Michal Grochol

Optical exciton Aharonov-Bohm effect, persistent current, and magnetization in semiconductor nanorings of type I and II

The optical exciton Aharonov-Bohm effect—i.e., an oscillatory component in the energy of optically active bright states—is investigated in nanorings. It is shown that a small effective electron mass, strong confinement of the electron, and high barrier for the hole, achieved, e.g., by an InAs nanoring embedded in an AlGaSb quantum well, are favorable for observing the optical exciton Aharonov-Bohm effect. The second derivative of the exciton energy with respect to the magnetic field is utilized to extract Aharonov-Bohm oscillations even for the lowest bright state unambiguously. A connection between the theories for infinitesimal narrow and finite width rings is established. Furthermore, the magnetization is compared to the persistent current, which oscillates periodically with the magnetic field and confirms thus the nontrivial connected topology of the wave function in the nanoring.

Noncircular semiconductor nanorings of types I and II: Emission kinetics in the excitonic Aharonov-Bohm effect

Transition energies and oscillator strengths of excitons in dependence on magnetic field are investigated in types I and II semiconductor nanorings. A slight deviation from circular (concentric) shape of the type II nanoring gives a better observability of the Aharonov-Bohm oscillations since the ground state is always optically active. Kinetic equations for the exciton occupation are solved with acoustic phonon scattering as the major relaxation process, and absorption and luminescence spectra are calculated, showing deviations from equilibrium. The presence of a nonradiative exciton decay leads to a quenching of the integrated photoluminescence with magnetic field.

Microcavity polaritons in disordered exciton lattices

We investigate the interaction of excitons in a two-dimensional lattice and photons in a planar cavity in the presence of disorder. The strong exciton-photon coupling is described in terms of polariton quasiparticles, which are scattered by a disorder potential. We consider three kinds of disorder: (i) inhomogeneous exciton energy, (ii) inhomogeneous exciton-photon coupling, and (iii) deviations from an ideal lattice. These three types of disorder are characteristic of different physical systems. Their separate analysis gives insight into the competition between randomness and light matter coupling. We consider conventional planar polariton structures (in which excitons are resonant with photon modes emitting in the direction normal to the cavity plane) and Bragg polariton structures (in which excitons in a lattice are resonant with photon modes at a finite angle satisfying the Bragg condition). We calculate the absorption spectra in the normal direction and at the Bragg angle by direct diagonalization of the exciton-photon Hamiltonian. We found that in some cases weak disorder increases the light matter coupling and leads to a larger polariton splitting. Moreover, the coupling of excitons and photons is less sensitive to disorder of type (ii) and (iii). This suggests that polaritonic structures realized with impurities in a semiconductor or with atoms in an optical lattice are a good candidate for the observation of some of the Bragg polariton features.

Multispin errors in the optical control of a spin quantum lattice

We study a spin lattice realized with an array of charged quantum dots and embedded in a cavity. Optically excited polaritons, i.e., exciton-cavity-mixed states, interact with the electron spins in the dots. Linearly polarized excitation induces two-spin and multispin interactions. We discuss how the multispin interaction terms, which represent a source of error for two-qubit quantum gates, can be suppressed using local control of the exciton energy. The exciton spontaneous emission and the photon leakage out of the cavity are taken into account. We show that using detuning conditional phase-shift gates with high fidelity can be obtained. The cavity provides long-range spin coupling and the resulting gate operation time is shorter than the spin decoherence time.

Bragg cavity polaritons in disordered planar lattices

We investigate polaritons resulting from excitons localized in arrays with energy and oscillator strength fluctuations embedded in microcavities. The polariton emission shape remains robust under oscillator strength fluctuations, but is more sensitive to energy fluctuations.

Exciton Aharonov‐Bohm Effect in Embedded Nanostructures

Exciton properties in an embedded semiconductor nanoring under perpendicular magnetic field are investigated. Due to the unique nonsimply connected topology of the exciton wave function, oscillations of the transition energies with magnetic field (exciton Aharonov‐Bohm effect) and a persistent current appear. The amplitudes of these effects depend on the effective strength of the Coulomb interaction.

Optical Properties of Semiconductor Nanostructures in Magnetic Field

In this work, the near bandgap linear optical properties of semiconductor quantum structures under applied magnetic field are investigated. These properties are determined mainly by a quasi-particle consisting of one electron and one hole called exciton. First, the exciton theory is developed starting with the one-electron Hamiltonian in a crystal, continuing with the Luttinger and Bir-Pikus Hamiltonian, and ending with the exciton Hamiltonian in the envelope function approximation. Further, concentrating on the quantum well and thus assuming strong confinement in the growth (z-) direction, the motion parallel and perpendicular to the xy-plane is factorized leading to the well-known single sublevel approximation. A magnetic field perpendicular to the xyplane is applied, and a general theorem describing the behavior of the energy eigenvalues is derived. This theorem is generally valid for any many-particle system. Last but not least, the strain calculation within the isotropic elasticity approach is described in detail. Second, disorder is taken into account. After discussing its properties, the standard ansatz of factorizing exciton relative and center-of-mass motion is introduced. The Schrödinger equation is solved numerically for both the full model and the factorization with artificially generated disorder potentials showing that the differences between them are pronounced especially for tail states. From the physical point of view it is shown that (i) the diamagnetic shift, i. e. energy change with magnetic field, is inversionally proportional to the localization of the wave function, (ii) the distribution of the diamagnetic shifts of individual exciton states exists and these shifts are non-monotonic in energy, (iii) the average value of the diamagnetic shift increases with energy, and (iv) absorption and consequently photoluminescence spectra become wider with increasing magnetic field. Furthermore, having structural information from the cross-sectional scanning tunneling microscopy of a given sample avaible, the statistical properties of the disorder in a real quantum well have been analyzed. This analysis enabled the numerical generation of new lateral disorder potentials which served as input in the simulation of exciton optical properties. In particular, temperature dependent photoluminescence spectra and diamagnetic shift statistics, have been compared with the experimental ones and very good agreement has been found. The second part of this thesis deals predominantly with highly symmetrical structures embedded in the quantum well: namely quantum rings and dots. First, adopting an ansatz for the wave function, the Hamiltonian matrix is derived discussing which matrix elements are non-zero according to the symmetry of the potential. Additionally, the expectation values of the current and magnetization operators are evaluated. Then, concentrating on the case of the highest (circular) symmetry, the model of zero width ring is introduced. Within this model the close relation between the oscillatory component of the exciton energy (exciton Aharonov-Bohm effect) and the persistent current is revealed. Examples for different material systems follow revealing the importance of the relation between exciton Bohr radius and ring diameter for oscillations and persistent current to be observed. The circular quantum dot is treated briefly. Finally, a case of the non-circular ring is discussed and it is shown that oscillations can be observed although with lower amplitude compared to circular case. Finally, the exciton emission kinetics is calculated, too. The limitations of the experimental observability of energy oscillations, photoluminescence quenching, caused by non-zero non-radiative channels are disclosed.