Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
arXiv:1501.06036 · doi:10.1103/PhysRevB.91.125408
Abstract
We present a numerically efficient technique to evaluate the Green's 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 Green's function of infinite pristine systems and an adaptive recursive Green's 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 Green's 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.
References in corpus (20)
- The electronic properties of graphene
- Detection of Individual Gas Molecules Absorbed on Graphene
- A tight-binding approach to uniaxial strain in graphene
- All-graphene integrated circuits via strain engineering
- Graphene Antidot Lattices - Designed Defects and Spin Qubits
- Electronic properties of graphene antidot lattices
- Weak Localization and Transport Gap in Graphene Antidot Lattices
- Gaps tunable by electrostatic gates in strained graphene
- Optical Properties of Strained Graphene
- A knitting algorithm for calculating Green functions in quantum systems
- Scalable Tight-Binding Model for Graphene
- Gaussian deformations in graphene ribbons: flowers and confinement
- Electronic structure of graphene hexagonal flake subjected to triaxial stress
- Pseudomagnetic fields in graphene nanobubbles of constrained geometry: A molecular dynamics study
- Electronic transport in disordered graphene antidot lattice devices
- Strain-induced modulation of magnetic interactions in graphene
- Dual-probe spectroscopic fingerprints of defects in graphene
- Designing electronic properties of two-dimensional crystals through optimization of deformations
- Transport of Massless Dirac Fermions in Non-topological Type Edge States
- Green Functions of Graphene: An Analytic Approach