Henri Saarikoski

Three real-space discretization techniques in electronic structure calculations

A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the main approaches include finite-difference methods, various types of finite-elements and wavelets. This paper reports on the results of several code development projects that approach problems related to the electronic structure using these three different discretization methods. We review the ideas behind these methods, give examples of their applications, and discuss their similarities and differences.

Testing of two-dimensional local approximations in the current-spin and spin-density-functional theories

We study a model quantum dot system in an external magnetic field by using both spin-density-functional theory and current-spin density-functional theory. The theories are used with local approximations for the spin-density and vorticity. The reliabilities of different parametrizations for the exchange-correlation functionals are tested by comparing the ensuing energetics with quantum Monte Carlo results. The limit where the vorticity dependence should be used in the exchange-correlation functionals is discussed.

Electronic structure of rectangular quantum dots

We study the ground-state properties of rectangular quantum dots by using the spin-density-functional theory and quantum Monte Carlo methods. The dot geometry is determined by an infinite hard-wall potential to enable comparison to manufactured, rectangular-shaped quantum dots. We show that the electronic structure is very sensitive to the shape of the dot, and, at realistic sizes, the noninteracting picture determines the general behavior. However, close to the degenerate points where Hunds rule applies, we find spin-density-wave-like solutions bracketing the partially polarized states. In the quasi-one-dimensional limit we find permanent charge-density waves, and at a sufficiently large deformation or low density, there are strongly localized stable states with a broken spin symmetry.

Stability of vortex structures in quantum dots

We study the stability and structure of vortices emerging in two-dimensional quantum dots in high magnetic fields. Our results obtained with exact diagonalization and density-functional calculations show that vortex structures can be found in various confining potentials. In nonsymmetric external potentials we find off-electron vortices that are localized giving rise to charge deficiency or holes in the electron density with rotating currents around them. We discuss the role of quantum fluctuations and show that vortex formation is observable in the energetics of the system. Our findings suggest that vortices can be used to characterize the solutions in high magnetic fields, giving insight into the underlying internal structure of the electronic wave function. (Less)

Control of the spin geometric phase in semiconductor quantum rings

Since the formulation of the geometric phase by Berry, its relevance has been demonstrated in a large variety of physical systems. However, a geometric phase of the most fundamental spin-1/2 system, the electron spin, has not been observed directly and controlled independently from dynamical phases. Here we report experimental evidence on the manipulation of an electron spin through a purely geometric effect in an InGaAs-based quantum ring with Rashba spin-orbit coupling. By applying an in-plane magnetic field, a phase shift of the Aharonov–Casher interference pattern towards the small spin-orbit-coupling regions is observed. A perturbation theory for a one-dimensional Rashba ring under small in-plane fields reveals that the phase shift originates exclusively from the modulation of a pure geometric-phase component of the electron spin beyond the adiabatic limit, independently from dynamical phases. The phase shift is well reproduced by implementing two independent approaches, that is, perturbation theory and non-perturbative transport simulations.

Vortex clusters in quantum dots.

We study electronic structures of two-dimensional quantum dots in strong magnetic fields using mean-field density-functional theory and exact diagonalization. Our numerically accurate mean-field solutions show a reconstruction of the uniform-density electron droplet when the magnetic field flux quanta enter one by one the dot in stronger fields. These quanta correspond to repelling vortices forming polygonal clusters inside the dot. We find similar structures in the exact treatment of the problem by constructing a conditional operator for the analysis. We discuss important differences and limitations of the methods used.

Simulation of field-assisted ion exchange for glass channel waveguide fabrication: effect of nonhomogeneous time-dependent electric conductivity

Abstract Nonhomogeneous time-dependent electric conductivity distribution during field-assisted ion exchange in glass is taken into account in the numerical modeling of optical waveguide fabrication. As an example, the influence of the nonhomogeneous conductivity on a buried channel waveguide is studied in detail. It is shown that there is a substantial variation of electric current density during the process, particularly in the waveguide region. The main difference in comparison to the previous more approximative models is seen to be a smaller refractive index increase for the waveguides.

Broken symmetry in density-functional theory: Analysis and cure

We present a detailed analysis of the broken-symmetry mean-field solutions using a four-electron rectangular quantum dot as a model system. Comparisons of the density-functional theory predictions with the exact ones showthat the symmetry-breaking results from the single-configuration wave function used in the mean-field approach. As a general cure we present a scheme that systematically incorporates several configurations into the density-functional theory and restores the symmetry. This cure is easily applicable to any density-functional approach.

Fast numerical solution of nonlinear diffusion equation for the simulation of ion-exchanged micro-optics components in glass

Abstract Modulation of the refractive index of glass using ion exchange is a common fabrication method for various micro-optics components, such as waveguide devices, microlenses, and diffractive elements. The design of elements with complicated optical functions has increased the demand for fast numerical simulation of the nonlinear ion-exchange process of two monovalent ions. In this paper, a linear implicit finite-difference Crank-Nicholson-type method is implemented for thermal two- and three-dimensional ion-exchange processes. The resulting system of linear equations is solved by using various iterative methods. Grid spacing, length of the time step, and the number of iterations are chosen so that desired accuracy is obtained within minimum computing time. The implemented methods are compared with the Peaceman-Rachford Alternating Direction Implicit (PR-ADI) and the explicit Du Fort-Frankel method in modeling a computer-synthesized diffractive optical element and a waveguide channel system.

Wigner molecules in polygonal quantum dots: A density-functional study

We investigate the properties of many-electron systems in two-dimensional polygonal (triangle, square, pentagon, hexagon) potential wells by using the density-functional theory. The development of the ground-state electronic structure as a function of the dot size is of particular interest. First, we show that in the case of two electrons, the Wigner molecule formation agrees with previous exact diagonalization studies. Then we present in detail how the spin symmetry breaks in polygonal geometries as the spin density-functional theory is applied. In several cases with more than two electrons, we find a transition to the crystallized state, yielding coincidence with the number of density maxima and the electron number. We show that this transition density, which agrees reasonably well with previous estimations, is rather insensitive to both the shape of the dot and the electron number.