The complete impurity scattering formalism in graphene

Abstract

We present the complete formalism that describes scattering in graphene at low-energies. We begin by analyzing the real-space free Green's function matrix, and its analytical expansions at low-energy, carefully incorporating the discrete lattice structure, and arbitrary forms of the atomic-orbital wave function. We then compute the real-space Green's function in the presence of an impurity. We express our results both in 2X2 and 4X4 forms (for the two sublattices and the two inequivalent valleys of the first Brillouin zone). We compare this with the 4X4 formalism proposed in cond-mat/0608228 and cond-mat/0702019, and show that the latter is incomplete. We describe how it can be adapted to accurately take into account the effects of inter-valley scattering on spatially-varying quantities such as the local density of states.

11 pages, 1 figure

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Cited by in corpus (29)

• Dirac materials
• Strain effect on the optical conductivity of graphene
• RKKY Interaction in Graphene from Lattice Green's Function
• Role of pseudospin in quasiparticle interferences in epitaxial graphene probed by high-resolution scanning tunneling microscopy
• Fourier Transform Scanning Tunneling Spectroscopy: the possibility to obtain constant energy maps and the band dispersion using a local measurement
• Purely Long-Range Coherent Interactions in Two-Dimensional Structured Baths
• Local density of states and Friedel oscillation in graphene
• Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
• Theory of quasiparticle interference in mirror symmetric 2D systems and its application to surface states of topological crystalline insulators
• Local density of states and scanning tunneling currents in graphene
• Surface Green's functions and boundary modes using impurities: Weyl semimetals and topological insulators
• Effect of impurities in high-symmetry lattice positions on the local density of states and conductivity of graphene
• Numerical simulation evidence of spectrum rearrangement in impure graphene
• Intravalley Multiple Scattering of Quasiparticles in Graphene
• In-gap impurity states as the hallmark of the Quantum Spin Hall phase
• A comprehensive study of electric, thermoelectric and thermal conductivities of Graphene with short range unitary and charged impurities
• Role played by strain on Plasmons, screening and energy loss in Graphene/substrate contacts
• Quasiparticle interference patterns in bilayer graphene with trigonal warping
• Emergence of strain-induced moiré patterns and pseudo-magnetic field confined states in graphene
• Robust wavefront dislocations of Friedel oscillations in gapped graphene
• Edge states, spin transport and impurity induced local density of states in spin-orbit coupled graphene
• Persistent Friedel oscillations in Graphene due to a weak magnetic field
• The local density of states in the presence of impurity scattering in graphene at high magnetic field
• Theory of quasiparticle interference in Kitaev quantum spin liquids
• Electron dynamics in graphene with spin-orbit couplings and periodic potentials
• Distinct quasiparticle interference patterns for surface impurity scattering on various Weyl semimetals
• Effect of Inter-Adatoms Correlations on the Local Density of States of Graphene
• Quasiparticle spectroscopy as a probe of the topological phase in graphene with heavy adatoms
• Surface states and quasiparticle interference in Bernal and rhombohedral graphite with and without trigonal warping