Session D12: Focus Session: Spin Dynamics and Magnetism in Quantum Dots

Trion spectroscopy and electrical control of a Single Mn Atom in a Quantum Dot

I present a microscopic theory for the photoluminescence (PL) of a single self-assembled CdTe quantum dot doped with a single Mn atom. The few-body problem of electrons and holes exchange-coupled to the Mn spin is diagonalized exactly. The model permits a complete understanding of the non-trivial 11 peak spectra reported recently [1] in terms of charge-dependent effective Hamiltonian for the Mn spin. Whereas in the neutral configuration the Mn in the quantum dot is paramagnetic, the electron-doped dot spin states are spin rotationally invariant and the hole-doped dot spins states are quantized along the growth direction. Preliminary results of the time resolved response of the Mn spin to suitably engineered laser pulses will be discussed, both for the case of charged [1] and neutral dots[2,3].\\ \\ $[1]$ Y. L\'eger, L. Besombes, J. Fern\`andez-Rossier, L. Maingault, and H. Mariette Phys. Rev. Lett. {\bf 97}, 107401 (2006) \\ $[2]$ J. Fern\'andez-Rossier Phys. Rev. B {\bf 73}, 045301 (2006)\\ $[3]$ A. O. Govorov and A. V. Kalameitsev, Phys. Rev. B {\bf 71}, 035338 (2005)   

Tailoring Magnetism in Quantum Dots

We study magnetism in magnetically doped quantum dots as a function of particle numbers, temperature, confining potential, and the strength of Coulomb interaction screening. We show that magnetism can be tailored by controlling the electron-electron Coulomb interaction, even without changing the number of particles. The interplay of strong Coulomb interactions and quantum confinement leads to enhanced inhomogeneous magnetization which persists at substantially higher temperatures than in the non-interacting case or in the bulk-like dilute magnetic semiconductors. We predict a series of electronic spin transitions which arise from the competition between the many-body gap and magnetic thermal fluctuations. Cond-mat/0612489. \newline [1] R. Abolfath, P. Hawrylak, I. \v{Z}uti\'c, preprint.   

The influence of quantum confinement on magnetism in quantum dots.

Owing to its simplicity, the vast majority of theoretical studies of magnetically doped quantum dots imply parabolic shape of the quantum confinement. However, several methods of fabricating quantum dots are more appropriately described by other forms of quantum confinement that remain largely unexplored. To assess the influence of the choice of confining potential and its strength, we perform a systematic comparison of magnetic phases of quantum dots described by parabolic and Gaussian confinement. We focus on the magnetization, carrier spin polarization, and magnetic transition temperature. We clarify which of these quantities could be strongly modified by the choice of non-parabolic quantum confinement and predict related experimental implications [1]. Cond-mat/0612489. \newline [1] R. Abolfath, P. Hawrylak, I. Zutic, preprint.   

Theory of phonon-induced spin relaxation in coupled lateral quantum dots

Electron spins in lateral quantum dots at GaAs/GaAlAs interfaces relax in milliseconds. Spin relaxation here means transitions from the upper to the lower Zeeman split orbital ground state, at an applied magnetic field. Both spin-orbit and electron-phonon couplings are needed for spin flips between spectrally distinct and opposite-spin states. We have carried out realistic numerical and analytical calculations of spin relaxation and spin dynamics in single and coupled lateral quantum dots [1]. Our results agree with existing experiments on single dots, while predict interesting effects for coupled dots. Most important, spin relaxation in coupled dots is dominated by spin hot spots--anticrossings of states of opposite spins--at practical couplings (say, 0.1 meV). Spin hot spots reduce spin relaxation to nanoseconds! Fortunately, spin hot spots are strongly anisotropic and there can be (rather singular) configurations, we call them {\it easy passages}, in which spin relaxation slows down to milliseconds as in single dots. For a (001) plane, for example, an easy passage occurs if coupled dots are oriented along [110] and the in-plane magnetic field lies perpendicular, along [1$\overline{1}$0]. This configuration should be used for spin-based quantum information processing. This easy passage also protects spin qubits from electrical field disturbances which occur in ``on-chip" single electron spin resonance experiments, as will be demonstrated theoretically using density matrix formalism for electron spins in the presence of both dissipation and driving oscillating electric and magnetic field [2]. \\ \noindent [1] P. Stano and J. Fabian, Phys. Rev. Lett. 96, 186602 (2006).\\ \noindent [2] P. Stano and J. Fabian, cond-mat/0611228.   

Control of electron spin and orbital resonance in quantum dots through spin-orbit interactions

Dynamics of a single electron in coupled lateral quantum dots in the presence of a static and oscillating electric and magnetic fields as well as phonon-induced relaxation and decoherence is investigated. Using symmetry arguments it is shown that spin and orbital resonance can be efficiently controlled by spin-orbit couplings. The so called easy passage configuration is shown to be particularly suitable for magnetic manipulation of spin qubits, ensuring long spin relaxation time and protecting the spin qubit from electric field disturbances connected with on-chip manipulation.   

Electron Spin Decoherence via Optical Phonons in Quantum Dots

Electron spin decoherence caused by elastic spin-phonon processes is investigated comprehensively in a zero-dimensional environment. Specifically, a theoretical treatment is developed for the processes associated with the anharmonic vibrations of optical phonons in the semiconductor quantum dots. The optical phonons possess relatively high energy that was reasons not involving them to the problem of quantum computing decoherence to present day. This is true if we associate spin decoherence with inelastic processes of spin relaxation that needs thermal activation of optical phonons. In the case of elastic processes the uncontrolled variation of spin phase can happen without presence of thermal phonons. Zero-point optical vibrations, which survive at low enough temperatures can contribute to spin decoherence. Advantage of the optical modes is conditioned by their relatively high contributions at small phonon wave vectors as well as sufficiently short optical phonon lifetime. Calculations of decoherence time T$_{2}$ under the g-factor optical phonon modulation predict relatively weak dependence on a magnetic field, $\sim $ B$^{-2}$, that leads to estimation T$_{2} \sim$ 10$^{-5}$ s in III-V semiconductor quantum dot at B=1 T.   

Towards Electrical Spin Injection into a Single InAs/GaAs Quantum Dot

We aim to isolate emission from a single InAs/GaAs self-assembled QD to elucidate the details of electrical spin injection from an Fe Schottky contact and consequent spin polarization in QDs. MBE growth methods have been developed to reduce the dot density to the order of 10$^{8}$/cm$^{2}$, which in turn also increases the uniformity of the dots, allowing us to resolve their atomic-like s, p, d, f{\ldots} quantum confined states. The aperture sizes of the surface-emitting LEDs are also reduced to the order of a hundred nanometers using ebeam lithography. As the density and aperture size decrease, the initially broad emission spectrum of the dot ensemble [1] breaks into distinct narrow features attributed to single dot emission at low biases. With increasing bias, the number of peaks increases and their linewidth broadens, suggesting contributions from emission from an increasing number of dots and/or from various charge states of the dot. At even higher bias, the sets of peaks merge and approach broad emissions. Progress towards electrical spin injection into a single QD, and details of the electroluminescence spectra as a function of bias and magnetic field will be discussed at the meeting. [1] C. H. Li et al. APL \textbf{86}, 132503 (2005).   

Quantum Point Contacts as Spin Injectors and Detectors for Studying Rasha Spin Precession in Semiconductor Quantum Wires

We have studied polarized spin transport in a device consisting of three quantum point contacts (QPCs) in series made on InGaAs/InP quantum-well (QW) structures. The QPCs were created by independent pairs of side gates, each pair for one QPC. By adjusting the bias voltages of the side gates, the widths of the QPCs are independently tuned to have transport in the fundamental mode. An external magnetic field of a few T causes spin splitting of the lowest one-dimensional (1D) subbands. The widths of the end QPCs are adjusted to position the Fermi level in the spin-split energy gap, while that of the central QPC is kept wide enough to populate both spin-split bands. Measurement of the conductance of the end QPCs at low temperatures ($\le $ 4.2K) showed a splitting of the first conductance quantization plateau. The end QPCs are used as spin injectors and detectors with 100{\%} efficiency to study spin-polarized transport in the central QPC. The 3-QPC device we have studied can conceivably be used to study Rashba spin precession in a 1D channel to check the concept of the Datta-Das spinFET.   

Spin Dynamics of InAs Quantum Dots with Uniform Height.

Spin splittings and relaxation times were studied by Time-Resolved Faraday Rotation (TRFR) in InAs self-assembled quantum dots. Three twenty-layer samples with different dopings were grown by the Indium-flush method. This technique produces a nearly constant dot-height of 2.5 nm. The TRFR was performed using a 1.3 ps pulse Ti:sapphire laser with the sample at 5.7 K. In the undoped and lightly doped samples, signals are observed from exitons in neutral dots and from electrons and trions in negatively charged dots. Simulations for both the neutral and charged dots account for the results very well. The in-plane electron g-factor is 0.42 and shows very little variation from sample to sample or with energy in spectral studies. We ascribe this to the fixed height of the dots. The hole g-factor can be extracted cleanly from the results for the heavily doped sample. Two of the samples exhibit mode-locking of the electrons spins at 12 ns demonstrating that T$_{2}$ is much longer than T$_{2}$*.   

Gating a ferromagnetic semiconductor

Ferromagnetic semiconductors have the potential of revolutionizing the way current electronic devices work: more so, because they are compatible with current fabrication lines and can easily be integrated with today's technology. Particular interest lies in III-V Diluted Magnetic Semiconductor (DMS), where the ferromagnetism is hole-mediated and the Curie temperature can therefore be tuned by changing the concentration of free carriers\footnote{T. Dietl \textit{et al.}, Phys. Rev. B \textbf{63}, 195205 (2001)}. In these systems, most of the effort is currently applied toward the fabrication of devices working at room-temperature: this implies high carrier density accompanied by low mobility and short mean free path. We will report our results for a ferromagnetic 2DHG system with low carrier density ($\sim 3.4E12$ cm$^{-2}$) and mobility ($\sim$ 1000 cm$^2/(Vs)$), and we will discuss the effects of local gating\footnote{H. Ohno \textit{et al.}, Nature \textbf{408}, 944 (2000)} in light of possible applications to the fabrication of ferromagnetic quantum dots.   

Non-equilibrium Kondo effect in a quantum dot: Real-time density matrix formulation with non-crossing approximation

We study the non-equilibrium electron transport through a quantum dot in the Kondo regime for an infinite-U Anderson model with the self-consistent non-crossing approximation (NCA). We apply the real-time density matrix (RTDM) formulation, which is appropriate for both equilibrium and non-equilibrium situations. We study the Kondo resonances by calculating the spectral function of the localized electron. Results are reported for both spin-degenerate and spin-resolved cases by applying external magnetic fields on the electron in the QD. It is well-known that NCA gives a spurious peak at the chemical potential as it neglect the vertex correction for the spin splitting case. We show that this spurious peak can be removed by using the exact result of the non-interacting Anderson model when calculating the empty state self-energy. We also discuss the differential conductance through the QD, which can be measured in a transport experiment. We find that the separation of the two Kondo peaks in the conductance for a spin resolved dot is smaller than twice of the Zeeman energy, and there exists a critical field below which the Kondo resonance does not split.   

Nuclear Polarisation in Quantum Wires

We consider the intriguing possibility that current flow within a quantum wire can produce nuclear polarisation. The quantum wire is special because electrons can only move along one direction. Also, because of its heterogeneous structure, spin-orbit effects come into play. Together, this means that electrons are only permitted to have spin up or down orientations within the wire. By exploiting this and the Overhauser effect, we calculate the degree of nuclear polarisation and the electronic conductance arising from the effect of a non-equilibrium current.