaction between 10(4)-10(6) nuclear spins and a spin of a single electron or valence-band hole. We also review the experimental techniques as well as the key theoretical ideas and the implications for quantum information science.

Large nuclear spin polarization in gate-defined quantum dots using a single-domain nanomagnet

The electron-nuclei (hyperfine) interaction is central to spin qubits in solid state systems. It can be a severe decoherence source but also allows dynamic access to the nuclear spin states. We study a double quantum dot exposed to an on-chip single-domain nanomagnet and show that its inhomogeneous magnetic field crucially modifies the complex nuclear spin dynamics such that the Overhauser field tends to compensate external magnetic fields. This turns out to be beneficial for polarizing the nuclear spin ensemble. We reach a nuclear spin polarization of ≃50%, unrivaled in lateral dots, and explain our manipulation technique using a comprehensive rate equation model.

Self-sustaining dynamical nuclear polarization oscillations in quantum dots

Early experiments on spin-blockaded double quantum dots revealed robust, large-amplitude current oscillations in the presence of a static (dc) source-drain bias. Despite experimental evidence implicating dynamical nuclear polarization, the mechanism has remained a mystery. Here we introduce a minimal albeit realistic model of coupled electron and nuclear spin dynamics which supports self-sustained oscillations. Our mechanism relies on a nuclear spin analog of the tunneling magnetoresistance phenomenon (spin-dependent tunneling rates in the presence of an inhomogeneous Overhauser field) and nuclear spin diffusion, which governs dynamics of the spatial profile of nuclear polarization. The proposed framework naturally explains the differences in phenomenology between vertical and lateral quantum dot structures as well as the extremely long oscillation periods.

Two- and three-electron Pauli spin blockade in series-coupled triple quantum dots

We investigate two- and three-electron spin blockade in three vertical quantum dots (QDs) coupled in series. Two-electron spin blockade is found in a region where sequential tunneling through all QDs is forbidden but tunneling involving virtual hopping through an empty QD is allowed. It is observed only for the hole cycle with a distinct bias threshold for access to the triplet state. Three-electron spin blockade involving the quadruplet state is observed for nonequibilium conditions where sequential tunneling is allowed and the triplet state is accessible. Our results shine light on the importance of the nonequibilium conditions to obtain sufficient population of triplet and quadruplet states necessary for spin blockade.

Suppression of Zeeman gradients by nuclear polarization in double quantum dots

We use electric dipole spin resonance to measure dynamic nuclear polarization in InAs nanowire quantum dots. The resonance shifts in frequency when the system transitions between metastable high and low current states, indicating the presence of nuclear polarization. We propose that the low and the high current states correspond to different total Zeeman energy gradients between the two quantum dots. In the low current state, dynamic nuclear polarization efficiently compensates the Zeeman gradient due to the g-factor mismatch, resulting in a suppressed total Zeeman gradient. We present a theoretical model of electron-nuclear feedback that demonstrates a fixed point in nuclear polarization for nearly equal Zeeman splittings in the two dots and predicts a narrowed hyperfine gradient distribution.

Observation of hysteretic transport due to dynamic nuclear spin polarization in a GaAs lateral double quantum dot

We report a new transport feature in a GaAs lateral double quantum dot that emerges for magnetic-field sweeps and shows hysteresis due to dynamic nuclear spin polarization (DNP). This DNP signal appears in the Coulomb blockade regime by virtue of the finite interdot tunnel coupling and originates from the crossing between ground levels of the spin triplet and singlet extensively used for nuclear spin manipulations in pulsed-gate experiments. The magnetic-field dependence of the current level is suggestive of unbalanced DNP between the two dots, which opens up the possibility of controlling electron and nuclear spin states via dc transport.

Voltage-selective bidirectional polarization and coherent rotation of nuclear spins in quantum dots

We propose and demonstrate that the nuclear spins of the host lattice in GaAs double quantum dots can be polarized in either of two opposite directions, parallel or antiparallel to an external magnetic field. The direction is selected by adjusting the dc voltage. This nuclear polarization manifests itself by repeated controlled electron-nuclear spin scattering in the Pauli spin-blockade state. Polarized nuclei are also controlled by means of nuclear magnetic resonance. This Letter confirms that the nuclear spins in quantum dots are long-lived quantum states with a coherence time of up to 1 ms, and may be a promising resource for quantum-information processing such as quantum memories for electron spin qubits.

Dynamical cooling of nuclear spins in double quantum dots

Electrons trapped in quantum dots can exhibit quantum-coherent spin dynamics over long timescales. These timescales are limited by the coupling of electron spins to the disordered nuclear spin background, which is a major source of noise and dephasing in such systems. We propose a scheme for controlling and suppressing fluctuations of nuclear spin polarization in double quantum dots, which uses nuclear spin pumping in the spin-blockade regime. We show that nuclear spin polarization fluctuations can be suppressed when electronic levels in the two dots are properly positioned near resonance. The proposed mechanism is analogous to that of optical Doppler cooling. The Overhauser shift due to fluctuations of nuclear polarization brings electron levels in and out of resonance, creating internal feedback to suppress fluctuations. Estimates indicate that a better than 10-fold reduction of fluctuations is possible.

Exchange control of nuclear spin diffusion in a double quantum dot

The influence of gate-controlled two-electron exchange on the relaxation of nuclear polarization in small ensembles (N∼10(6)) of nuclear spins is examined in a GaAs double quantum dot system. Waiting in the (2,0) charge configuration, which has large exchange splitting, reduces the nuclear diffusion rate compared to that of the (1,1) configuration. Matching exchange to Zeeman splitting significantly increases the nuclear diffusion rate.

Dynamic nuclear polarization in double quantum dots

We theoretically investigate the controlled dynamic polarization of lattice nuclear spins in GaAs double quantum dots containing two electrons. Three regimes of long-term dynamics are identified, including the buildup of a large difference in the Overhauser fields across the dots, the saturation of the nuclear polarization process associated with formation of so-called "dark states", and the elimination of the difference field. We show that in the case of unequal dots, buildup of difference fields generally accompanies the nuclear polarization process, whereas for nearly identical dots, buildup of difference fields competes with polarization saturation in dark states. The elimination of the difference field does not, in general, correspond to a stable steady state of the polarization process.

Spin bottleneck in resonant tunneling through double quantum dots with different Zeeman splittings

We investigated the electron transport property of the InGaAs/GaAs double quantum dots, the electron g factors of which are different from each other. We found that in a magnetic field, the resonant tunneling is suppressed even if one of the Zeeman sublevels is aligned. This is because the other misaligned Zeeman sublevels limit the total current. A finite broadening of the misaligned sublevel partially relieves this bottleneck effect, and the maximum current is reached when interdot detuning is half the Zeeman energy difference.

Stationary and transient leakage current in the Pauli spin blockade

We study the effects of cotunneling and a nonuniform Zeeman splitting on the stationary and transient leakage current through a double quantum dot in the Pauli spin blockade regime. We find that the stationary current due to cotunneling vanishes at low temperature and large applied magnetic field, allowing for the dynamical (rapid) preparation of a pure spin ground state, even at large voltage bias. Additionally, we analyze current that flows between blocking events, characterized, in general, by a fractional effective charge e*. This charge can be used as a sensitive probe of spin-relaxation mechanisms and can be used to determine the visibility of Rabi oscillations.

Quantitative estimation of exchange interaction energy using two-electron vertical double quantum dots

We use Pauli-spin blockade in two-electron vertical double quantum dots to quantitatively estimate the exchange energy J in a wide range of interdot level detuning Delta and fully compare it with calculations. Pauli-spin blockade is lifted via a singlet- (S-)triplet (T) transition mediated by hyperfine coupling, which abruptly occurs in our devices when the S-T transition energy or J is compensated by the Zeeman energy. We use this feature to derive J depending on Delta between the S-S and T-T resonances. The obtained J versus Delta including the resonance effect is perfectly reproduced by Hubbard model calculations.

Negative differential resistance in nanoscale transport in the Coulomb blockade regime

Motivated by recent experiments, we have studied the transport behavior of coupled quantum dot systems in the Coulomb blockade regime using the master (rate) equation approach. We explore how electron-electron interactions in a donor-acceptor system, resembling weakly coupled quantum dots with varying charging energy, can modify the system's response to an external bias, taking it from normal Coulomb blockade behavior to negative differential resistance (NDR) in the current-voltage characteristics.

Measurement of temporal correlations of the overhauser field in a double quantum dot

In quantum dots made from materials with nonzero nuclear spins, hyperfine coupling creates a fluctuating effective Zeeman field (Overhauser field) felt by electrons, which can be a dominant source of spin qubit decoherence. We characterize the spectral properties of the fluctuating Overhauser field in a GaAs double quantum dot by measuring correlation functions and power spectra of the rate of singlet-triplet mixing of two separated electrons. Away from zero field, spectral weight is concentrated below 10 Hz, with approximately 1/f2 dependence on frequency f. This is consistent with a model of nuclear spin diffusion, and indicates that decoherence can be largely suppressed by echo techniques.

Electric field induced nuclear spin resonance mediated by oscillating electron spin domains in GaAs-based semiconductors

We demonstrate an alternative nuclear spin resonance using a radio frequency (rf) electric field [nuclear electric resonance (NER)] instead of a magnetic field. The NER is based on the electronic control of electron spins forming a domain structure. The rf electric field applied to a gate excites spatial oscillations of the domain walls and thus temporal oscillations of the hyperfine field to nuclear spins. The rf power and burst duration dependence of the NER spectrum provides insight into the interplay between nuclear spins and the oscillating domain walls.

The role of many-particle excitations in Coulomb blockaded transport

We discuss the role of electron-electron and electron-phonon correlations in current flow in the Coulomb blockade regime, focusing specifically on non-trivial signatures arising from the breakdown of mean-field theory. By solving transport equations directly in Fock space, we show that electron-electron interactions manifest as gateable excitations experimentally observed in the current-voltage characteristic. While these excitations might merge into an incoherent sum that allows occasional simplifications, a clear separation of excitations into slow 'traps' and fast 'channels' can lead to further novelties such as negative differential resistance, hysteresis and random telegraph signals. Analogous novelties for electron-phonon correlation include the breakdown of commonly anticipated Stokes-anti-Stokes intensities, and an anomalous decrease in phonon population upon heating due to reabsorption of emitted phonons.

Dynamic nuclear polarization with single electron spins

We polarize nuclear spins in a GaAs double quantum dot by controlling two-electron spin states near the anticrossing of the singlet (S) and m(S)= +1 triplet (T+) using pulsed gates. An initialized S state is cyclically brought into resonance with the T+ state, where hyperfine fields drive rapid rotations between S and T+, "flipping" an electron spin and "flopping" a nuclear spin. The resulting Overhauser field approaches 80 mT, in agreement with a simple rate-equation model. A self-limiting pulse sequence is developed that allows the steady-state nuclear polarization to be set using a gate voltage.

Nuclear tuning and detuning of the electron spin resonance in a quantum dot: theoretical consideration

We study nuclear spin dynamics in a quantum dot close to the conditions of electron spin resonance. We show that at a small frequency mismatch, the nuclear field detunes the resonance. Remarkably, at larger frequency mismatch, its effect is opposite: The nuclear system is bistable, and in one of the stable states, the field accurately tunes the electron spin splitting to resonance. In this state, the nuclear field fluctuations are strongly suppressed, and nuclear spin relaxation is accelerated.

Dynamic nuclear polarization at high magnetic fields

Dynamic nuclear polarization (DNP) is a method that permits NMR signal intensities of solids and liquids to be enhanced significantly, and is therefore potentially an important tool in structural and mechanistic studies of biologically relevant molecules. During a DNP experiment, the large polarization of an exogeneous or endogeneous unpaired electron is transferred to the nuclei of interest (I) by microwave (microw) irradiation of the sample. The maximum theoretical enhancement achievable is given by the gyromagnetic ratios (gamma(e)gamma(l)), being approximately 660 for protons. In the early 1950s, the DNP phenomenon was demonstrated experimentally, and intensively investigated in the following four decades, primarily at low magnetic fields. This review focuses on recent developments in the field of DNP with a special emphasis on work done at high magnetic fields (> or =5 T), the regime where contemporary NMR experiments are performed. After a brief historical survey, we present a review of the classical continuous wave (cw) DNP mechanisms-the Overhauser effect, the solid effect, the cross effect, and thermal mixing. A special section is devoted to the theory of coherent polarization transfer mechanisms, since they are potentially more efficient at high fields than classical polarization schemes. The implementation of DNP at high magnetic fields has required the development and improvement of new and existing instrumentation. Therefore, we also review some recent developments in microw and probe technology, followed by an overview of DNP applications in biological solids and liquids. Finally, we outline some possible areas for future developments.

Electrical control of spin relaxation in a quantum dot

We demonstrate electrical control of the spin relaxation time T1 between Zeeman-split spin states of a single electron in a lateral quantum dot. We find that relaxation is mediated by the spin-orbit interaction, and by manipulating the orbital states of the dot using gate voltages we vary the relaxation rate W identical withT1(-1) by over an order of magnitude. The dependence of W on orbital confinement agrees with theoretical predictions, and from these data we extract the spin-orbit length. We also measure the dependence of W on the magnetic field and demonstrate that spin-orbit mediated coupling to phonons is the dominant relaxation mechanism down to 1 T, where T1 exceeds 1 s.

Electrically driven reverse overhauser pumping of nuclear spins in quantum dots

We propose a new mechanism for polarizing nuclear spins in quantum dots, based on periodic modulation of the hyperfine coupling by electric driving at the electron spin resonance frequency. Dynamical nuclear polarization results from resonant excitation rather than hyperfine relaxation mediated by a thermal bath, and thus is not subject to Overhauser-like detailed balance constraints. This allows polarization in the direction opposite to that expected from the Overhauser effect. Competition of the electrically driven and bath-assisted mechanisms can give rise to spatial modulation and sign reversal of polarization on a scale smaller than the electron confinement radius in the dot.

Large nuclear overhauser fields detected in vertically coupled double quantum dots

We report the electrical induction and detection of dynamic nuclear polarization in the spin-blockade regime of double GaAs vertical quantum dots. The nuclear Overhauser field measurement relies on bias voltage control of the interdot spin exchange coupling and measurement of dc current at variable external magnetic fields. The largest Overhauser field observed was about 4 T, corresponding to a nuclear polarization approximately 40% for the electronic g factor typical of these devices, |g*| approximately 0.25. A phenomenological model is proposed to explain these observations.

Semiconductor spintronics

Spintronics refers commonly to phenomena in which the spin of electrons in a solid state environment plays the determining role. In a more narrow sense spintronics is an emerging research field of electronics: spintronics devices are based on a spin control of electronics, or on an electrical and optical control of spin or magnetism. While metal spintronics has already found its niche in the computer industry—giant magnetoresistance systems are used as hard disk read heads—semiconductor spintronics is yet to demonstrate its full potential. This review presents selected themes of semiconductor spintronics, introducing important concepts in spin transport, spin injection, Silsbee-Johnson spin-charge coupling, and spin-dependent tunneling, as well as spin relaxation and spin dynamics. The most fundamental spin-dependent interaction in nonmagnetic semiconductors is spin-orbit coupling. Depending on the crystal symmetries of the material, as well as on the structural properties of semiconductor based heterostructures, the spin-orbit coupling takes on different functional forms, giving a nice playground of effective spin-orbit Hamiltonians. The effective Hamiltonians for the most relevant classes of materials and heterostructures are derived here from realistic electronic band structure descriptions. Most semiconductor device systems are still theoretical concepts, waiting for experimental demonstrations. A review of selected proposed, and a few demonstrated devices is presented, with detailed description of two important classes: magnetic resonant tunnel structures and bipolar magnetic diodes and transistors. In view of the importance of ferromagnetic semiconductor materials, a brief discussion of diluted magnetic semiconductors is included. In most cases the presentation is of tutorial style, introducing the essential theoretical formalism at an accessible level, with case-study-like illustrations of actual experimental results, as well as with brief reviews of relevant recent achievements in the field.

Suppression of spin relaxation in an InAs nanowire double quantum dot

We investigate the triplet-singlet relaxation in a double quantum dot defined by top gates in an InAs nanowire. In the Pauli spin blockade regime, the leakage current can be mainly attributed to spin relaxation. While at weak and strong interdot coupling relaxation is dominated by two individual mechanisms, the relaxation is strongly reduced at intermediate coupling and finite magnetic field. In addition we observe a characteristic bistability of the spin-nonconserving current as a function of magnetic field. We propose a model where these features are explained by the polarization of nuclear spins enabled by the interplay between hyperfine and spin-orbit mediated relaxation.

Self-polarization and dynamical cooling of nuclear spins in double quantum dots

The spin-blockade regime of double quantum dots features coupled dynamics of electron and nuclear spins resulting from the hyperfine interaction. We explain observed nuclear self-polarization via a mechanism based on feedback of the Overhauser shift on electron energy levels, and propose to use the instability toward self-polarization as a vehicle for controlling the nuclear spin distribution. In the dynamics induced by a properly chosen time-dependent magnetic field, nuclear spin fluctuations can be suppressed significantly below the thermal level.

Effect of exchange interaction on spin dephasing in a double quantum dot

We measure singlet-triplet dephasing in a two-electron double quantum dot in the presence of an exchange interaction which can be electrically tuned from much smaller to much larger than the hyperfine energy. Saturation of dephasing and damped oscillations of the spin correlator as a function of time are observed when the two interaction strengths are comparable. Both features of the data are compared with predictions from a quasistatic model of the hyperfine field.

Electron transport in a double quantum dot governed by a nuclear magnetic field

We investigate theoretically electron transfer in a double dot in a situation where spin blockade is lifted by nuclear magnetic field: this has been recently achieved in experiment [F. Koppens, Science 309, 1346 (2005)]. We show that for a given realization of nuclear magnetic field spin blockade can be restored by tuning external magnetic field; this may be useful for quantum manipulation of the device.

Knight-field-enabled nuclear spin polarization in single quantum dots

We demonstrate dynamical nuclear-spin polarization in the absence of an external magnetic field by resonant circularly polarized optical excitation of a single electron or hole charged quantum dot. Optical pumping of the electron spin induces an effective inhomogeneous magnetic (Knight) field that determines the direction along which nuclear spins could polarize and enables nuclear-spin cooling by suppressing depolarization induced by nuclear dipole-dipole interactions. Our experiments constitute a first step towards a quantum measurement of the Overhauser field.

Optical pump-probe measurements of local nuclear spin coherence in semiconductor quantum wells

We demonstrate local manipulation and detection of nuclear spin coherence in semiconductor quantum wells by an optical pump-probe technique combined with pulse rf NMR. The Larmor precession of photoexcited electron spins is monitored by time-resolved Kerr rotation (TRKR) as a measure of nuclear magnetic field. Under the irradiation of resonant pulsed rf magnetic fields, Rabi oscillations of nuclear spins are traced by TRKR signals. The intrinsic coherence time evaluated by a spin-echo technique reveals the dependence on the orientation of the magnetic field with respect to the crystalline axis as expected by the nearest neighbor dipole-dipole interaction.

Control and Detection of Singlet-Triplet Mixing in a Random Nuclear Field

We observed mixing between two-electron singlet and triplet states in a double quantum dot, caused by interactions with nuclear spins in the host semiconductor. This mixing was suppressed when we applied a small magnetic field or increased the interdot tunnel coupling and thereby the singlet-triplet splitting. Electron transport involving transitions between triplets and singlets in turn polarized the nuclei, resulting in marked bistabilities. We extract from the fluctuating nuclear field a limitation on the time-averaged spin coherence time T2* of 25 nanoseconds. Control of the electron-nuclear interaction will therefore be crucial for the coherent manipulation of individual electron spins.

Electrical pump-and-probe study of spin singlet-triplet relaxation in a quantum dot

Spin relaxation from a triplet excited state to a singlet ground state in a semiconductor quantum dot is studied by employing an electrical pump-and-probe method. Spin relaxation occurs via co-tunneling when the tunneling rate is relatively large, confirmed by a characteristic square dependence of the relaxation rate on the tunneling rate. When co-tunneling is suppressed by reducing the tunneling rate, the intrinsic spin relaxation is dominated by spin-orbit interaction. We discuss a selection rule of the spin-orbit interaction based on the observed double-exponential decay of the triplet state.

Triplet–singlet spin relaxation via nuclei in a double quantum dot

The spin of a confined electron, when oriented originally in some direction, will lose memory of that orientation after some time. Physical mechanisms leading to this relaxation of spin memory typically involve either coupling of the electron spin to its orbital motion or to nuclear spins. Relaxation of confined electron spin has been previously measured only for Zeeman or exchange split spin states, where spin-orbit effects dominate relaxation; spin flips due to nuclei have been observed in optical spectroscopy studies. Using an isolated GaAs double quantum dot defined by electrostatic gates and direct time domain measurements, we investigate in detail spin relaxation for arbitrary splitting of spin states. Here we show that electron spin flips are dominated by nuclear interactions and are slowed by several orders of magnitude when a magnetic field of a few millitesla is applied. These results have significant implications for spin-based information processing.

Effects of inversion asymmetry on electron-nuclear spin coupling in semiconductor heterostructures: possible role of spin-orbit interactions

We show that electron-nuclear spin coupling in semiconductor heterostructures is strongly modified by their potential inversion asymmetry. This is demonstrated in a GaAs quantum well, where we observe that the current-induced nuclear spin polarization at Landau-level filling factor nu=2/3 is completely suppressed when the quantum well is made largely asymmetric with gate voltages. Furthermore, we find that the nuclear spin relaxation rate is also modified by the potential asymmetry. These findings strongly suggest that even a very weak Rashba spin-orbit interaction can play a dominant role in determining the electron-nuclear spin coupling.