General Green's function formalism for layered systems: Wave function approach
arXiv:1612.02983 · doi:10.1103/PhysRevB.95.075421
Abstract
The single-particle Green's function (GF) of mesoscopic structures plays a central role in mesoscopic quantum transport. The recursive GF technique is a standard tool to compute this quantity numerically, but it lacks physical transparency and is limited to relatively small systems. Here we present a numerically efficient and physically transparent GF formalism for a general layered structure. In contrast to the recursive GF that directly calculates the GF through the Dyson equations, our approach converts the calculation of the GF to the generation and subsequent propagation of a scattering wave function emanating from a local excitation. This viewpoint not only allows us to reproduce existing results in a concise and physically intuitive manner, but also provides analytical expressions of the GF in terms of a generalized scattering matrix. This identifies the contributions from each individual scattering channel to the GF and hence allows this information to be extracted quantitatively from dual-probe STM experiments. The simplicity and physical transparency of the formalism further allows us to treat the multiple reflection analytically and derive an analytical rule to construct the GF of a general layered system. This could significantly reduce the computational time and enable quantum transport calculations for large samples. We apply this formalism to perform both analytical analysis and numerical simulation for the two-dimensional conductance map of a realistic graphene p-n junction. The results demonstrate the possibility of observing the spatially-resolved interference pattern caused by negative refraction and further reveal a few interesting features, such as the distance-independent conductance and its quadratic dependence on the carrier concentration, as opposed to the linear dependence in uniform graphene.
22 pages, 12 figures
References in corpus (39)
- The electronic properties of graphene
- Density functional method for nonequilibrium electron transport
- Chiral tunneling and the Klein paradox in graphene
- Electronic transport in two dimensional graphene
- Shot Noise in Mesoscopic Conductors
- Andreev reflection and Klein tunneling in graphene
- Kwant: a software package for quantum transport
- Veselago Lens for Electrons: Focusing and Caustics in Graphene p-n Junctions
- Colloquium: The transport properties of graphene: An introduction
- Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
- Exceptional ballistic transport in epitaxial graphene nanoribbons
- Klein tunneling in graphene: optics with massless electrons
- General Green's function formalism for transport calculations with spd-Hamiltonians and giant magnetoresistance in Co and Ni based magnetic multilayers
- Electron optics with ballistic graphene junctions
- Electron Beam Supercollimation in Graphene Superlattices
- The recursive Green's function method for graphene
- Observation of negative refraction of Dirac fermions in graphene
- Conductance calculations for quantum wires and interfaces: mode matching and Green functions
- Efficient implementation of the nonequilibrium Green function method for electronic transport calculations
- Electrostatic confinement of electrons in an integrable graphene quantum dot
- A knitting algorithm for calculating Green functions in quantum systems
- First-principles scattering matrices for spin-transport
- Green's function technique for studying electron flow in 2D mesoscopic samples
- Efficient and realistic device modeling from atomic detail to the nanoscale
- Conductance and conductance fluctuations of narrow disordered quantum wires
- Real space finite difference method for conductance calculations
- Graphene-based electronic spin lenses
- One-dimensional Coulomb problem in Dirac materials
- Modeling Klein tunneling and caustics of electron waves in graphene
- Asymmetric I-V characteristics and magnetoresistance in magnetic point contacts
- Friedel Oscillation-Induced Energy Gap Manifested as Transport Asymmetry at Monolayer-Bilayer Graphene Boundaries
- Patched Green's function techniques for two dimensional systems: Electronic behaviour of bubbles and perforations in graphene
- Optimal traps in graphene
- Parallel implementation of the recursive Green's function method
- Electron interference in ballistic graphene nanoconstrictions
- Theoretical analysis of a dual-probe scanning tunneling microscope setup on graphene
- Efficient quantum transport simulation for bulk graphene heterojunctions
- Dual-probe spectroscopic fingerprints of defects in graphene
- Hidden quantum mirage by negative refraction in semiconductor P-N junctions
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