Modeling Nanodevices: From Semiconductor Heterostructures to Josephson Junction Arrays
In this thesis we study the physical properties of two distinct physical systems. First, a generalized propagation matrix method is used to study how scattering off local Einstein phonons affects resonant electron transmission through quantum wells. In particular, the parity and the number of the phonon mediated satellite resonances are found to depend on the available scattering channels. For a large number of phonon channels, the formation of low-energy impurity bands is observed. Furthermore, an effective theory is developed which accurately describes the phonon generated sidebands for sufficiently small electron-phonon coupling. Finally, the current-voltage characteristics caused by phonon assisted transmission satellites are discussed for a specific double barrier geometry. In the second part of this thesis we numerically investigate the complex interplay between frustration and disorder in a magnetically frustrated Josephson junction array on the square lattice with site dilution, modeled by the fully frustrated classical XY model on the same lattice. This system has a superconducting ground state featuring a vortex crystal induced by frustration. In absence of dilution this system is known to exhibit two thermal transitions: a Kosterlitz- Thouless transition at which superconductivity and quasi-long-range phase order disappear, and a higher-temperature transition at which the vortex crystal melts - the two critical temperatures delimit a chiral phase. We find that dilution enhances the width of the chiral phase, and that at a critical dilution superconductivity is suppressed down to zero temperature, while chiral order survives - the corresponding ground state of the system becomes therefore a chiral phase glass. At an even higher dilution chiral order disappears in the ground state, leaving the system in a vortex and phase glass state. We reconstruct the complex phase diagram via extensive Monte Carlo simulations, and we investigate the main signatures of the various phases in the transport properties (I-V characteristics).
The dissertation is not yet available.