Transport through a quantum dot subject to spin and charge bias

Spin and charge transport through a quantum dot coupled to external nonmagnetic leads is analyzed theoretically in terms of the non-equilibrium Green function formalism based on the equation of motion method. The dot is assumed to be subject to spin and charge bias, and the considerations are focused on the Kondo effect in spin and charge transport. It is shown that the differential spin conductance as a function of spin bias reveals a typical zero-bias Kondo anomaly which becomes split when either magnetic field or charge bias are applied. Significantly different behavior is found for mixed charge/spin conductance. The influence of electron-phonon coupling in the dot on tunneling current as well as on both spin and charge conductance is also analyzed.     

Nonequilibrium Keldysh formalism for interacting leads—Application to quantum dot transport driven by spin bias

The conductance through a mesoscopic system of interacting electrons coupled to two adjacent leads is conventionally derived via the Keldysh nonequilibrium Green’s function technique, in the limit of noninteracting leads [Y. Meir, N.S. Wingreen, Phys. Rev. Lett. 68 (1992) 2512]. We extend the standard formalism to cater for a quantum dot system with Coulombic interactions between the quantum dot and the leads. The general current expression is obtained by considering the equation of motion of the time-ordered Green’s function of the system. The nonequilibrium effects of the interacting leads are then incorporated by determining the contour-ordered Green’s function over the Keldysh loop and applying Langreth’s theorem. The dot–lead interactions significantly increase the height of the Kondo peaks in density of states of the quantum dot. This translates into two Kondo peaks in the spin differential conductance when the magnitude of the spin bias equals that of the Zeeman splitting. There also exists a plateau in the charge differential conductance due to the combined effect of spin bias and the Zeeman splitting. The low-bias conductance plateau with sharp edges is also a characteristic of the Kondo effect. The conductance plateau disappears for the case of asymmetric dot–lead interaction.     

Large spin figure of merit in a double quantum dot coupled to noncollinear ferromagnetic electrodes

The spin thermoelectric effects are studied in a Rashba double quantum dot (QD) attached to ferromagnetic leads with noncollinear magnetic moments. The spin conductance G(s), spin thermopower S(s), electron thermal conductance κ(el) and spin thermoelectric figure of merit Z(s)T are calculated by using Green's function method. We find that the magnitude of the spin figure of merit can be remarkably enhanced by the coexistence of the Rashba spin-orbit interaction in the QDs and the leads' spin polarization, and can reach even as high as 3 by optimizing the parameters of the structure. The angle between the leads' magnetic moments can act as a powerful means to manipulate the properties of the spin figure of merit.     

Electrically tunable spin polarization in a carbon nanotube spin diode

We have studied the current through a carbon-nanotube quantum dot with one ferromagnetic and one normal-metal lead. For the values of gate voltage at which the normal lead is resonant with the single available nondegenerate energy level on the dot, we observe a pronounced decrease in the current for one bias direction. We show that this rectification is spin dependent, and that it stems from the interplay between the spin accumulation and the Coulomb blockade on the quantum dot. The degree of resulting spin polarization is fully and precisely tunable using the gate and bias voltages.     

Electronic spin precession and interferometry from spin-orbital entanglement in a double quantum dot

A double quantum dot inserted in parallel between two metallic leads can entangle the electron spin with the orbital (dot index) degree of freedom. An Aharonov-Bohm orbital phase can be transferred to the spinor wave function, providing a geometrical control of the spin precession around a fixed magnetic field. A fully coherent behavior occurs in a mixed orbital-spin Kondo regime. Evidence for the spin precession can be obtained, either using spin-polarized metallic leads or by placing the double dot in one branch of a metallic loop.     

Restoring coherence lost to a slow interacting mesoscopic spin bath

For a two-state quantum object interacting with a slow mesoscopic interacting spin bath, we show that a many-body solution of the bath dynamics conditioned on the quantum-object state leads to an efficient control scheme to recover the lost quantum-object coherence through disentanglement. We demonstrate the theory with the realistic problem of one electron spin in a bath of many interacting nuclear spins in a semiconductor quantum dot. The spin language can be easily generalized to a quantum object in contact with a bath of interacting multilevel quantum units with the caveat that the bath is mesoscopic and its dynamics is slow compared with the quantum object.     

Cotunneling current through a two-level quantum dot coupled to magnetic leads: the role of exchange interaction

The cotunneling current through a two-level quantum dot weakly coupled to ferromagnetic leads is studied in the Coulomb blockade regime. The cotunneling current is calculated analytically under simple but realistic assumptions as follows: (i)?the quantum dot is described by the universal Hamiltonian, (ii)?it is doubly occupied, and (iii)?it displays a fast spin relaxation. We find that the dependence of the differential conductance on the bias voltage is significantly affected by the exchange interaction on the quantum dot. In particular, for antiparallel magnetic configurations in the leads, the exchange interaction results in the appearance of interference-type contributions from the inelastic processes to the cotunneling current. Such dependence of the cotunneling current on the tunneling amplitude phases should also occur in multi-level quantum dots weakly coupled to ferromagnetic leads near the mesoscopic Stoner instabilities.     

Detection of single spin decoherence in a quantum dot via charge currents

We consider a quantum dot attached to leads in the Coulomb blockade regime that has a spin 1 / 2 ground state. We show that, by applying an ESR field to the dot spin, the stationary current in the sequential tunneling regime exhibits a new resonance peak whose linewidth is determined by the single spin decoherence time T2. The Rabi oscillations of the dot spin are shown to induce coherent current oscillations from which T2 can be deduced in the time domain. We describe a spin inverter which can be used to pump current through a double dot via spin flips generated by ESR.     

Quantum spin and charge pumping through double quantum dots with ferromagnetic leads

The pumping of electrons through double quantum dots (DQDs) attached to ferromagnetic leads have been theoretically investigated by using the nonequilibrium Green?s function method. It is found that an oscillating electric field applied to the quantum dot may give rise to the pumped charge and spin currents. In the case that both leads are ferromagnet, a pure spin current can be generated in the antiparallel magnetization configuration, where no net charge current exists. The possibility of manipulating the pumped spin current is explored by tuning the dot level and the ac field. By making use of various tunings, the magnitude and direction of the pumped spin current can be well controlled. For the case that only one lead is ferromagnetic, both of the charge and spin currents can be pumped and flow in opposite directions on the average. The control of the magnitude and direction of the pumped charge and spin currents is also discussed by means of the magnetic flux threading through the DQD ring.     

Transport properties of quantum dots

Linear and nonlinear transport through a quantum dot that is weakly coupled to ideal quantum leads is investigated in the parameter regime where charging and geometrical quantization effects coexist. The exact eigenstates and spins of a finite number of correlated electrons confined within the dot are combined with a rate equation. The current is calculated in the regime of sequential tunneling. The analytic solution for an Anderson impurity is given. The phenomenological charging model is compared with the quantum mechanical model for interacting electrons. The current-voltage characteristics show Coulomb blockade. The excited states lead to additional fine-structure in the current voltage characteristics. Asymmetry in the coupling between the quantum dot and the leads causes asymmetry in the conductance peaks which is reversed with the bias voltage. The spin selection rules can cause a ‘spin blockade’ which decreases the current when certain excited states become involved in the transport. In two-dimensional dots, peaks in the linear conductance can be suppressed at low temperatures, when the total spins of the corresponding ground states differ by more than 1/2. In a magnetic field, an electron number parity effect due to the different spins of the many-electron ground states is predicted in addition to the vanishing of the spin blockade effect. All of the predicted features are consistent with recent experiments.     

Spin polarized Kondo transport through a quantum dot connected to ferromagnetic leads

We study the spin dependent transport through a quantum dot connected to ferromagnetic leads. Using the non-equilibrium generalization of the non-crossing approximation for finite Coulomb repulsion U, we compute the spin polarized conductance, the local average occupancies and the local densities of states in the Kondo regime. We show that transport properties are strongly affected if we allow double occupancy by using a finite value for U. In the framework of our model, we have successfully reproduced the recent experimental finding of an electrically controlled magnetic moment on a carbon nanotube quantum dot coupled to ferromagnetic nickel leads [3]. Besides, in addition to the well known splitting of the Kondo peak in the density of states due to the presence of ferromagnetic leads, we find that the additional splitting due to non-zero bias voltage leads to an unexpected increase of the total conductance, which has also been observed by Hauptmann et al.     

Generating and reversing spin accumulation by temperature gradient in a quantum dot attached to ferromagnetic leads

We propose to generate and reverse the spin accumulation in a quantum dot (QD) by using the temperature difference between the two ferromagnetic leads connected to the dot. The electrons are driven purely by the temperature gradient in the absence of an electric bias and a magnetic field. In the Coulomb blockade regime, we find two ways to reverse the spin accumulation. One is by adjusting the QD energy level with a fixed temperature gradient, and the other is by reversing the temperature gradient direction for a fixed value of the dot level. The spin accumulation in the QD can be enhanced by the magnitudes of both the leads’ spin polarization and the asymmetry of the dot-lead coupling strengths. The present device is quite simple, and the obtained results may have practical usage in spintronics or quantum information processing.     

Spin-dependent transport through quantum dot with inelastic interactions

Using the Keldysh nonequilibrium Green function method, we theoretically investigate the electron transport properties of a quantum dot coupled to two ferromagnetic electrodes, with inelastic electron-phonon interaction and spin flip scattering present in the quantum dot. It is found that the electron-phonon interaction reduces the current, induces new satellite polaronic peaks in the differential conductance spectrum, and at the same time leads to oscillatory tunneling magnetoresistance effect. Spin flip scattering suppresses the zero-bias conductance peak and splits it into two, with different behaviors for parallel and anti-parallel magnetic configuration of the two electrodes. Consequently, a negative tunneling magnetoresistance effect may occur in the resonant tunneling region, with increasing spin flip scattering rate.     

Tunable spin current through a T-shaped double quantum dot molecule

We present a spin current generator based on a T-shaped double quantum dot (TDQD) molecule connected with two leads, and the coherent spin-flip effect is taken into account within the TDQD. The spin current from the right output terminal is obtained, more importantly, the properties of the spin current are investigated in detail, these results offer us a way to manipulate the spin current with the system parameters.     

Interplay of spin and charge channels in zero-dimensional systems

We study the interplay of charge and spin (zero-mode) channels in quantum dots. The latter affects the former in the form of a distinct signature on the differential conductance. We also obtain both longitudinal and transverse spin susceptibilities. All these observables, underlain by spin fluctuations, become accentuated as one approaches the Stoner instability. The nonperturbative effects of zero-mode interaction are described in terms of the propagation of gauge bosons associated with charge [U(1)] and spin [SU(2)] fluctuations in the dot, while transverse spin fluctuations are analyzed perturbatively.     

Spin filter,spin amplifier and spin diode in graphene nanodisk

Graphene nanodisk is a graphene derivative with a closed edge. The trigonal zigzag nanodisk with size N has N-fold degenerated zero-energy states. It can be interpreted as a quantum dot with an internal degree of freedom. The ground state of nanodisk is a quasi-ferromagnet, which is a ferromagnetic-like state with a finite but very long life time. We investigate spin-filter effects in the system made of nanodisks and leads. A novel feature of the nanodisk spin filter is that its spin can be controlled by the spin current. We propose some applications for spintronics, such as spin memory, spin amplifier and spin diode. It is argued that a spin current is reinforced (rectified) by feeding it into a nanodisk spin amplifier (diode). Graphene nanodisk would be a promising candidate of future electronic and spintronic nanodevices.     

Nearly noninvasive readout and manipulation of spin in double quantum dot using spin bias

Dynamics of two quantum dots coupled to electrodes with spin bias is investigated theoretically by means of the master equations. The two dots are coupled via exchange interaction. When the exchange interaction is much smaller than the lead-dot 2 coupling and dot 2 is under a symmetric spin bias, an initially fully polarized electron spin in dot 1 undergoes an oscillation with ignorable attenuation. Meanwhile, the direction of charge current flowing through dot 2 oscillates in the same period as that of the spin in dot 1. This allows to reverse or nearly noninvasively read out the spin in dot 1, by switching on and off the exchange interaction for a duration of half-integer or integer periods of the oscillation, respectively.     

Transport through artificial single-molecule magnets: Spin-pair state sequential tunneling and Kondo effects

The transport properties of an artificial single-molecule magnet based on a CdTe quantum dot doped with a single Mn+2 ion(S=5/2) are investigated by the non-equilibrium Green function method.We consider a minimal model where the Mn-hole exchange coupling is strongly anisotropic so that spin-flip is suppressed and the impurity spin S and a hole spin s entering the quantum dot are coupled into spin pair states with(2S+1) sublevels.In the sequential tunneling regime,the differential conductance exhibits(2S+1) possible peaks,corresponding to resonance tunneling via(2S+1) sublevels.At low temperature,Kondo physics dominates transport and(2S+1) Kondo peaks occur in the local density of states and conductance.These peaks originate from the spin-singlet state formed by the holes in the leads and on the dot via higher-order processes and are related to the parallel and antiparallel spin pair states.     

Generation and manipulation of spin current via a hybrid four-terminal single-molecule junction

We present a new device which consists of a molecular quantum dot (MQD) attached to a normal-metal, two ferromagnetic (FM), and a superconducting leads. The spin-related Andreev reflection (AR) current and the spin-dependent single-particle tunneling current through the normal-metal terminal are obtained, and it is found that the spin current exhibits the transistor-like behavior. The joint effects of the coherent spin flip and the angle between magnetic moments of the two FM leads on the spin current are also studied, these results provide the possibility to manipulate the spin current with the system parameters.     

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.