The recursive Green's function method for graphene

Abstract

We describe how to apply the recursive Green's function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several disorder mechanisms at the microscopic level, as well as inhomogeneous gating, finite temperature, and, to some extend, dephasing. We present algorithms for computing the conductance, density of states, and current densities for armchair and zigzag atomic edge alignments. Several numerical results are presented to illustrate the usefulness of the method.

26 pages, 15 figures; submitted to Journal of Computational Electronics (special issue on graphene)

References in corpus (37)

• The electronic properties of graphene
• Energy Gaps in Graphene Nanoribbons
• Charged Impurity Scattering in Graphene
• Atomic Structure of Graphene on SiO2
• Electronic States of Graphene Nanoribbons
• A tight-binding approach to uniaxial strain in graphene
• Emergence of magnetism in graphene materials and nanostructures
• The Kernel Polynomial Method
• Colloquium: The transport properties of graphene: An introduction
• Quantum-limited shot noise in graphene
• Quantum transport of massless Dirac fermions in graphene
• Defect scattering in graphene
• On the roughness of single- and bi-layer graphene membranes
• Electron transport in disordered graphene
• Conductance quantization and transport gap in disordered graphene nanoribbons
• Edge disorder induced Anderson localization and conduction gap in graphene nanoribbons
• Coulomb blockade in graphene nanoribbons
• Graphene as an electronic membrane
• Topological delocalization of two-dimensional massless Dirac fermions
• Modeling electronic structure and transport properties of graphene with resonant scattering centers
• Electronic transport properties of graphene nanoribbons
• Perfectly Conducting Channel and Universality Crossover in Disordered Nano-Graphene Ribbons
• Unified description of the dc conductivity of monolayer and bilayer graphene at finite densities based on resonant scatterers
• Conductivity and Fano factor in disordered graphene
• A knitting algorithm for calculating Green functions in quantum systems
• Effective contact model for transport through weakly-doped graphene
• Spatial distribution of local currents of massless Dirac fermions in quantum transport through graphene nanoribbons
• Crossover from quantum to Boltzmann transport in graphene
• Effect of short- and long-range scattering in the conductivity of graphene: Boltzmann approach vs tight-binding calculations
• Finite difference method for transport properties of massless Dirac fermions
• Transport regimes in surface disordered graphene sheets
• I-V curve signatures of nonequilibrium-driven band gap collapse in magnetically ordered zigzag graphene nanoribbon two-terminal devices
• Finite-difference method for transport of two-dimensional massless Dirac fermions in a ribbon geometry
• Efficient quantum transport simulation for bulk graphene heterojunctions
• Wave packet approach to transport in mesoscopic systems
• Atomistic deconstruction of current flow in graphene based hetero-junctions
• The role of the disorder range and electronic energy in the graphene nanoribbons perfect transmission

Cited by in corpus (134)

• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Linear Scaling Quantum Transport Methodologies
• Giant thermoelectric effect in graphene-based topological insulators with nanopores
• Strained fold assisted transport in graphene systems
• Gaussian deformations in graphene ribbons: flowers and confinement
• Majorana Fermions and Multiple Topological Phase Transition in Kitaev Ladder Topological Superconductors
• Topological Anderson insulating phases in the long-range Su-Schrieffer-Heeger model
• Twist- and gate-tunable proximity spin-orbit coupling, spin relaxation anisotropy, and charge-to-spin conversion in heterostructures of graphene and transition-metal dichalcogenides
• Electronic transport in disordered graphene antidot lattice devices
• Electronic transport in disordered MoS${}_2$ nanoribbons
• Imaging Dirac fermions flow through a circular Veselago lens
• Disorder-induced Majorana zero modes in a dimerized Kitaev superconductor chain
• Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
• Confinement-Induced Chiral Edge Channel Interaction in Quantum Anomalous Hall Insulators
• A computational study of two-terminal transport of Floquet quantum Hall insulators
• Disorder effects of vacancies on the electronic transport properties of realistic topological insulators nanoribbons: the case of bismuthene
• Evaluation of diffuse mismatch model for phonon scattering at disordered interfaces
• Spectral properties, topological patches, and effective phase diagrams of finite disordered Majorana nanowires
• Random gauge field effects on the conductivity of graphene sheets with disordered ripples
• Electron interference in ballistic graphene nanoconstrictions
• Block Lanczos density-matrix renormalization group method for general Anderson impurity models: Application to magnetic impurity problems in graphene
• Nanostructured graphene for spintronics
• Resonant transport in Kekule-distorted graphene nanoribbons
• Valley Hall Effect and Non-Local Resistance in Locally Gapped Graphene
• Conductance across strain junctions in graphene nanoribbons
• Disorder effect on the anisotropic resistivity of phosphorene determined by a tight-binding model
• The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions
• Anomalous near-field heat transfer in carbon-based nano-structures with edge states
• Structural and electronic properties of realistic two-dimensional amorphous topological insulators
• Electron trajectories and magnetotransport in nanopatterned graphene under commensurability conditions
• Matrix product state algorithms for Gaussian fermionic states
• Impurity invisibility in graphene: Symmetry guidelines for the design of efficient sensors
• Impact of complex adatom-induced interactions on quantum spin Hall phases
• An efficient method for computing the electronic transport properties of a multi-terminal system
• Dual Topological Insulator Device with Disorder Robustness
• Graphene on graphene antidot lattices: Electronic and transport properties
• General Green's function formalism for layered systems: Wave function approach
• Engineering topological phases with a three-dimensional nodal-loop semimetal
• Transport gap engineering by contact geometry in graphene nanoribbons: Experimental and theoretical studies on artificial materials
• Electronic transport in metallic carbon nanotubes with mixed defects within the strong localization regime
• Emergent Energy Dissipation in Quantum Limit
• Fano resonances in hexagonal zigzag graphene rings under external magnetic flux
• Phosphorene pnp junctions as perfect electron waveguides
• Majorana bound state engineering via efficient real-space parameter optimization
• Stability of topological properties of bismuth (111) bilayer
• Efficient Chebyshev polynomial approach to quantum conductance calculations: Application to twisted bilayer graphene
• Chiral-Flux-Phase-Based Topological Superconductivity in Kagome Systems with Mixed Edge Chiralities
• Conductance fluctuations in disordered 2D topological insulator wires: From quantum spin-Hall to ordinary quantum phases
• Conductance Peak Density in Nanowires
• A numerical method to efficiently calculate the transport properties of large systems: an algorithm optimized for sparse linear solvers
• Disorder assisted transmission due to charge puddles in monolayer graphene: Transmission enhancement and local currents
• Resonant tunneling in disordered borophene nanoribbons with line defects
• Electron transport properties of graphene nanoribbons with Gaussian deformation
• Moiré effects in graphene--hBN heterostructures
• Gap engineering in strained fold-like armchair graphene nanoribbons
• Electronic transport in graphene nanoribbons with sublattice-asymmetric doping
• Valley filtering by a line-defect in graphene: quantum interference and inversion of the filter effect
• Emergence of bound states in ballistic magnetotransport of graphene antidots
• Electronic transport in bent carbon nanotubes
• ${\mathcal{L}}^2$ localization landscape for highly-excited states
• Tunable valley filtering in dynamically strained $\alpha$-${\mathcal{T}}_3$ lattices
• Quantum Interference Effects in Topological Nanowires In a Longitudinal Magnetic Field
• GPUQT: An efficient linear-scaling quantum transport code fully implemented on graphics processing units
• Breakdown of topological protection due to non-magnetic edge disorder in two-dimensional materials in the Quantum Spin Hall phase
• Charge redistribution in correlated heterostuctures within nonequilibrium real-space dynamical mean-field theory
• Recursive Green's functions optimized for atomistic modelling of large superlattice-based devices
• Electric gating induced bandgaps and enhanced Seebeck effect in zigzag bilayer graphene ribbons
• Effect of proximity-induced spin-orbit coupling in graphene mesoscopic billiards
• Strong plasmon-phonon splitting and hybridization in 2D materials revealed through a self-energy approach
• A 50/50 electronic beam splitter in graphene nanoribbons as a building block for electron optics
• Landauer transport as a quasisteady state on finite chains under unitary quantum dynamics
• Effective contact model for geometry-independent conductance calculations in graphene
• Tunable spin-polarized edge transport in inverted quantum-well junctions
• Current flow in biased bilayer graphene: the role of sublattices
• Disorder-induced topology in quench dynamics
• Perfect transmission at oblique incidence by trigonal warping in graphene P-N junctions
• Transmission from reverse reaction coordinate mappings
• Coherent wave transmission in quasi-one-dimensional systems with Lévy disorder
• Resonance Effects in Correlated Multilayer Heterostructures
• Enhancement of the Seebeck effect in bilayer armchair graphene nanoribbons by tuning the electric fields
• Spatial mapping of disordered 2D materials: the conductance Sudoku
• Pseudo-spin triplet superconductivity in transition-metal dichalcogenide monolayers and Andreev reflection in the lateral heterostructures of 2$H$-NbSe${}_2$
• Local equilibrium charge and spin currents in two-dimensional topological systems
• Delocalization in infinite disordered 2D lattices of different geometry
• Thermoelectric properties of in-plane $90^0$-bent graphene nanoribbons with nanopores
• Floquet states of Valley-Polarized Metal with One-way Spin or Charge Transport in Zigzag Nanoribbons
• Significant reduction in semiconductor interface resistance via interfacial atomic mixing
• Chirality-2 fermion induced anti-Klein tunneling in 2D checkerboard lattice
• Wannier Diagram and Brown-Zak Fermions of Graphene on Hexagonal Boron-Nitride
• Semimetallic features in quantum transport through a gate-defined point contact in bilayer graphene
• Transport in Selectively Magnetically Doped Topological Insulator Wires
• RKKY interaction in one-dimensional flat-band lattices
• Switching valley filtered current directions in multi-terminal graphene systems
• Perfectly Conducting Graphene Electronic Waveguide with Curved Channels
• Stabilizing topological superconductivity in disordered spin-orbit coupled semiconductor-superconductor heterostructures
• Disorder effects in planar semiconductor-superconductor structures: Majorana wires versus Josephson junctions
• Efficient calculation of the Green's function in scattering region for electron-transport simulations
• Stepped Graphene-based Aharonov-Bohm Interferometers
• Resonant tunneling through protected quantum dots at phosphorene edges
• Valley selecting current partition at zero-line mode of quantum anomalous Hall topologies
• A physics-defined recurrent neural network to compute coherent light wave scattering on the millimetre scale
• Observation of Wigner cusps in a metallic carbon nanotube
• Scattering strength of potassium on a carbon nanotube with known chirality
• Coherent Transport in Y-Junction Graphene Waveguide
• Atomistic modeling of a superconductor-transition-metal dichalcogenide-superconductor Josephson junction
• Unambiguous Simulation of Diffusive Charge Transport in Disordered Nanoribbons
• Current vortices in hexagonal graphene quantum dots
• Bound states in and out of the continuum in nanoribbons with wider sections: A novel recursive S-matrix method
• Mode Delocalization in Disordered Photonic Chern Insulator
• Quantum Corrections to Thermopower and Conductivity in Graphene
• Microscopic Green's function approach for generalized Dirac Hamiltonians
• Effects of domain walls in bilayer graphene in an external magnetic field
• Klein tunneling of the electronic states in the gate voltage modulated skyrmion crystal
• Strain-induced thermoelectricity in pentacene
• Noise-Tolerance of Majorana Teleportation in Mesoscopic Topological Superconductors
• A microscopic formulation of dynamical spin injection in ferromagnetic-nonmagnetic heterostructures
• Photodriven Mott insulating heterostructures: A steady-state study of impact ionization processes
• Geometrical spin manipulation in Dirac flakes
• Ballistic guided electrons against disorder in graphene nanoribbons
• Perpendicular electronic transport and moiré-induced resonance in twisted interfaces of three-dimensional graphite
• Quantum transport of Dirac fermions in selected graphene nanosystems away from the charge-neutrality point
• Disordered Si:P nanostructures as switches and wires for nanodevices
• Investigating transverse Hall conductances using two-terminal setups
• Memory efficient Fock-space recursion scheme for computing many-fermion resolvents
• Controlling the Interferometers of Zero-Line Modes in Graphene by Pseudomagnetic field
• High-root topological edge-state bands
• Surface spectroscopy and surface-bulk hybridization of Weyl semimetals
• Robust non-integer conductance in disordered 2D Dirac semimetals
• Effect of fluorine patterns on electronic transport in fluorinated graphene
• Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization
• Introducing Open boundary conditions in modeling nonperiodic materials and interfaces: the impact of the periodic assumption
• The impact of dimensionality on universality of quantum Hall transitions
• Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal