Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

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.

Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions

“…The Green's functions required are calculated using efficient recursive techniques to return the matrix elements required [56,57]. Fine oscillations, similar to those noted in Ref.…”

Quantum transport in graphene in presence of strain-induced pseudo-Landau levels

“…The triaxial strain for r < R gives rise to a constant PMF, whereas for r > R an r-dependent PMF of opposite sign develops 21 . The field of opposite sign within the smoothing region arises because we apply the smoothing to the physical strain, and not to the derived PMF.…”

“…Both calculations include a 0.05% concentration of impurities. The red curve indicate the LDOS in the center of the pseudomagnetic dot averaged over both sublattices for r < 1 nm (note that the zeroth level resides completely on the Bsublattice 21,22 ). The full DOS (blue) becomes the sum of the unstrained region (dashed, black), the inner part of the strained region (red) and the outer part (not shown).…”

“…This displacement field gives rise to a constant PMF 23 given by B s . Here we ignore out-of-plane and curvature 21,24,25 components of the strain field in order to get a simple connection between the strain and the magnitude of the PMF. This is justified when in-plane strain dominates (to induce pLLs) and no sharp bends are present [26][27][28] .…”

Anomalous magnetism in hydrogenated graphene

“…As long as the dimensions of the pristine and the defected Hamiltonian are the same, the procedure can deal with more than one defect without computational overhead. Notice that this method does not require the analytic evaluation of the host crystal Green's function necessary in a recently proposed method [30], and it can be applied to a very large class of systems, including superconductors [31]. The combination of Eqs.…”