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When a nanostructure is coupled between two leads, the electron transmission probability as a function of energy, E, is used in the Landauer formula to obtain the electrical conductance of the nanodevice. The electron transmission probability as a function of energy, T (E), is calculated from the appropriate solution of the time independent Schrodinger equation. Recently, a large class of nanostructures called quantum dragons have been discovered. Quantum dragons are nanodevices with correlated disorder but still can have electron transmission probability unity for all energies when connected to appropraite (idealized) leads. Hence for a single channel setup, the electrical conductivity is G₀ = 2e₂/h where e is the charge of an electron and h is Planck's constant. Thus quantum dragons have the minimum electrical conductance allowed by quantum mechanics. These quantum dragons have potential applications in nanoelectronics. It is shown that for dimerized leads coupled to a simple two-slice (l = 2, m = 1) device, the matrix method gives the same expression for the electron transmission probability as renormalization group methods and as the well known Green's function method. If a nanodevice has m atoms per slice, with l slices to calculate the electron transmission probability as a function of energy via the matrix method requires the solution of the inverse of a (2 + ml) × (2 + ml) matrix. This matrix to invert is of large dimensions for large m and l. Taking the inverse of such a matrix could be done numerically, but getting an exact solution may not be possible. By using the mapping technique, this reduces this large matrix to invert into a simple (l + 2) × (l + 2) matrix to invert, which is easier to handle but has the same solution. By using the map-and-tune approach, quantum dragon solutions are shown to exist for single-layer planar rectangular crystals with different boundary conditions. Each chapter provides two different ways on how to find quantum dragons. This work has experimental relevance, since this could pave the way for planar rectangular nanodevices with zero electrical resistance to be found. In the presence of randomness of the single-band tight-binding parameters in the nanodevice, an interesting quantum mechanical phenomenon called Fano resonance of the electron transmission probability is shown to be observed.

The magnetic properties of a 15uc thick LSMO thin film on SrTiO3 (STO) substrate atT=150K was investigated using the technique of ferromagnetic resonance (FMR). The FMRmeasurement of the 15uc thick LSMO thin film at a frequency f = 9.75GHz and powerP = 0.6325mW as a function of the angle between the static magnetic field H, and theeasy direction of magnetization within the sample plane in the "in-plane" (IP) configuration displayed an FMR spectrum. This resonance spectrum shows unequal resonance field peaks. The unequal peaks in the resonance field may be attributed to the uniaxial anisotropy field which satisfies the conditions for ferromagnetic resonance. The unequal peaks in the resonance field shows a maximum and minimum with negative and positive curvature which either increases or decreases with respect to the resonance field respectively. This increase or decrease in the resonance field depends on the magnetization direction. It has been shown that for a thick 15uc LSMO thin film at T = 150K the center position and the full width half maximum (FWHM) of the resonance field were 1070.1875 Oe and 159.3125 Oe respectively.