Theory of photo-induced ferro-magnetism in dilute magnetic semiconductors

The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file.Title from title screen of research.pdf file (viewed on August 6, 2007)Vita.Thesis (Ph. D.) University of Missouri-Columbia 2006.This thesis is a theoretical study of photo-induced ferro-magnetism in dilute magnetic semiconductors. When light is incident on these systems, electrons and holes are created across the band gap. These particles interact with the impurity magnetic moments and mediate ferro-magnetism when temperature is lowered. This is a situation similar to the famous Rabi problem of a two state system coupled to time-dependent oscillating electric field. Ours is a multi-state system with electrons and holes coupled to an oscillating electric field. This is a generalization of the Rabi problem which shows also a phase transition from para to ferromagnetic state. We first study some model one and two state systems. We show by performing appropriate unitary transformations, it is possible to eliminate the time from the time-dependent Hamiltonians and get the eigen energies. Since our system of electrons and holes in contact with the photon bath is in a steady state, we calculate the free energy of the system. We study the problem of phase transition in two different ways, one by constructing Bogoliubov-Valatin quasi particles and the other by BCS wave function approach as in the low-temperature superconducting phenomenon. This also establishes that BCS and BV approaches are equivalent mean-led methods. We calculate magnetization of the system in a self-consistent mean-field way. The magnetization and thereby the critical temperature is dependent on the photon energy incident on the system. By increasing the light coupling to the particles the transition temperature increases. Also by increasing the frequency of the light, the transition temperature is increased. Since more and more of the electrons and holes are created, these carriers mediate more with the magnetic moments and flip their moments into the ferro-magnetic state. It is also found that even when light energy is below the band-gap there is still magnetization and a ferro-magnetic state is still possible. It is interesting to find a linear dependence of critical temperature Tc on the coupling J².Includes bibliographical reference

One-dimensional photonic crystal: The Kronig-Penney model

URL:http://link.aps.org/doi/10.1103/PhysRevB.68.045121 DOI:10.1103/PhysRevB.68.045121We formulate the photonic band-structure problem for a one-dimensional photonic crystal in terms of the reflection and transmission coefficients, obtaining a transcendental photonic band equation. The reflection and the transmission coefficients may be evaluated by using the standard transfer-matrix method. The structure of the equation reveals the existence of gaps, analogous to the Kronig-Penney model in the electronic band-structure problem. As an example, the photonic band equation is solved for the simple case of the “Kronig-Penney” dielectric structure, consisting of alternating slabs of refractive indices n1 and n2.We acknowledge support of this work by the U. S. Department of Energy Grant No. DE-FG02-00ER45818

Kronig-Penney model with the tail-cancellation method

http://dx.doi.org/10.1119/1.1326074The Kronig-Penney model of an electron moving in a periodic potential is solved by the so-called tail-cancellation method. The problem also serves as a simple illustration of the tail-cancellation method itself

Photoinduced magnetism in the ferromagnetic semiconductors

We study the enhancement of the magnetic transition temperature $T_c$ due to incident light in ferromagnetic semiconductors such as EuS. The photoexcited carriers mediate an extra ferromagnetic interaction due to the coupling with the localized magnetic moments. The Hamiltonian consists of a Heisenberg model for the localized moments and an interaction term between the photoexcited carriers and the localized moments. The model predicts a small enhancement of the transition temperature in semi-quantitative agreement with the experiments.Comment: 5 pages, 5 figure

Spin Polarization via Electron Tunneling through an Indirect-Gap Semiconductor Barrier

We study the spin dependent tunneling of electrons through a zinc-blende semiconductor with the indirect X (or D) minimum serving as the tunneling barrier. The basic difference between tunneling through the G vs. the X barrier is the linear-k spin-orbit splitting of the two spin bands at the X point, as opposed to the k3 Dresselhaus splitting at the G point. The linear coefficient of the spin splitting b at the X point is computed for several semiconductors using density-functional theory and the transport characteristics are calculated using the barrier tunneling model. We show that both the transmission coefficient as well as the spin polarization can be large, suggesting the potential application of these materials as spin filters.Comment: 9 page

Schrodinger equation for the one particle density matrix of thermal systems: An alternative formulation of Bose-Einstein condensation

We formulate a linear Schrodinger equation with the temperature-dependent potential for the one-particle density matrix and obtain the condensation temperature of the Bose-Einstein condensate from a bound-state condition for the Schrodinger equation both with and without the confining trap. The results are in very good agreement with those of the full statistical physics treatment. This is an alternative to the Bose-Einstein condensation in the standard ideal Bose gas treatment.Comment: 4 pages, 2 figure

A quantum mechanical relation connecting time, temperature, and cosmological constant of the universe: Gamow's relation revisited as a special case

Considering our expanding universe as made up of gravitationally interacting particles which describe particles of luminous matter and dark matter and dark energy which is described by a repulsive harmonic potential among the points in the flat 3-space, we derive a quantum mechanical relation connecting, temperature of the cosmic microwave background radiation, age, and cosmological constant of the universe. When the cosmological constant is zero, we get back the Gamow's relation with a much better coefficient. Otherwise, our theory predicts a value of the cosmological constant $2.0 10^{-56} {\rm {cm^{-2}}}$ when the present values of cosmic microwave background temperature of 2.728 K and age of the universe 14 billion years are taken as input.Comment: 4 pages, 1 figure, Study of the Universe from a condensed matter point of view, section III corrected with a single body potentia