Spin and polarized current from Coulomb blockaded quantum dots

Spin-filtered measurements of Andreev bound states in semiconductor-superconductor nanowire devices

Semiconductor nanowires coupled to superconductors can host Andreev bound states with distinct spin and parity, including a spin-zero state with an even number of electrons and a spin-1/2 state with odd-parity. Considering the difference in spin of the even and odd states, spin-filtered measurements can reveal the underlying ground state. To directly measure the spin of single-electron excitations, we probe an Andreev bound state using a spin-polarized quantum dot that acts as a bipolar spin filter, in combination with a non-polarized tunnel junction in a three-terminal circuit. We observe a spin-polarized excitation spectrum of the Andreev bound state, which can be fully spin-polarized, despite strong spin-orbit interaction in the InSb nanowires. Decoupling the hybrid from the normal lead causes a current blockade, by trapping the Andreev bound state in an excited state. Spin-polarized spectroscopy of hybrid nanowire devices, as demonstrated here, is proposed as an experimental tool to support the observation of topological superconductivity.

Influence of temperature on the magnetic oscillations in graphene with spin splitting: a new approach

We analyze the magnetic oscillations (MO) due to the de Haas-van Alphen effect, in pristine graphene under a perpendicular magnetic field, taking into account the Zeeman effect. We consider a constant Fermi energy, such that the valence band is always full and only the conduction band is available. At zero temperature the MO consist of two sawtooth peaks, one for each spin. Both peaks have the same frequency, but different amplitude and phase. We show that, in order to observe the spin splitting in the MO, Fermi energy of about 0.1 eV is required. At low temperatures we obtain that the MO can be expressed as the MO at zero temperature, plus small Fermi-Dirac like functions, each centered around the MO peaks. Using this expression, we show that the spin splitting is observable in the MO only when the thermal energy is smaller than the Zeeman energy. We also analyze the shift of the MO extrema as the temperature increases. We show that it depends on the magnetic field, which implies a broken periodicity at nonzero temperature. Finally, we obtain an analytical expression for the MO envelope. The results obtained could be used to infer temperature changes from the MO extrema shift and vice versa.

Measuring the Degeneracy of Discrete Energy Levels Using a GaAs/AlGaAs Quantum Dot

We demonstrate an experimental method for measuring quantum state degeneracies in bound state energy spectra. The technique is based on the general principle of detailed balance and the ability to perform precise and efficient measurements of energy-dependent tunneling-in and -out rates from a reservoir. The method is realized using a GaAs/AlGaAs quantum dot allowing for the detection of time-resolved single-electron tunneling with a precision enhanced by a feedback control. It is thoroughly tested by tuning orbital and spin degeneracies with electric and magnetic fields. The technique also lends itself to studying the connection between the ground-state degeneracy and the lifetime of the excited states.

Single-electron Spin Resonance in a Quadruple Quantum Dot

Electron spins in semiconductor quantum dots are good candidates of quantum bits for quantum information processing. Basic operations of the qubit have been realized in recent years: initialization, manipulation of single spins, two qubit entanglement operations, and readout. Now it becomes crucial to demonstrate scalability of this architecture by conducting spin operations on a scaled up system. Here, we demonstrate single-electron spin resonance in a quadruple quantum dot. A few-electron quadruple quantum dot is formed within a magnetic field gradient created by a micro-magnet. We oscillate the wave functions of the electrons in the quantum dots by applying microwave voltages and this induces electron spin resonance. The resonance energies of the four quantum dots are slightly different because of the stray field created by the micro-magnet and therefore frequency-resolved addressable control of each electron spin resonance is possible.

Pseudospin-resolved transport spectroscopy of the Kondo effect in a double quantum dot

We report measurements of the Kondo effect in a double quantum dot, where the orbital states act as pseudospin states whose degeneracy contributes to Kondo screening. Standard transport spectroscopy as a function of the bias voltage on both dots shows a zero-bias peak in conductance, analogous to that observed for spin Kondo in single dots. Breaking the orbital degeneracy splits the Kondo resonance in the tunneling density of states above and below the Fermi energy of the leads, with the resonances having different pseudospin character. Using pseudospin-resolved spectroscopy, we demonstrate the pseudospin character by observing a Kondo peak at only one sign of the bias voltage. We show that even when the pseudospin states have very different tunnel rates to the leads, a Kondo temperature can be consistently defined for the double quantum dot system.

Transport through graphene quantum dots

We review transport experiments on graphene quantum dots and narrow graphene constrictions. In a quantum dot, electrons are confined in all lateral dimensions, offering the possibility for detailed investigation and controlled manipulation of individual quantum systems. The recently isolated two-dimensional carbon allotrope graphene is an interesting host to study quantum phenomena, due to its novel electronic properties and the expected weak interaction of the electron spin with the material. Graphene quantum dots are fabricated by etching mono-layer flakes into small islands (diameter 60-350 nm) with narrow connections to contacts (width 20-75 nm), serving as tunneling barriers for transport spectroscopy. Electron confinement in graphene quantum dots is observed by measuring Coulomb blockade and transport through excited states, a manifestation of quantum confinement. Measurements in a magnetic field perpendicular to the sample plane allowed to identify the regime with only a few charge carriers in the dot (electron-hole transition), and the crossover to the formation of the graphene specific zero-energy Landau level at high fields. After rotation of the sample into parallel magnetic field orientation, Zeeman spin splitting with a g-factor of g ≈ 2 is measured. The filling sequence of subsequent spin states is similar to what was found in GaAs and related to the non-negligible influence of exchange interactions among the electrons.

Mesoscopic stoner instability in metallic nanoparticles revealed by shot noise

We study sequential tunneling through a metallic nanoparticle close to the Stoner instability coupled to parallel magnetized electrodes. Increasing the bias voltage successively opens transport channels associated with excitations of the nanoparticle's total spin. For the current this leads just to a steplike increase. The Fano factor, in contrast, shows oscillations between large super-Poissonian and sub-Poissonian values as a function of bias voltage. We explain the enhanced Fano factor in terms of generalized random-telegraph noise and propose the shot noise as a convenient tool to probe the mesoscopic Stoner instability.

Single-shot correlations and two-qubit gate of solid-state spins

Measurement of coupled quantum systems plays a central role in quantum information processing. We have realized independent single-shot read-out of two electron spins in a double quantum dot. The read-out method is all-electrical, cross-talk between the two measurements is negligible, and read-out fidelities are ~86% on average. This allows us to directly probe the anticorrelations between two spins prepared in a singlet state and to demonstrate the operation of the two-qubit exchange gate on a complete set of basis states. The results provide a possible route to the realization and efficient characterization of multiqubit quantum circuits based on single quantum dot spins.

Coplanar stripline antenna design for optically detected magnetic resonance on semiconductor quantum dots

We report on the development and testing of a coplanar stripline antenna that is designed for integration in a magneto-photoluminescence experiment to allow coherent control of individual electron spins confined in single self-assembled semiconductor quantum dots. We discuss the design criteria for such a structure which is multi-functional in the sense that it serves not only as microwave delivery but also as electrical top gate and shadow mask for the single quantum dot spectroscopy. We present test measurements on hydrogenated amorphous silicon, demonstrating electrically detected magnetic resonance using the in-plane component of the oscillating magnetic field created by the coplanar stripline antenna necessary due to the particular geometry of the quantum dot spectroscopy. From reference measurements using a commercial electron spin resonance setup in combination with finite element calculations simulating the field distribution in the structure, we obtain a magnetic field of 0.12 mT at the position where the quantum dots would be integrated into the device. The corresponding π-pulse time of ≈0.5 μs meets the requirements set by the high sensitivity optical spin read-out scheme developed for the quantum dot.

Spin-to-charge conversion of mesoscopic spin currents

Recent theoretical investigations have shown that spin currents can be generated by passing electric currents through spin-orbit coupled mesoscopic systems. Measuring these spin currents has, however, not been achieved to date. We show how mesoscopic spin currents in lateral heterostructures can be measured with a single-channel voltage probe. In the presence of a spin current, the charge current I(qpc) through the quantum point contact connecting the probe is odd in an externally applied Zeeman field B, while it is even in the absence of spin current. Furthermore, the zero-field derivative ∂(B)I(qpc) is proportional to the magnitude of the spin current, with a proportionality coefficient that can be determined in an independent measurement. We confirm these findings numerically.

Linear response spin admittance of a quantum dot subject to a spin bias

We compute the linear response spin admittance of a non-equilibrium quantum dot subject to a spin bias and an ac charge bias with small amplitude. As a function of the position of the resonant level (i.e. the gate voltage) the spin admittance shows a set of two peaks around the gate voltage at which the resonant or the upper level of the dot is in the vicinity of the equilibrium Fermi level in the leads. The peak heights can be related to the average number of quantum dot electrons. The frequency dependence of the spin admittance shows features resulting from the photon-assisted tunneling through the dot.

Resonant tunnelling features in quantum dots

We present a systematic review of features due to resonant electron tunnelling, observable in transport spectroscopy experiments on quantum dots and single donors. The review covers features attributable to intrinsic properties of the dot (orbital, spin and valley states) as well as extrinsic effects (phonon/photon emission/absorption, features in the charge reservoirs, coupling to nearby charge centres). We focus on the most common operating conditions, neglecting effects due to strong coupling to the leads. By discussing the experimental signatures of each type of feature, we aim at providing practical methods to distinguish between their different physical origins. The correct classification of the resonant tunnelling features is an essential requirement to understand the details of the confining potential or to predict the performance of the dot for quantum information processing.

Interacting quantum dot coupled to a kondo spin: a universal Hamiltonian study

We study a Kondo spin coupled to a mesoscopic interacting quantum dot that is described by the "universal Hamiltonian." The problem is solved numerically by diagonalizing the system Hamiltonian in a good-spin basis and analytically in the weak and strong Kondo coupling limits. The ferromagnetic exchange interaction within the dot leads to a stepwise increase of the ground-state spin (Stoner staircase), which is modified nontrivially by the Kondo interaction. We find that the spin-transition steps move to lower values of the exchange coupling for weak Kondo interaction, but shift back up for sufficiently strong Kondo coupling. The interplay between Kondo and ferromagnetic exchange correlations can be probed with experimentally tunable parameters.

Driven coherent oscillations of a single electron spin in a quantum dot

The ability to control the quantum state of a single electron spin in a quantum dot is at the heart of recent developments towards a scalable spin-based quantum computer. In combination with the recently demonstrated controlled exchange gate between two neighbouring spins, driven coherent single spin rotations would permit universal quantum operations. Here, we report the experimental realization of single electron spin rotations in a double quantum dot. First, we apply a continuous-wave oscillating magnetic field, generated on-chip, and observe electron spin resonance in spin-dependent transport measurements through the two dots. Next, we coherently control the quantum state of the electron spin by applying short bursts of the oscillating magnetic field and observe about eight oscillations of the spin state (so-called Rabi oscillations) during a microsecond burst. These results demonstrate the feasibility of operating single-electron spins in a quantum dot as quantum bits.

Detecting entanglement using a double-quantum-dot turnstile

We propose a scheme based on using the singlet ground state of an electron spin pair in a double-quantum-dot nanostructure as a suitable setup for detecting entanglement between electron spins via the measurement of an optimal entanglement witness. Using time-dependent gate voltages and magnetic fields the entangled spins are separated and coherently rotated in the quantum dots and subsequently detected at spin-polarized quantum point contacts. We analyze the coherent time evolution of the entangled pair and show that by counting coincidences in the four exits an entanglement test can be done. This setup is close to present-day experimental possibilities and can be used to produce pairs of entangled electrons "on demand."

Interplay between the mesoscopic Stoner and Kondo effects in quantum dots

We consider electrons confined to a quantum dot interacting antiferromagnetically with a spin-1 / 2 Kondo impurity. The electrons also interact among themselves ferromagnetically with a dimensionless coupling J , where J =1 denotes the bulk Stoner transition. We show that as J approaches 1 there is a regime with enhanced Kondo correlations, followed by one where the Kondo effect is destroyed and impurity is spin polarized opposite to the dot electrons. The most striking signature of the first, Stoner-enhanced Kondo regime is that a Zeeman field increases the Kondo scale, in contrast to the case for noninteracting dot electrons. Implications for experiments are discussed.

Imaging a single-electron quantum dot

Images of a single-electron quantum dot were obtained in the Coulomb blockade regime at liquid He temperatures using a cooled scanning probe microscope (SPM). The charged SPM tip shifts the lowest energy level in the dot and creates a ring in the image corresponding to a peak in the Coulomb-blockade conductance. Fits to the line shape of the ring determine the tip-induced shift of the energy of the electron state in the dot. SPM manipulation of electrons in quantum dots promises to be useful in understanding, building, and manipulating circuits for quantum information processing.

Tuning the nonlocal spin-spin interaction between quantum dots with a magnetic field

We describe a device where the nonlocal spin-spin interaction between quantum dots (QDs) can be turned on and off with a small magnetic field. The setup consists of two QDs at the edge of two two-dimensional electron gases (2DEGs). The QDs' spins are coupled through a RKKY-like interaction mediated by the electrons in the 2DEGs. A magnetic field B(z) perpendicular to the plane of the 2DEG is used as a tuning parameter. When the cyclotron radius is commensurate with the interdot distance, the spin-spin interaction is amplified by a few orders of magnitude. The sign of the interaction is controlled by finely tuning B(z). Our setup allows for several dots to be coupled in a linear arrangement and it is not restricted to nearest-neighbor interaction.

Cotunneling spectroscopy in few-electron quantum dots

Few-electron quantum dots are investigated in the regime of strong tunneling to the leads. Inelastic cotunneling is used to measure the two-electron singlet-triplet splitting above and below a magnetic field driven singlet-triplet transition. Evidence for a nonequilibrium two-electron singlet-triplet Kondo effect is presented. Cotunneling allows orbital correlations and parameters characterizing entanglement of the two-electron singlet ground state to be extracted from dc transport.

Measurements of Kondo and spin splitting in single-electron transistors

We measure the spin splitting in a magnetic field B of localized states in single-electron transistors using a new method, inelastic spin-flip cotunneling. Because it involves only internal excitations, this technique gives the most precise value of the Zeeman energy Delta=/g/mu(B)B. In the same devices we also measure the splitting with B of the Kondo peak in differential conductance. The Kondo splitting appears only above a threshold field as predicted by theory. However, the magnitude of the Kondo splitting at high fields exceeds 2/g/mu(B)B in disagreement with theory.

Zeeman energy and spin relaxation in a one-electron quantum dot

We have measured the relaxation time, T1, of the spin of a single electron confined in a semiconductor quantum dot (a proposed quantum bit). In a magnetic field, applied parallel to the two-dimensional electron gas in which the quantum dot is defined, Zeeman splitting of the orbital states is directly observed by measurements of electron transport through the dot. By applying short voltage pulses, we can populate the excited spin state with one electron and monitor relaxation of the spin. We find a lower bound on T1 of 50 micros at 7.5 T, only limited by our signal-to-noise ratio. A continuous measurement of the charge on the dot has no observable effect on the spin relaxation.

Spin current through a quantum dot in the presence of an oscillating magnetic field

Nonequilibrium spin transport through an interacting quantum dot is analyzed. The coherent spin oscillations in the dot provide a generating source for spin current. In the interacting regime, the Kondo effect is influenced in a significant way by the presence of the processing magnetic field. In particular, when the precession frequency is tuned to resonance between spin-up and spin-down states of the dot, Kondo singularity for each spin splits into a superposition of two resonance peaks. The Kondo-type cotunneling contribution is manifested by a large enhancement of the pumped spin current in the strong coupling low temperature regime.