A knitting algorithm for calculating Green functions in quantum systems

Abstract

We propose a fast and versatile algorithm to calculate local and transport properties such as conductance, shot noise, local density of state or local currents in mesoscopic quantum systems. Within the non equilibrium Green function formalism, we generalize the recursive Green function technique to tackle multiterminal devices with arbitrary geometries. We apply our method to analyze two recent experiments: an electronic Mach-Zehnder interferometer in a 2D gas and a Hall bar made of graphene nanoribbons in quantum Hall regime. In the latter case, we find that the Landau edge state pinned to the Dirac point gets diluted upon increasing carrier density.

7 pages, 5 figures, version for PRB

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Cited by in corpus (60)

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• The recursive Green's function method for graphene
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• Electron density and transport in top-gated graphene nanoribbon devices: First-principles Green function algorithms for systems containing large number of atoms
• Optimal block-tridiagonalization of matrices for coherent charge transport
• Dynamical control of interference using voltage pulses in the quantum regime
• Coherent transport through graphene nanoribbons in the presence of edge disorder
• Controlled coupling of spin-resolved quantum Hall edge states
• Spin Transfer Torque in Antiferromagnetic Spin-Valves: From Clean to Disordered Regimes
• Theoretical, numerical, and experimental study of a flying qubit electronic interferometer
• I-V curve signatures of nonequilibrium-driven band gap collapse in magnetically ordered zigzag graphene nanoribbon two-terminal devices
• Semiclassical magnetotransport in graphene n-p junctions
• Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
• Charged impurity scattering and mobility in gated silicon nanowires
• A computational study of two-terminal transport of Floquet quantum Hall insulators
• Recursive Green's function method for multi-terminal nanostructures
• Graphene-based heterojunction between two topological insulators
• Tunable thermopower in a graphene-based topological insulator
• Scalable Atomistic Simulations of Quantum Electron Transport using Empirical Pseudopotentials
• Graphene Nanogap for Gate Tunable Quantum Coherent Single Molecule Electronics
• Assessment of the notions of band offsets, wells and barriers at nanoscale semiconductor heterojunctions
• Quantum Hall effect in graphene with twisted bilayer stripe defects
• Inverse quantum spin Hall effect generated by spin pumping from precessing magnetization into a graphene-based two-dimensional topological insulator
• An efficient method for computing the electronic transport properties of a multi-terminal system
• Phase shifts and phase $\pi$-jumps in four-terminal waveguide Aharonov-Bohm interferometers
• General Green's function formalism for layered systems: Wave function approach
• Numerical cookbook for electronic quantum transport at finite frequency
• Atomistic calculation of the thermal conductance of large scale bulk-nanowire junctions
• Switching of electrical current by spin precession in the first Landau level of an inverted-gap semiconductor
• Multiscale approach to spin transport in magnetic multilayers
• Proposal for a Datta-Das transistor in the quantum Hall regime
• Improved recursive Green's function formalism for quasi one-dimensional systems with realistic defects
• Crossed Andreev reflection versus electron transfer in graphene nanoribbons
• Quantum Transport in Graphene Nanoribbons with Realistic Edges
• Efficient Chebyshev polynomial approach to quantum conductance calculations: Application to twisted bilayer graphene
• Stopping electrons with radio-frequency pulses in the quantum Hall regime
• Time-dependent simulation and analytical modelling of electronic Mach-Zehnder interferometry with edge-states wave packets
• Quantum transport through resistive nanocontacts: Effective one-dimensional theory and conductance formulas for non-ballistic leads
• Quantum coherence and its dephasing in the giant spin Hall effect and nonlocal voltage generated by magnetotransport through multiterminal graphene bars
• Breaking time-reversal and translational symmetry at edges of $d$-wave superconductors: microscopic theory and comparison with quasiclassical theory
• A numerical method to efficiently calculate the transport properties of large systems: an algorithm optimized for sparse linear solvers
• Pushing the limit of quantum transport simulations
• Spectral footprints of impurity scattering in graphene nanoribbons
• Destroyed quantum Hall effect in graphene with [0001] tilt grain boundaries
• Recursive Green's functions optimized for atomistic modelling of large superlattice-based devices
• DMPK Equation for the Edge Transport of Quantum Spin Hall Insulator
• Focused Crossed Andreev Reflection
• Theory of ballistic quantum transport in presence of localized defects
• Effects of domain walls in bilayer graphene in an external magnetic field
• Quantum effects in linear and non-linear transport of T-shaped ballistic junction
• Dots and Boxes Algorithm for Peierls Substitution: Application to Multidomain Topological Insulators
• Improved performance in quantum transport calculations: A divide-and-conquer method based on S-matrices
• General method for calculating transport properties of disordered mesoscopic systems based on the nonequilibrium Green's function formalism
• Investigating transverse Hall conductances using two-terminal setups
• KNIT : An open source code for quantum transport in multi-terminal systems
• Classical and quantum spreading of a charge pulse
• Introducing Open boundary conditions in modeling nonperiodic materials and interfaces: the impact of the periodic assumption
• AC/DC spin current in ferromagnet/superconductor/normal metal trilayer systems