Quantum Transport Theory of Nanostructures: Transient Response and Properties of Defects

With graphene opening the world of 2D materials in 2004, the field has since evolved to encompass many novel materials and exotic properties. The fundamentals of the field have been established and how to use these new materials for practical purposes are now as equally important as fundamental research into them.
This work is concerned with, in part, the theoretical characterization of defects in graphene with the purpose of better understanding their role in the electrical properties of devices. Non-equilibrium Greens functions (NEGF) are relied on throughout the thesis for this purpose.
The characterization efforts include investigating what role graphene grain-boundaries (GBs) have on the electrical properties of a poly-crystalline graphene flake by understanding the electronic and transport properties of GBs at an individual basis. A large dataset of bi-crystal models of GBs are constructed by an automated workflow and characterized using the NEGF approach. The theoretical conductivity across the GBs and perpendicular to the GBs are simulated together with the response to a voltage bias, gating and phonon interaction.
This characterization effort also includes investigating how a newly developed method for doping graphene, through controlled implantation of nitrogen defects, can be used for creating nanometer scale devices that confine electrons to mesoscopic states over tens of nanometers. Large-scale simulations are carried out using tight-binding and complex absorbing potentials that show quantized conductance through a model constriction, which partially remains when nitrogen scatterers are introduced into the model.
Moreover, what effect the smallest possible defect, another atom, has on the local electronic properties in graphene is calculated and compared to experimental measurements with chemisorption of a single selenium atom. This turns out to reveal the Berry phase of graphene in the theoretical and experimental spatially resolved local density of states. The inter-layer coupling in hetero-structures of nanoporous graphene and graphene is also investigated by an effective tight-binding model. The inter-layer coupling shows a dependence on the twist-angle, and this carries over to the Talbot effect known from pristine nanoporous graphene being dependent on the angle.
Simultaneously beside the evolving field of 2D materials, practical methods have been developed for generating terahertz frequency pulses. The terahertz region used to be a frequency region with no practical way of probing material properties. The STM, which is the apex of experimental characterization techniques because of its atomic resolution, has been combined with THz pulses to create THz-STM measurements. The conditions that THz-STM creates are characterized by electrons that are driven strongly out of equilibrium at the junction between the sample and STM tip.
In the other part of this work, strides are made in describing the electronic structure and transport when sub-nanometer sized junctions are exposed to strong, transient, single-cycle THz bias pulses as is encountered in THz-STM. For this purpose, a method and accompanying code has been put together, relying on a NEGF-based auxiliary mode approach that uses eigendecomposition to enable large device region simulation. This provide a framework for ab initio modeling of time-dependent, strongly driven open systems at arbitrary frequency, at the level of density functional theory. The code gives the framework to understand e.g. THz-STM in a way that accounts for the atomic configuration of the nano-junction and the magnitude of the electric field. Several systems are investigated in theoretical THz-STM setups, such as junctions consisting of spin-polarized hydrogen on graphene, an armchair nanoribbon and a gold-tip nano-junction. Examples of how to use the code are provided together with accompanying explanations.