Influence of Magnetic Field on Electron Energy Levels in Semconductor Quantum Dots in the Presence of Spin-Orbit Interactions

Spins in semiconductor quantum dots are among the most promising candidates for the realization of a scalable quantum bit (qubit), the basic building block of a quantum computer. With this motivation, spin and orbital properties of quantum dots in three different semiconductor systems are investigated in this thesis: depletion mode quantum dots in GaAs/AlGaAs heterostructures as well as in silicon-germanium core-shell nanowires (GeSi NW), and accumulation mode quantum dots formed in a fin field-effect transistor (FinFET). The chronological order of this thesis reflects two major shifts of focus of the semiconductor spin qubit research in recent years: a transition from lateral GaAs quantum dots towards scalable, silicon-based systems and a change from electrons towards holes as the host of the spin qubit because of better prospects for spin manipulation and spin coherence. In a lateral GaAs single electron quantum dot, a new in-plane magnetic-field-assisted spectroscopy is demonstrated, which allows one to deduce the three dimensional confinement potential landscape of the quantum dot orbitals, which gives insight into the alignment of the ellipsoidal quantum dot with respect to the crystal axes. With this full model of the confinement at hand, the dependence of the spin relaxation on the direction and strength of an in-plane magnetic field is investigated. To mitigate the spin relaxation anisotropy due to anisotropic in-plane confinement of the quantum dot, said confinement is symmetrized by tuning the gate voltages to obtain a circular quantum dot. Then, the experimentally observed spin relaxation anisotropy can be attributed to the interplay of Rashba and Dresselhaus spin-orbit interaction (SOI) present in GaAs. By using a theoretical model, the strength and the relative sign of the Rashba and Dresselhaus SOI was obtained for the first time in such a quantum dot. From the dependence of the spin relaxation on the magnetic field strength, hyperfine induced phonon mediated spin relaxation was demonstrated -- a process predicted more than 15 years ago. Here, the hyperfine interaction leads to a mixing of spin and orbital degrees of freedom and facilitates spin relaxation. Limited by this relaxation process, a spin relaxation time of 57 +/- 15 s was measured -- setting the current record for spin lifetime in a nanostructure. Inspired by the unprecedented knowledge of the confinement and the SOI in the quantum dots used, a new theory to quantify the various corrections to the g-factor was developed. Later, these theoretical predictions have been experimentally validated by measurements of the g-factor anisotropy using pulsed-gate spectroscopy. Due to short spin qubit coherence time in GaAs, which is limited by the nuclear spins, a better approach is to build a spin qubit in a semiconductor vacuum with little or no nuclear spins. Because holes have minimal overlap with the nuclei of the semiconductor due to the p-type symmetry of their wave function, this type of decoherence is strongly suppressed when changing the host of the spin qubit from electrons to holes. The longer coherence times in combination with the predicted emergence of a direct type of Rashba SOI (DRSOI) -- a particularly strong and electrically controllable SOI -- motivated the investigation of hole quantum dots in GeSi NW. In this system, anisotropic behavior of the leakage current through a double quantum dot in Pauli spin blockade was observed. This anisotropy is qualitatively explained by a phenomenological model, which involves an anisotropic g-factor and an effective spin-orbit field. While the dominant type of SOI could not be resolved conclusively, the obtained data is not inconsistent with the expectation of DRSOI. Because each wire has to be placed manually, this NW based system lacks scalability. Hole and electron quantum dots in an industry-compatible silicon FinFET structure, conversely, are promising candidates for scalable spin qubits and, therefore, hold the potential to be used in a spin-based quantum computer. Recently, DRSOI was predicted to also emerge in narrow silicon channels such as FinFETs. In this thesis, the formation of accumulation mode hole quantum dots in such a FinFET structure is reported -- an important first step towards the realization of a scalable, all-electrically controllable, DRSOI hole spin qubit.

The two-dimensional circular quantum dot in a double semiconductor heterostructure is simulated by a new axially symmetric smooth potential of finite depth and width. The presence of additional potential parameters in this model allows us to describe the individual properties of different kinds of quantum dots. The influence of the Rashba and Dresselhaus spin-orbit interactions on electron states in quantum dot is investigated. The total Hamiltonian of the problem is written as a sum of unperturbed part and perturbation. First, the exact solution of the unperturbed Schrödinger equation was constructed. Each energy level of the unperturbed Hamiltonian was doubly degenerated. Further, the analytical approximate expression for energy splitting was obtained within the framework of perturbation theory, when the strengths of two spin-orbit interactions are close. The numerical results show the dependence of energy levels on potential parameters.

We investigate the influence of an external magnetic field on spin phase relaxation of single electrons in semiconductor quantum dots induced by the hyperfine interaction. The basic decay mechanism is attributed to the dispersion of local effective nuclear fields over the ensemble of quantum dots. The characteristics of electron spin dephasing is analyzed by taking an average over the nuclear spin distribution. We find that the dephasing rate can be estimated as a spin precession frequency caused primarily by the mean value of the local nuclear magnetic field. Furthermore, it is shown that the hyperfine interaction does not fully depolarize electron spin. The loss of initial spin polarization during the dephasing process depends strongly on the external magnetic field, leading to the possibility of effective suppression of this mechanism.

The Rashba and Dresselhaus spin-orbit interactions effects on the optical properties of a quantum ring

Solutions of the Schr¨odinger equation are obtained for electrons in two-dimensional circular semiconductor quantum dots and rings in the presence of both external uniform constant magnetic field and the Rashba and Dresselhaus spin-orbit interactions of equal strengths. Confinement is simulated by realistic square well potentials. The dependence of the energy levels on the magnetic field and the strength of spin-orbit interaction is presented in detail.

In this study, the energy levels of spherical quantum dot (QD) and spherical quantum anti-dot (QAD) with hydrogenic impurity in the center, in the presence of spin-orbit interaction (SOI) and weak external magnetic field have been studied. To this aim, solving the Schrodinger equation for the discussed systems by using the finite difference method, the wave functions and energies of these systems are calculated. Then the effect of the external magnetic field, system radius size and height of potential barrier on the energy levels and also the linear, nonlinear and total absorption coefficients, (ACs), of the mentioned systems are studied. Numerical results show that the SOI in both models causes a split of 2p level into two sub-levels of 2p_(1/2)and 2p_(3/2) where the low index indicates the total angular momentum J. Also, considering the electron spin, under an applied magnetic field, the 1s and 2p levels split into two sub-levels and six sub-levels, respectively. Furthermore, in this research, it is proved that energy changes are significantly different as a function of radius size and height of the potential barrier in QD and QAD models and the ACs of these systems behave differently according to the incident photon energy at the same condition.

We study the effect of an in-plane magnetic field on the zitterbewegung (ZB) of electrons in a semiconductor quantum well (QW) and in a quantum dot (QD) with the Rashba and Dresselhaus spin–orbit interactions (SOIs). We obtain a general expression of the time-evolution of the position vector and current of the electron in a semiconductor QW. The amplitude of the oscillatory motion is directly related to the Berry connection in momentum space. We find that in presence of the magnetic field the ZB in a QW does not vanish when the strengths of the Rashba and Dresselhaus SOIs are equal. The in-plane magnetic field helps to sustain the ZB in QWs even at a low value of k0d (where d is the width of the Gaussian wavepacket and k0 is the initial wavevector). The trembling motion of an electron in a semiconductor QW with high Landé g-factor (e.g. InSb) is sustained over a long time, even at a low value of k0d. Further, we study the ZB of an electron in QDs within the two sub-band model numerically. The trembling motion persists in time even when the magnetic field is absent as well as when the strengths of the SOI are equal. The ZB in QDs is due to the superposition of oscillatory motions corresponding to all possible differences of the energy eigenvalues of the system. This is an another example of multi-frequency ZB phenomenon.

Absorption coefficient and refractive index changes of a quantum ring in the presence of spin-orbit couplings: Temperature and Zeeman effects

Interacting electrons in a semiconductor quantum dot at strong magnetic fields exhibit a rich set of states, including correlated quantum fluids and crystallites of various symmetries. We develop in this paper a perturbative scheme based on the correlated basis functions of the composite-fermion theory, that allows a systematic improvement of the wave functions and the energies for low-lying eigenstates. For a test of the method, we study systems for which exact results are known, and find that practically exact answers are obtained for the ground state wave function, ground state energy, excitation gap, and the pair correlation function. We show how the perturbative scheme helps resolve the subtle physics of competing orders in certain anomalous cases.

Spin–spin and spin–orbit interaction effects of two-electron quantum dots

We present a spintronic single photon source which emits circularly polarized light, where the helicity is determined by an applied magnetic field. Photons are emitted from an electrically operated spin light-emitting diode consisting of the diluted magnetic semiconductor ZnMnSe and an InGaAs quantum dot as single photon source. The circular polarization degree of the emitted light is high (96 % at 6 T). Autocorrelation traces recorded with a Hanbury Brown-Twiss setup in pulsed operation mode prove the emitted light to be antibunched. The two circular polarization states of the emitted photons could be used for representing quantum states | 0 > and | 1 > in quantum cryptography implementations.First results of the high frequency electron spin resonance experiment are presented, where a microwave resonator was adopted to be integrated into the spectroscopy setup in the magneto cryostat. Resonances of the Mn spins at 53 GHz and 2 T magnetic field with spin relaxation measurements were done on the way to spin manipulation of electrons in semiconductor quantum dots. KeywordsElectron Spin ResonanceCircular PolarizationDilute Magnetic SemiconductorSpin ManipulationElectron Spin Resonance ExperimentThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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.

The influence of an external transverse magnetic field on the heat transfer between a low-temperature argon plasma flow and the channel walls is experimentally investigated for Reynolds numbers in the laminar and transition regions of the flow. It is shown that the magnetic field has only a slight effect on heat transfer within the range of parameters studied. Application of a magnetic field leads to a decrease in heat transfer. From the general statements of magnetohydrodynamics, it is known [1] that an external magnetic field can have a pronounced effect on the flow of an electrically conducting medium and, in the case of ' nonisothermal flow, even on the heat transfer with the environment or with the channel walls. The nature of the influence of the magnetic field depends on various factors. The principal factors are: therelative orientation of the vectors of magnetic induction and of the mean flow rate; the flow regime; the specific characteristics of the conducting medium; the magnitude of magnetic-field induction; and the electrical conductivity of the channel walls. Theoretical and experimental investigations of heat transfer in magnetic fields are concerned mostly with flows of electrically conducting fluids (liquid metals and electrolytes) in channels. A fairly complete survey of the progress in this field is to be found in [2]. Heat transfer involved in low-temperature plasma flows in a magnetic field is characterized by such specific features as the presence of appreciable temperature and conductivity gradients both across the flow and along the channel axis, the Hall effect, and ion recombination. Methods based on approximate physical simulation of plasma flows by conducting fluids are suitable for studying heat transfer of plasma flows only within certain well established limits. Only few papers [3,4] deal with the experimental investigation of the influence of magnetic fields on the heat transfer in low-temperature plasma channel flows. These papers deal primarilywithqualitative determinations of the nature of the influence of a magnetic field in the turbulent range of Reynolds numbers. The aim of the present investigation was to determine the nature and magnitude of the influence of a transverse magnetic field on the heat transfer at the inlet section of the channel for various flow rates, various wall temperatures, and various orientations of the crosssection of a rectangular channel with respect to the magnetic field direction. The influence of a readily ionizable addition introduced into the flow on the behavior of heat transfer in the presence of an applied magnetic field is also studied. 1. The experimental equipment was composed essentially of a plasmatron, a mixing chamber, a useful channel length, a rear eham-

Chapter 15 - Quantum Structured Solar Cells

The spin dynamics in solid state systems is governed by the competition between spin-orbit interaction (SOI) and the Zeeman effect. The SOI couples orbital motion of electron spins with an electric field. The Zeeman effect lifts the spin degeneracy in a magnetic field. In InGaAs -based 2DEGs, it is known that the Rashba SOI energy E SOI can be controlled by an electric field applied on the gate electrode.1 In the presence of SOI, weak localization (WL) due to time reversal symmetric interference changes to weak anti-localization (WAL). We have found crossover from WL to WAL by applying the gate voltage in InGaAs 2DEGs. Applying an in-plane magnetic field to the 2DEG does not affect the orbital motion of the electrons, but only modifies the Zeeman spin splitting energy E Z . This allows tuning the ratio between E SOI and E Z very accurately. We have studied how the interplay between SOI and Zeeman coupling affects the electron transport and the spin dynamics in InGaAs -based 2DEGs. From the quantitative analysis of the magnetoconductance, measured in the presence of an in-plane magnetic field, we conclude that this interplay results in a spin-induced breaking of time reversal symmetry (TRS) and in an enhancement of the spin relaxation time. Both effects are due to a partial alignment of the electron spin along the applied magnetic field, and are found to be in excellent agreement with recent theoretical predictions.2 We find that the electron dephasing time saturates when E Z becomes comparable to E SOI . Moreover, we show that the spin-induced electron dephasing time is a universal function of the ratio E Z /E SOI within the experimental accuracy, i.e. it is independent of any details of the quantum well.3 This universal behavior is explained by the recent theory.4 The suppression of WAL is observed by applying in-plane magnetic field because of the enhancement of the spin relaxation time, and this suppression also appears in narrow InGaAs wires since the effective magnetic field direction is confined by wires. In gate fitted narrow wires, the large enhancement of spin relaxation time is obtained when the Rashba SOI is decreased. The spin relaxation time is more than one order longer than that of 2DEG case. This enhancement suggests that the Rashba SOI strength approaches the Dresselhaus SOI strength. We have numerically investigated the angular dependence of in-plane magnetoconductance in disordered wires with both Rashba and Dresselhaus SOIs. A new method is proposed to determine the relative strength of Rashba and Dresselhaus SOI from transport measurements without the need of fitting parameters.5 This in-plane magnetic field measurement provides fruitful information on spin related transport. Note from Publisher: This article contains the abstract only.