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We present a numerically efficient technique to evaluate the Greens function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches, are connected using self energy terms which encode the information of the extended parts of the system. The calculation scheme uses a combination of analytic expressions for the Greens function of infinite pristine systems and an adaptive recursive Greens function technique for the patches. The method allows for an efficient calculation of both local electronic and transport properties, as well as the inclusion of multiple probes in arbitrary geometries embedded in extended samples. We apply the Patched Greens function method to evaluate the local densities of states and transmission properties of graphene systems with two kinds of deviations from the pristine structure: bubbles and perforations with characteristic dimensions of the order of 10-25 nm, i.e. including hundreds of thousands of atoms. The strain field induced by a bubble is treated beyond an effective Dirac model, and we demonstrate the existence of both Friedel-type oscillations arising from the edges of the bubble, as well as pseudo-Landau levels related to the pseudomagnetic field induced by the nonuniform strain. Secondly, we compute the transport properties of a large perforation with atomic positions extracted from a TEM image, and show that current vortices may form near the zigzag segments of the perforation.
We study the electronic structure of graphene with a single substitutional vacancy using a combination of the density-functional, tight-binding, and impurity Greens function approaches. Density functional studies are performed with the all-electron s
The problem of the strain of smectics subjected to a force distributed over a line in the basal plane has been solved.
An analytical general analysis of the electromagnetic Dyadic Greens Function for two-dimensional sheet (or a very thin film) is presented, with an emphasis on on the case of graphene. A modified steepest descent treatment of the fields from a point d
We present first-principles calculations of silicene/graphene and germanene/graphene bilayers. Various supercell models are constructed in the calculations in order to reduce the strain of the lattice-mismatched bilayer systems. Our energetics analys
Hexagonal boron nitride is the only substrate that has so far allowed graphene devices exhibiting micron-scale ballistic transport. Can other atomically flat crystals be used as substrates for making quality graphene heterostructures? Here we report