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 current is lifted. The rates of the spin-flip transitions are consistent with the transition matrix elements and strongly dependent on the tip position. Probing the spin densities and identification of the final transition state are discussed.
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…
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.
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…
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…
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.
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.
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…
We investigate the two-terminal nonlinear conductance of a Coulomb-blockaded quantum dot attached to chiral edge states. Reversal of the applied magnetic field inverts the system chirality and leads to a different polarization charge. As a result, the current--voltage characteristic is not an even function of the magnetic field. We show that the corresponding magnetic-field asymmetry arises from single-charge effects and vanishes in the limit of high temperature.
We present transport measurements on a lateral double dot produced by combining local anodic oxidation and electron beam lithography. We investigate the tunability of our device and demonstrate, that we can switch between capacitive and tunnel coupling. In the regime of capacitive coupling we observe the phenomenon of spin blockade in a magnetic field and analyze the influence of capacitive interdot coupling on this effect.
We obtain analytic formulae for the spacing between conductance peaks in the Coulomb blockade regime, based on the universal Hamiltonian model of quantum dots. New random matrix theory results are developed in order to treat correlations between two and three consecutive spacings in the energy level spectrum. These are generalizations of the Wigner surmise for the probability distribution of single level spacing. The analytic formulae are shown to be in good agreement with numerical evaluation.
We show that the low temperature electron transport properties of chemically functionalized graphene can be explained as sequential tunneling of charges through a two dimensional array of graphene quantum dots (GQD). Below 15 K, a total suppression of current due to Coulomb blockade through GQD array was observed. Temperature dependent current-gate voltage characteristics show Coulomb oscillations with energy scales of 6.2-10 meV corresponding to GQD sizes of 5-8 nm while resistance data exhibit an Efros-Shklovskii variable range hopping arising from structural and size induced disorder.
We report measurements of spin transitions for GaAs quantum dots in the Coulomb blockade regime, and compare ground and excited state transport spectroscopy to direct measurements of the spin polarization of emitted current. Transport spectroscopy reveals both spin-increasing and spin-decreasing transitions as well as higher-spin ground states, and allows g-factors to be measured down to a single electron. The spin of emitted current in the Coulomb blockade regime, measured using spin-sensitive electron focusing, is found to be polarized along the direction of the applied magnetic field regard…
We report measurements of mesoscopic fluctuations of elastic cotunneling in Coulomb blockaded quantum dots. Unlike resonant tunneling on Coulomb peaks, cotunneling in the valleys is sensitive to charging effects. We observe a larger magnetic field scale for the cotunneling (valley) fluctuations compared to the peaks, as well as an absence of "weak localization" (reduced conductance at B = 0) in valleys. Cotunneling fluctuations remain correlated over several valleys while peak conductance correlations decreases quickly.
Charge localization seems unlikely to occur in two vertically coupled symmetric quantum dots even if a small bias voltage breaks the exact isospin-symmetry of the system. However for a three-electron double quantum dot we find a strong localization of charges at certain vertically applied magnetic fields. The charge localization is directly connected to new ground state transitions between eigenstates differing only in parity. The transitions are driven by magnetic field dependent Coulomb correlations between the electrons and give rise to strong isospin blockade signatures in transport throug…
We study the spectrum and the transport properties of two identical, vertically coupled quantum dots in a perpendicular magnetic field. We find correlation-induced energy crossings in a magnetic field sweep between states differing only in the vertical degree of freedom. Considering the influence of a slight asymmetry between the dots caused by the applied source-drain voltage in vertical transport experiments these crossings convert to anticrossings accompanied by the build-up of charge polarization which is tunable by the perpendicular magnetic field. The polarization strongly affects the ve…
Hyperfine interaction (HFI) in carbon nanotube and graphene quantum dots is due to the presence of 13C atoms. We theoretically show that in these structures the short-range nature of the HFI gives rise to a coupling between the valley degree of freedom of the electron and the nuclear spin, in addition to the usual electron spin-nuclear spin coupling. We predict that this property of the HFI affects the Pauli blockade transport in carbon-based double quantum dots. In particular, we show that transport is blocked only if both the spin and the valley degeneracies of the quantum dot levels are lif…
Electric dipole spin resonance (EDSR) is a commonly used tool for manipulation and spectroscopy of quantum-dot-based spin qubits. When an EDSR experiment is embedded in a transport setup and Pauli spin blockade is used as means for spin-state read-out, then measured resonant responses in the leakage current indeed carry information about the level structure of the system under study. However, the actual line shape of these current resonances differs substantially from experiment to experiment, varying from being symmetric to asymmetric and from being a peak to a dip, a thorough understanding o…
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. We analyze two cooling mechanisms: electron exchange with the cold contacts and emission of phonons. Together with the usual linear Ohmic heating of the dot electrons we consider possible effects of dynamic localization. The combination of the abovementioned factors may result in a drastic change of the shape of the Coulomb blockade peak with …
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…
A complete numerical description of the charge and spin dynamics of a two-electron system confined in narrow nanowire quantum dots under oscillating electric field is presented in the context of recent electric dipole spin resonance experiments. We find that the spin-orbit coupling results in lifting the spin blockade by phonon mediated relaxation provided that the initially occupied state is close in energy to the ground state. This leads to suppression of the blockade from the triplet state with spins polarized parallel to the external magnetic field B. At higher B, after singlet-triplet gro…
Quantum fluctuations of Coulomb blockade are investigated as a function of the coupling to reservoirs in semiconductor quantum dots. We use fluctuations in the distance between peaks $ΔN$ apart to characterize both the amplitude and correlation of peak motion. For strong coupling, peak motion is greatly enhanced at low temperature, but does not show an increase in peak-to-peak correlation. These effects can lead to anomalous temperature dependence in the Coulomb valleys, similar to behavior ascribed to Kondo physics.
We present a theoretical study of the Pauli or spin-valley blockade for double quantum dots in semiconducting carbon nanotubes. In our model we take into account the following characteristic features of carbon nanotubes: (i) fourfold (spin and valley) degeneracy of the quantum dot levels, (ii) the intrinsic spin-orbit interaction which is enhanced by the tube curvature, and (iii) valley-mixing due to short-range disorder, i.e., substitutional atoms, adatoms, etc. We find that the spin-valley blockade can be lifted in the presence of short-range disorder, which induces two independent random (i…
We investigate quantum dots in semiconductor PbTe nanowire devices. Due to the accessibility of ambipolar transport in PbTe, quantum dots can be occupied both with electrons and holes. Owing to a very large dielectric constant in PbTe of order 1000, we do not observe Coulomb blockade which typically obfuscates the orbital and spin spectra. We extract large and highly anisotropic effective Lande g-factors, in the range 20-44. The absence of Coulomb blockade allows direct readout, at zero source-drain bias, of spin-orbit hybridization energies of up to 600 microelectronvolt. These spin propertie…
