We investigate spin relaxation in a silicon double quantum dot via leakage current through Pauli blockade as a function of interdot detuning and magnetic field. A dip in leakage current as a function of magnetic field on a \sim 40 mT field scale is attributed to spin-orbit mediated spin relaxation. On a larger (\sim 400 mT) field scale, a peak in leakage current is seen in some, but not all, Pauli-blocked transitions, and is attributed to spin-flip cotunneling. Both dip and peak structure show good agreement between theory and experiment.
Pauli spin blockade in quantum dot systems occurs when the charge transport is allowed only for some spin states, and it has been an efficient tool in spin-based qubit devices in semiconductors. We theoretically investigate a Pauli spin blockade in a triple quantum dot molecule consisting of three identical quantum dots in a semiconductor in the presence of an external magnetic field through the molecule. When the three-electron state is on resonance with two- or four-electron states, the Aharonov-Bohm oscillation and the Zeeman splitting lead to a periodic spin blockade effect. We focus on th…
We study the effects of cotunneling and a non-uniform 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 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 mech…
We present measurements on gate-defined double quantum dots in Ge-Si core-shell nanowires, which we tune to a regime with visible shell filling in both dots. We observe a Pauli spin blockade and can assign the measured leakage current at low magnetic fields to spin-flip cotunneling, for which we measure a strong anisotropy related to an anisotropic g-factor. At higher magnetic fields we see signatures for leakage current caused by spin-orbit coupling between (1,1)-singlet and (2,0)-triplet states. Taking into account these anisotropic spin-flip mechanisms, we can choose the magnetic field dire…
We investigate the influence of thermal energy on the current flow and electron spin states in double quantum dots in series. The quadruplet Pauli spin blockade, which is caused by the quadruplet and doublet states, occurs at low temperatures affecting the transport properties. As the temperature increases, the quadruplet Pauli spin blockade occurs as a result of the thermal energy, even in regions where it does not occur at low temperatures. This is because the triplet state is formed in one dot as a result of the gradual change of the Fermi distribution function of the electrodes with increa…
Self-sustained current oscillation observed in spin-blockaded double quantum dots is explained as a consequence of periodic motion of dynamically polarized nuclear spins (along a limit cycle) in the spin-blockaded regime under an external magnetic field and a spin-transfer torque. It is shown, based on the Landau-Lifshtz-Gilbert equation, that a sequence of semistable limit cycle, Hopf and homoclinic bifurcations occurs as the external field is tuned. The divergent period near the homoclinic bifurcation explains well why the period in the experiment is so long and varies by many orders of magn…
We propose a spin-sensitive scanning probe microscopy experiment on double quantum dots in Pauli blockade conditions. Electric spin resonance is induced by an AC voltage applied to the scanning gate which induces lifting of the Pauli blockade of the current. The stationary Hamiltonian eigenstates are used as a basis for description of the spin dynamics with the AC potential of the probe. For the two-electron system we evaluate the transitions rates from triplet $\mathrm{T}_+$ state to singlet $\mathrm{S}$ or triplet $\mathrm{T}_0$ states, i.e. to conditions in which the Pauli blockade of the c…
Quantum computation relies on accurate measurements of qubits not only for reading the output of the calculation, but also to perform error correction. Most proposed scalable silicon architectures utilize Pauli blockade of triplet states for spin-to-charge conversion. In recent experiments, there have been instances when instead of conventional triplet blockade readout, Pauli blockade is sustained only between parallel spin configurations, with $|T_0\rangle$ relaxing quickly to the singlet state and leaving $|T_+\rangle$ and $|T_-\rangle$ states blockaded -- which we call \textit{parity readou…
We study electron transport in a double quantum dot in the Pauli spin blockade regime, in the presence of strong spin-orbit coupling. The effect of spin-orbit coupling is incorporated into a modified interdot tunnel coupling. We elucidate the role of the external magnetic field, the nuclear fields in the dots, and spin relaxation. We find qualitative agreement with experimental observations, and we propose a way to extend the range of magnetic fields in which blockade can be observed.
In analogy to the Coulomb and the Pauli spin blockade, based on the electrostatic repulsion and the Pauli exclusion principle respectively, the concept of valley blockade in Silicon nanostructures is explored. The valley parity operator is defined. Valley blockade is determined by the parity conservation of valley composition eigenvectors in quantum transport. A Silicon quantum changeover switch based on a triple of donor quantum dots capable to separate electrons having opposite valley parity by virtue of the valley parity conservation is proposed. The quantum changeover switch represents a n…
Scanning-probe magnetometry is a valuable experimental tool to investigate magnetic phenomena at the micro- and nanoscale. We theoretically analyze the possibility of measuring magnetic fields via the electrical current flowing through quantum dots. We characterize the shot-noise-limited magnetic-field sensitivity of two devices: a single dot in the Coulomb blockade regime, and a double dot in the Pauli blockade regime. Constructing such magnetometers using carbon nanotube quantum dots would benefit from the large, strongly anisotropic and controllable g tensors, the low abundance of nuclear s…
We study spin correlation in a double quantum dot containing a few electrons in each dot (around 10). Clear current rectification with negative differential conductance is observed in the cotunneling regime, which is well explained by a Pauli spin blockade. The current feature is discussed in connection with exchange singlet-triplet splitting based on two simple models, one of which takes coherent interdot coupling and the other incoherent interdot coupling into account.
Pauli blockade mechanisms -- whereby carrier transport through quantum dots is blocked due to selection rules even when energetically allowed -- are a direct manifestation of the Pauli exclusion principle, as well as a key mechanism for manipulating and reading out spin qubits. Pauli spin blockade is well established for systems such as GaAs QDs, but is to be further explored for systems with additional degrees of freedom, such as the valley quantum numbers in carbon-based materials or silicon. Here we report experiments on coupled bilayer graphene double quantum dots, in which the spin and va…
We measure transport at finite bias through a double quantum dot formed by top-gates in an InAs nanowire. Pauli spin-bockade is confirmed with several electrons in the dot. This is expected due to the small exchange interactions in InAs and the large singlet-triplet splitting, which can be measured and tuned by a gate voltage.
Silicon quantum dots are attractive candidates for the development of scalable, spin-based qubits. Pauli spin blockade in double quantum dots provides an efficient, temperature independent mechanism for qubit readout. Here we report on transport experiments in double gate nanowire transistors issued from a CMOS process on 300 mm silicon-on-insulator wafers. At low temperature the devices behave as two few-electron quantum dots in series. We observe signatures of Pauli spin blockade with a singlet-triplet splitting ranging from 0.3 to 1.3 meV. Magneto-transport measurements show that transition…
Based on the spin-blockade model for organic magnetoresistance we present an analytic expression for the polaron-bipolaron transition rate, taking into account the effective nuclear fields on the sites. We reveal the physics producing qualitatively different magnetoconductance line shapes as well as the ultrasmall magnetic field effect, and we study the role of the ratio between the intersite hopping rate and the typical magnitude of the nuclear fields. Our findings are in agreement with recent experiments and numerical simulations.
We report on hole compact double quantum dots fabricated using conventional CMOS technology. We provide evidence of Pauli spin blockade in the few hole regime which is relevant to spin qubit implementations. A current dip is observed around zero magnetic field, in agreement with the expected behavior for the case of strong spin-orbit. We deduce an intradot spin relaxation rate $\approx$120\,kHz for the first holes, an important step towards a robust hole spin-orbit qubit.
We prepare a triple quantum dot with a separate contact lead to each dot to study Pauli spin blockade in the tunnel-coupled three dots in a row. We measure the tunneling current flowing between the center dot and either the left or right dot with the left and right leads as a common source and the center lead as a drain. In the biased stability diagram, we establish Pauli spin blockade in the respective neighboring dots, with features similarly obtained in double quantum dot systems. We further realize Pauli spin blockade with two different conditions by tuning the inter-dot coupling gates: st…
We investigate transient dynamic response of an Anderson impurity quantum dot to a family of ramp-up driving voltage applied to the single coupling lead. Transient current is calculated based on a hierarchical equations of motion formalism for open dissipative systems [J. Chem. Phys. 128, 234703 (2008)]. In the nonlinear response and nonadiabatic charging regime, characteristic resonance features of transient response current reveal distinctly and faithfully the energetic configuration of the quantum dot. We also discuss and comment on both the physical and numerical aspects of the theoretical…
Pauli spin blockade (PSB) is a significant physical effect in double quantum dot (DQD) systems. In this paper, we start from the fundamental quantum model of the DQD with the electron-electron interaction being considered, and then systematically study the PSB effect in DQD by using a recently developed non-perturbative method, the hierarchical equations of motion (HEOM) approach. The physical picture of the PSB is elucidated explicitly and the gate voltage manipulation is described minutely, which are both qualitatively consistent with the experimental measurements. When dotdot exchange inter…
We study the conductance spectrum of graphene quantum dots, both single and multiple cases. The single electron tunneling phenomenon is investigated and the periodicity, amplitude and line shape of the Coulomb blockade oscillations at low temperatures are obtained. Further, we discuss the transport behavior when multiple dots are assembled in array and find a phase transition of conductance spectra from individual Coulomb blockade to collective Coulomb blockade.
Double quantum dots are convenient solid-state platforms to encode quantum information. Two-electron spin states can be conveniently detected and manipulated using strong quantum selection rules based on the Pauli exclusion principle, leading to the well-know Pauli spin blockade of electron transport for triplet states. Coherent spin states would be optimally preserved in an environment free of nuclear spins, which is achievable in silicon by isotopic purification. Here we report on a deliberately engineered, gate-defined silicon metal-oxide-semiconductor double quantum dot system. The electro…
We present measurements of resonant tunneling through discrete energy levels of a silicon double quantum dot formed in a thin silicon-on-insulator layer. In the absence of piezoelectric phonon coupling, spontaneous phonon emission with deformation-potential coupling accounts for inelastic tunneling through the ground states of the two dots. Such transport measurements enable us to observe a Pauli spin blockade due to effective two-electron spin-triplet correlations, evident in a distinct bias-polarity dependence of resonant tunneling through the ground states. The blockade is lifted by the exc…
We detect in real time inter-dot 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 lifting of a Pauli spin blockade and the tunneling times ratio eta=T_b/T_d characterizes the blockade efficiency. We find pronounced changes in the behavior of eta upon increasing the magnetic field, with eta increasing, saturating and increasing again. We explain this behavior as due to the …
We demonstrate double quantum dots fabricated in undoped Si/SiGe heterostructures relying on a double top-gated design. Charge sensing shows that we can reliably deplete these devices to zero charge occupancy. Measurements and simulations confirm that the energetics are determined by the gate-induced electrostatic potentials. Pauli spin blockade has been observed via transport through the double dot in the two electron configuration, a critical step in performing coherent spin manipulations in Si.
We report Pauli spin blockade in an impurity defined carbon nanotube double quantum dot. We observe a pronounced current suppression for negative source-drain bias voltages which is investigated for both symmetric and asymmetric coupling of the quantum dots to the leads. The measured differential conductance agrees well with a theoretical model of a double quantum dot system in the spin-blockade regime which allows us to estimate the occupation probabilities of the relevant singlet and triplet states. This work shows that effective spin-to-charge conversion in nanotube quantum dots is feasible…
Spin-polarized transport of photo-electrons in bulk, p-type GaAs is investigated in the Pauli blockade regime. In contrast to usual spin diffusion processes in which the spin polarization decreases with distance traveled due to spin relaxation, images of the polarized photo-luminescence reveal a spin-filter effect in which the spin polarization increases during transport over the first 2 microns from 26 % to 38 %. This is shown to be a direct consequence of the Pauli Principle and the associated quantum degeneracy pressure which results in a spin-dependent increase in the minority carrier diff…
Pauli spin blockade (PSB) in double quantum dots (DQDs) has matured into a prime technique for precise measurements of nanoscale system parameters. In this work we demonstrate that systems with site-dependent g-tensors and spin-polarized leads allow for a complete characterization of the g-tensors in the dots by magnetotransport experiments alone. Additionally, we show that special polarization configurations can enhance the often elusive magnetotransport signal, rendering the proposed technique robust against noise in the system, and inducing a giant magnetoresistance effect. Finally, we inco…
We report the observation of a giant positive magnetoresistance in millimetre scale hydrogenated graphene with magnetic field oriented in the plane of the graphene sheet. A positive magnetoresistance in excess of 200\% at a temperature of 300 mK was observed in this configuration, reverting to negative magnetoresistance with the magnetic field oriented normal to the graphene plane. We attribute the observed positive, in-plane, magnetoresistance to Pauli-blockade of hopping conduction induced by spin polarization. Our work shows that spin polarization in concert with electron-electron interacti…
We present a theory of zero-bias anomalies and dephasing rates for a Coulomb-blockaded quantum dot, driven out of equilibrium by coupling to voltage biased source and drain leads. We interpret our results in terms of the statistics of voltage fluctuations in the system.
Motivated by a recent experiment [F. Pei et al., Nat. Nanotech. 7, 630 (2012)], we theoretically study the Pauli blockade transport effect in a double quantum dot embedded in a bent carbon nanotube. We establish a model for Pauli blockade, taking into account the strong g-factor anisotropy that is linked to the local orientation of the nanotube axis in each quantum dot. We provide a set of conditions under which our model is approximately mapped to the spin-blockade model of Jouravlev and Nazarov [O. N. Jouravlev and Y. V. Nazarov, Phys. Rev. Lett. 96, 176804 (2006)]. The results we obtain for…
Pauli blockade occurs when the excited electrons fill up the states near the conduction bands and block subsequent absorption in semiconductors, and has been widely applied in mode-locking for passively-pulsed-laser systems. In this letter, we report the first direct observation that the Pauli blockade is broken by ultrafast cooling of hot electrons in optically-pumped graphene. With femtosecond spectroscopy, we demonstrate that the time scale to excite an electron (~100 fs) is of the same order as that of the electron decay via electron-electron scattering, which allows the electron excitatio…
We theoretically investigate the quantum transport properties of a triangular triple quantum dot (TTQD) ring connected with two reservoirs by means of analytical derivation and accurate hierarchical-equations-of-motion calculation. A bias-induced chiral current in the absence of magnetic field is firstly demonstrated, which results from that the coupling between spin gauge field and spin current in the nonequilibrium TTQD induces a scalar spin chirality that lifts the chiral degeneracy and thus the time inversion symmetry. The chiral current is proved to oscillate with bias within the Coulomb …
We extend the theory of Coulomb blockade oscillations to quantum dots which are deformed by the confining potential. We show that shape deformations can generate sequences of conductance resonances which carry the same internal wavefunction. This fact may cause strong correlations of neighboring conductance peaks. We demonstrate the relevance of our results for the interpretation of recent experiments on semiconductor quantum dots.
We study the mechanism of nuclear spin relaxation in quantum dots due to the electron exchange with 2D gas. We show that the nuclear spin relaxation rate is dramatically affected by the Coulomb blockade and can be controlled by gate voltage. In the case of strong spin-orbit coupling the relaxation rate is maximal in the Coulomb blockade valleys whereas for the weak spin-orbit coupling the maximum of the nuclear spin relaxation rate is near the Coulomb blockade peaks.
Pauli exclusion principle can lead to a supression of transport through double quantum dots, even if both quantum dots are connected by a resonant driving ac field. In this work, we study how this effect, known as spin blockade, can be removed by means of the influence of the driving field on the contacts to the leads.
Recent experimental observations of current blockades in 2-D material quantum-dot platforms have opened new avenues for spin and valley-qubit processing. Motivated by experimental results, we construct a model capturing the delicate interplay of Coulomb interactions, inter-dot tunneling, Zeeman splittings, and intrinsic spin-orbit coupling in a double quantum dot structure to simulate the Pauli blockades. Analyzing the relevant Fock-subspaces of the generalized Hamiltonian, coupled with the density matrix master equation technique for transport across the setup, we identify the generic class o…
It is demonstrated that parallel weakly coupled quantum dots exhibit non-equilibrium blockade regimes caused by a full occupation in the spin triplet state, in analogy to the Pauli spin blockade in serially weakly coupled quantum dots. Charge tends to accumulate in the two-electron triplet for bias voltages that support transitions between the singlet and three-electron states.
We implement a technique for measuring the singlet-triplet energy splitting responsible for spin-to-charge conversion in semiconductor quantum dots. This method, which requires fast, single-shot charge measurement, reliably extracts an energy in the limits of both large and small splittings. We perform this technique on an undoped, accumulation-mode Si/SiGe triple-quantum dot and find that the measured splitting varies smoothly as a function of confinement gate biases. Not only does this demonstration prove the value of having an $in~situ$ excited-state measurement technique as part of a stand…
By using bosonization method and unitary transformation, we give a general relation between the dimensionless tunneling conductance and the fractional Coulomb blockade conductance peak splitting which is valid both for weak and strong transmission between two quantum dots, and show that the tunneling conductance has a linear temperature dependence in the low energy and low temperature limit.
The total spin of correlated electrons in a quantum dot changes with magnetic field and this effect is generally linked to the change in the total angular momentum from one magic number to another, which can be understood in terms of an `electron molecule' picture for strong fields. Here we propose to exploit this fact to realize a spin blockade, i.e., electrons are prohibited to tunnel at specific values of the magnetic field. The spin-blockade regions have been obtained by calculating both the ground and excited states. In double dots the spin-blockade condition is found to be less stringent…
Pauli-spin blockade (PSB) is a transport phenomenon in double quantum dots that allows for a type of spin to charge conversion often used to probe fundamental physics such as spin relaxation and singlet-triplet coupling. In this paper we theoretically explore Pauli-spin blockade as a function of magnetic field B applied parallel to the substrate. In the well-studied low magnetic field regime, where PSB occurs in the forward $(1,1)\rightarrow(0,2)$ tunneling direction, we highlight some aspects of PSB that are not discussed in detail in existing literature, including the change in size of both …
We derive closed expressions for the universal weak localization peak of the average conductance peak heights in Coulomb blockade quantum dots in the crossover from orthogonal to unitary symmetry. The scale for the crossover is independent of the number of channels in each lead, in contrast with the case of open dots. The functional form of the weak localization peak is independent of temperature. We also derive analytically the variance of the conductance peak heights as a function of the crossover parameter.
Manipulation and readout of spin qubits in quantum dots made in III-V materials successfully rely on Pauli blockade that forbids transitions between spin-triplet and spin-singlet states. Quantum dots in group IV materials have the advantage of avoiding decoherence from the hyperfine interaction by purifying them with only zero-spin nuclei. Complications of group IV materials arise from the valley degeneracies in the electronic bandstructure. These lead to complicated multiplet states even for two-electron quantum dots thereby significantly weakening the selection rules for Pauli blockade. Only…
We present Coulomb Blockade measurements of two few-electron quantum dots in series which are configured such that the electrochemical potential of one of the two dots is aligned with spin-selective leads. The charge transfer through the system requires co-tunneling through the second dot which is $not$ in resonance with the leads. The observed amplitude modulation of the resulting current is found to reflect spin blockade events occurring through either of the two dots. We also confirm that charge redistribution events occurring in the off-resonance dot are detected indirectly via changes in …
We demonstrate direct measurements of the spin-orbit interaction and Landé g factors in a semiconductor nanowire double quantum dot. The device is made from a single-crystal pure-phase InAs nanowire on top of an array of finger gates on a Si/SiO$_2$ substrate and the measurements are performed in the Pauli spin-blockade regime. It is found that the double quantum dot exhibits a large singlet-triplet energy splitting of $Δ_{ST}\sim 2.3$ meV, a strong spin-orbit interaction of $Δ_{SO}\sim 140$ $μ$eV, and a large and strongly level-dependent Landé g factor of $\sim 12.5$. These results imply that…
We analyze coherent spin phenomena in triple quantum dots in triangular configuration under crossed DC and AC magnetic fields. In particular, we discuss the interplay between Aharonov-Bohm current oscillations, coherent electron trapping and spin blockade under electron spin resonance conditions. We demonstrate that, for certain field frequencies, AC magnetic fields induce an antiresonant behavior in the current, allowing for both removal and restoration of entangled spin blockaded states by tuning the AC field frequency. Our theoretical predictions indicate how to manipulate spin qubits in a …
Signatures of "mesoscopic Coulomb blockade" are reported for quantum dots with one fully transmitting point-contact lead, T1 = 1, T2 << 1. Unlike Coulomb blockade (CB) in weak-tunneling devices (T1, T2 << 1), one-channel CB is a mesoscopic effect requiring quantum coherence. Several distinctive features of mesoscopic CB are observed, including a reduction in CB upon breaking time-reversal symmetry with a magnetic field, relatively large fluctuations of peak position as a function of magnetic field, and strong temperature dependence on the scale of the quantum level spacing.
We study the addition energy spectra of phosphorene quantum dots focusing on the role of dot size, edges passivation, number of layers and dielectric constant of the substrate where the dots are deposited. We show that for sufficiently low dielectric constants ($\varepsilon_{sub} < 4$), Coulomb blockade can be observed in dot sizes larger than 10 nm, for both passivated and unpassivated edges. For higher dielectric constants (up to $\varepsilon_{sub} = 30$), Coulomb blockade demands smaller dot sizes, but this depends whether the edges are passivated or not. This dramatic role played by the su…
We study conductance through a quantum dot under Coulomb blockade conditions in the presence of an external periodic perturbation. The stationary state is determined by the balance between the heating of the dot electrons by the perturbation and cooling by electron exchange with the cold contacts. We show that Coulomb blockade peak can have a peculiar shape if heating is affected by dynamic localization, which can be an experimental signature of this effect.
We study the effect of the exchange interaction on the Coulomb blockade peak height statistics in chaotic quantum dots. Because exchange reduces the level repulsion in the many body spectrum, it strongly affects the fluctuations of the peak conductance at finite temperature. We find that including exchange substantially improves the description of the experimental data. Moreover, it provides further evidence of the presence of high spin states (S>1) in such systems.
We find the leakage current through a double quantum dot in the Pauli spin blockade regime accounting for inelastic (spin-flip) cotunneling processes. Taking the energy-dependence of this spin-flip mechanism into account allows for an accurate description of the current as a function of applied magnetic fields, gate voltages, and an inter-dot tunnel coupling. In the presence of an additional local dephasing process or nonuniform magnetic field, we obtain a simple closed-form analytical expression for the leakage current giving the full dependence on an applied magnetic field and energy detunin…
