| As a result of the computing power provided by the current technology, computational methods now play an important role in modeling and designing materials at the nanoscale.;The focus of this dissertation is two-fold: first, new computational methods to model nanoscale transport are introduced, then state-of-the-art tools based on density functional theory are employed to explore the properties of phosphorene, a novel low dimensional material with great potential for applications in nanotechnology.;A Wannier function description of the electron density is combined with a generalized Slater-Koster interpolation technique, enabling the introduction of a new computational method for constructing first-principles model Hamiltonians for electron and hole transport that maintain the density functional theory accuracy at a fraction of the computational cost. As a proof of concept, this new approach is applied to model polythiophene, a polymer ubiquitous in organic photovoltaic devices.;A new low dimensional material, phosphorene - a single layer of black phosphorous - the phosphorous analogue of graphene was first isolated in early 2014 and has attracted considerable attention. It is a semiconductor with a sizable band gap, which makes it a perfect candidate for ultrathin transistors. Multi-layer phosphorene transistors have already achieved the highest hole mobility of any two-dimensional material apart from graphene.;Phosphorene is prone to oxidation, which can lead to degradation of electrical properties, and eventually structural breakdown. The calculations reported here are some of the first to explore this oxidation and reveal that different types of oxygen defects are readily introduced in the phosphorene lattice, creating electron traps in some situations. These traps are responsible for the non-ambipolar behavior observed by experimental collaborators in air-exposed few-layer black phosphorus devices. Calculation results predict that air exposure of phosphorene creates a new family of two-dimensional oxides, which has been later confirmed by X-ray photoemission measurements. These oxides can form protective coatings for phosphorene and have interesting tunable electronic properties.;Finally, Wannier function interpolation has been used to demonstrate that a saddle-point van Hove singularity is present near the phosphorene Fermi energy, as observed in some layered cuprate high temperature superconductors; this leads to an intriguing strain-induced ferromagnetic instability. |
