Yuli V. Nazarov

Spin relaxation in semiconductor quantum dots

Quantum dots ~QD’s ! are small conductive regions in semiconductor structures that contain a tunable number of carriers. The shape and size of quantum dots can be controlled by the gate voltage. The localized electronic states in QD’s can be significantly modified by a magnetic field. All this provides a valuable opportunity to study the properties of the electron quantum states in detail and manipulate the electrons in these artificial atoms in a controllable way ~see Refs. 1 and 2 for review!. The spin states in quantum dots are considered to be promising for physical realization of the quantum computation algorithm. 3 Quantum computation requires coherent coupling between the dots, the coherence to be preserved on sufficiently long time scales. That makes it relevant to provide a complete theoretical estimation of the typical spin dephasing time of the electron in the QD. Transport experiments with QD’s have revealed that the current through a quantum dot can be influenced by the spin effects. 4 It opens up a possibility to estimate spin relaxation rates by means of transport measurement. 5 The origin of this effect is that the spin-flip process can provide a bottleneck for the energy relaxation in the dot, i.e., for transitions between the excited and ground states. Indeed, in the absence of the spin flip the total spin of the dot is a good quantum number and no transition is allowed between the states of different total spins. To illustrate, let us consider a QD with two electrons which can be placed in two levels. The ground state corresponds to two electrons in the lowest level having opposite spins ( S 50). One of the excited states corresponds to two electrons in different levels having the same spin direction ( S51). Due to the Pauli principle, the electron in the upper level cannot get to the lower level without changing its spin. Therefore, the relaxation to the ground state of the dot has to be accompanied by a spin flip. In contrast to the situation in two-dimensional ~2D! electron gas the electrons confined in the dot experience no electron-electron scattering ~see Ref. 6!. The only source of dissipation is the interaction with phonons. Moreover, although the electron-electron interaction is quite important in determining the energies of the states and the number of electrons in the dot, it is less important for the structure of the wave functions. To calculate the matrix elements, we approximate the many-electron wave functions by the Slater determinants. In this way, we can treat the spin-flip processes within the one-electron approach. The electron-electron interaction can change only the numerical factors in our results. Since most controllable QD’s are made on the basis of 2D electron gas GaAs heterostructures with the @100# growth direction, we concentrate on the spin-flip mechanisms that are relevant for GaAs, and for this confinement direction. Such mechanisms are very specific for AIIIBV compounds. The unit cell has no inversion symmetry, which gives rise to a strong spin-orbit splitting in the electron spectrum. The splitting is known 7,8 to be the main source of the spin-flip both in the 3D and 2D cases. Besides, the piezoelectric effect provides a strong coupling of electrons to the acoustic phonons. Such coupling may be important for the inelastic relaxation in the GaAs crystal both with and without a spinflip.

Spin-flip transitions between Zeeman sublevels in semiconductor quantum dots

We have studied spin-flip transitions between Zeeman sublevels in GaAs electron quantum dots. Several different mechanisms which originate from spin-orbit coupling are shown to be responsible for such processes. It is shown that spin-lattice relaxation for the electron localized in a quantum dot is much less effective than for the free electron. The spin-flip rates due to several other mechanisms not related to the spin-orbit interaction are also estimated.

Supercurrent reversal in quantum dots

When two superconductors are electrically connected by a weak link—such as a tunnel barrier—a zero-resistance supercurrent can flow. This supercurrent is carried by Cooper pairs of electrons with a combined charge of twice the elementary charge, e. The 2e charge quantum is clearly visible in the height of voltage steps in Josephson junctions under microwave irradiation, and in the magnetic flux periodicity of h/2e (where h is Plancks constant) in superconducting quantum interference devices. Here we study supercurrents through a quantum dot created in a semiconductor nanowire by local electrostatic gating. Owing to strong Coulomb interaction, electrons only tunnel one-by-one through the discrete energy levels of the quantum dot. This nevertheless can yield a supercurrent when subsequent tunnel events are coherent. These quantum coherent tunnelling processes can result in either a positive or a negative supercurrent, that is, in a normal or a π-junction, respectively. We demonstrate that the supercurrent reverses sign by adding a single electron spin to the quantum dot. When excited states of the quantum dot are involved in transport, the supercurrent sign also depends on the character of the orbital wavefunctions.

Novel circuit theory of Andreev reflection

We review here a novel circuit theory of superconductivity. The existing circuit theory of Andreev reflection has been revised to account for decoherence between electrons and holes and the twofold nature of the distribution function. The description of arbitrary connectors has been elaborated on. In this way one can cope with most of the factors that limited the applicability of the old circuit theory. We give a simple example and discuss numerical implementation of the theory.

Diffusive Conductors as Andreev Interferometers

We present a novel mechanism of phase-dependent electric transport in diffusive normal metal-superconductor structures. We provide a detailed theoretical and numerical analysis of recent unexplained experiments essentially explaining them.

Nucleus-mediated spin-flip transitions in GaAs quantum dots

Spin-flip rates in GaAs quantum dots can be quite slow, thus opening up the possibilities to manipulate spin states in the dots. We present here estimations of inelastic spin-flip rates mediated by hyperfine interaction with nuclei. Under general assumptions the nucleus-mediated rate is proportional to the phonon relaxation rate for the corresponding non-spin-flip transitions. The rate can be accelerated in the vicinity of a singlet-triplet excited state crossing. The small proportionality coefficient depends inversely on the number of nuclei in the quantum dot. We compare our results with known mechanisms of spin-flip in GaAs quantum dots.

Enhancement of kondo effect in quantum dots with an even number of electrons

We investigate the Kondo effect in a quantum dot with almost degenerate spin-singlet and triplet states for an even number of electrons. We show that the Kondo temperature as a function of the energy difference between the states Delta reaches its maximum around Delta = 0 and decreases with increasing Delta. The Kondo effect is thus enhanced by competition between singlet and triplet states. Our results explain recent experimental findings. We evaluate the linear conductance in the perturbative regime.

Coulomb blockade without tunnel junctions

Tunnel junctions are not needed to provide single electron effects in a metallic island. Eventually the tunnel junction may be replaced by an arbitrary scatterer. To formulate this in exact terms, we derive and analyze the effective action that describes an arbitrary scatterer. It is important that even a diffusive scatterer provides a sufficient isolation for single electron effects to persist. We also consider the fluctuations of the effective charging energy.

Locking electron spins into magnetic resonance by electron–nuclear feedback

When electrons are transported through a semiconductor quantum dot, they interact with nuclear spin in the host material. This interaction—often considered to be a nuisance—is now shown to provide a feedback mechanism that actively pulls the electron-spin Larmor frequency into resonance with that of an external microwave driving field.

Full Current Statistics in Diffusive Normal-Superconductor Structures

We study the current statistics in normal diffusive conductors in contact with a superconductor. Using an extension of the Keldysh Greens function method we are able to find the full distribution of charge transfers for all temperatures and voltages. For the non-Gaussian regime, we show that the equilibrium current fluctuations are enhanced by the presence of the superconductor. We predict an enhancement of the nonequilibrium current noise for temperatures below and voltages of the order of the Thouless energy E(Th) = D/L(2). Our calculation fully accounts for the proximity effect in the normal metal and agrees with experimental data.