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- Creators: Menéndez, Jose
Description
The theory of geometric quantum mechanics describes a quantum system as a Hamiltonian dynamical system, with a projective Hilbert space regarded as the phase space. This thesis extends the theory by including some aspects of the symplectic topology of the quantum phase space. It is shown that the quantum mechanical uncertainty principle is a special case of an inequality from J-holomorphic map theory, that is, J-holomorphic curves minimize the difference between the quantum covariance matrix determinant and a symplectic area. An immediate consequence is that a minimal determinant is a topological invariant, within a fixed homology class of the curve. Various choices of quantum operators are studied with reference to the implications of the J-holomorphic condition. The mean curvature vector field and Maslov class are calculated for a lagrangian torus of an integrable quantum system. The mean curvature one-form is simply related to the canonical connection which determines the geometric phases and polarization linear response. Adiabatic deformations of a quantum system are analyzed in terms of vector bundle classifying maps and related to the mean curvature flow of quantum states. The dielectric response function for a periodic solid is calculated to be the curvature of a connection on a vector bundle.
ContributorsSanborn, Barbara (Author) / Suslov, Sergei K (Thesis advisor) / Suslov, Sergei (Committee member) / Spielberg, John (Committee member) / Quigg, John (Committee member) / Menéndez, Jose (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2011
Description
High-performance III-V semiconductors based on ternary alloys and superlattice systems are fabricated, studied, and compared for infrared optoelectronic applications. InAsBi is a ternary alloy near the GaSb lattice constant that is not as thoroughly investigated as other III-V alloys and that is challenging to produce as Bi has a tendency to surface segregate and form droplets during growth rather than incorporate. A growth window is identified within which high-quality droplet-free bulk InAsBi is produced and Bi mole fractions up to 6.4% are obtained. Photoluminescence with high internal quantum efficiency is observed from InAs/InAsBi quantum wells. The high structural and optical quality of the InAsBi materials examined demonstrates that bulk, quantum well, and superlattice structures utilizing InAsBi are an important design option for efficient infrared coverage.
Another important infrared material system is InAsSb and the strain-balanced InAs/InAsSb superlattice on GaSb. Detailed examination of X-ray diffraction, photoluminescence, and spectroscopic ellipsometry data provides the temperature and composition dependent bandgap of bulk InAsSb. The unintentional incorporation of approximately 1% Sb into the InAs layers of the superlattice is measured and found to significantly impact the analysis of the InAs/InAsSb band alignment. In the analysis of the absorption spectra, the ground state absorption coefficient and transition strength of the superlattice are proportional to the square of the electron-hole wavefunction overlap; wavefunction overlap is therefore a major design parameter in terms of optimizing absorption in these materials. Furthermore in addition to improvements through design optimization, the optical quality of the materials studied is found to be positively enhanced with the use of Bi as a surfactant during molecular beam epitaxy growth.
A software tool is developed that calculates and optimizes the miniband structure of semiconductor superlattices, including bismide-based designs. The software has the capability to limit results to designs that can be produced with high structural and optical quality, and optimized designs in terms of maximizing absorption are identified for several infrared superlattice systems at the GaSb lattice constant. The accuracy of the software predictions are tested with the design and growth of an optimized mid-wave infrared InAs/InAsSb superlattice which exhibits superior optical and absorption properties.
Another important infrared material system is InAsSb and the strain-balanced InAs/InAsSb superlattice on GaSb. Detailed examination of X-ray diffraction, photoluminescence, and spectroscopic ellipsometry data provides the temperature and composition dependent bandgap of bulk InAsSb. The unintentional incorporation of approximately 1% Sb into the InAs layers of the superlattice is measured and found to significantly impact the analysis of the InAs/InAsSb band alignment. In the analysis of the absorption spectra, the ground state absorption coefficient and transition strength of the superlattice are proportional to the square of the electron-hole wavefunction overlap; wavefunction overlap is therefore a major design parameter in terms of optimizing absorption in these materials. Furthermore in addition to improvements through design optimization, the optical quality of the materials studied is found to be positively enhanced with the use of Bi as a surfactant during molecular beam epitaxy growth.
A software tool is developed that calculates and optimizes the miniband structure of semiconductor superlattices, including bismide-based designs. The software has the capability to limit results to designs that can be produced with high structural and optical quality, and optimized designs in terms of maximizing absorption are identified for several infrared superlattice systems at the GaSb lattice constant. The accuracy of the software predictions are tested with the design and growth of an optimized mid-wave infrared InAs/InAsSb superlattice which exhibits superior optical and absorption properties.
ContributorsWebster, Preston Thomas (Author) / Johnson, Shane R (Thesis advisor) / Zhang, Yong-Hang (Committee member) / Menéndez, Jose (Committee member) / Vasileska, Dragica (Committee member) / Arizona State University (Publisher)
Created2016