Dirac Green's function approach to graphene-superconductor junctions with well defined edges
arXiv:1101.5299 · doi:10.1088/0953-8984/22/27/275304
Abstract
This work presents a novel approach to describe spectral properties of graphene layers with well defined edges. We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations and derive the Green functions for normal and superconducting graphene layers. Importing the idea used in tight-binding (TB) models of a microscopic hopping that couples different regions, we are able to set up and solve an algebraic Dyson's equation describing a graphene-superconductor junction. For this coupled system we analytically derive the Green functions and use them to calculate the local density of states and the spatial variation of the induced pairing correlations in the normal region. Signatures of specular Andreev reflections are identified.
13 pages, 5 figures
References in corpus (28)
- Electronic States of Graphene Nanoribbons
- Bipolar supercurrent in graphene
- Tailoring the atomic structure of graphene nanoribbons by STM lithography
- Specular Andreev reflection in graphene
- Phase Coherent Transport of Charges in Graphene Quantum Billiard
- AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
- Andreev - Saint James reflections: a probe of cuprate superconductors
- Josephson effect in ballistic graphene
- Josephson Current and Multiple Andreev Reflections in Graphene SNS Junctions
- Conductance Quantization in Graphene Nanoribbons
- Tunneling conductance of graphene NIS junctions
- Crossed Andreev reflection in a graphene bipolar transistor
- Quantum transport through a graphene nanoribbon-superconductor junction
- Proximity Induced Superconductivity and Multiple Andreev Reflections in Few-Layer-Graphene
- Dirac-fermions and conductance-oscillations in (s,d)-wave superconductor/normal graphene junctions
- Self-consistent solution for proximity effect and Josephson current in ballistic graphene SNS Josephson junctions
- Excitation gap of a graphene channel with superconducting boundaries
- Andreev reflection in graphene nanoribbons
- Microscopic theory of the proximity effect in superconductor-graphene nanostructures
- Subharmonic gap structure in short ballistic graphene junctions
- Near zero modes in condensate phases of the Dirac theory on the honeycomb lattice
- Josephson effect in mesoscopic graphene strips with finite width
- Reentrance effect in a graphene n-p-n junction coupled to a superconductor
- Proximity induced interface bound states in superconductor-graphene junctions
- Dirac fermion quantization on graphene edges: Isospin-orbit coupling, zero modes and spontaneous valley polarization
- Fine structure of the local pseudogap and Fano effect for superconducting electrons near a zigzag graphene edge
- Long range crossed Andreev reflections in high Tc superconductors
- -junction qubit in monolayer graphene
Cited by in corpus (27)
- Superconducting proximity effect in three-dimensional topological insulators in the presence of a magnetic field
- Odd-Frequency Triplet Superconductivity at the Helical Edge of a Toplogical Insulator
- Edge effects in graphene nanostructures: I. From multiple reflection expansion to density of states
- Microscopic theory of Cooper pair beam splitters based on carbon nanotubes
- Conductance signatures of odd-frequency superconductivity in quantum spin Hall systems using a quantum point contact
- Tunable hybridization of Majorana bound states at the quantum spin Hall edge
- Selective focusing of electrons and holes in a graphene-based superconducting lens
- Transition between ordinary and topological insulator regimes in two-dimensional resonant magnetotransport
- Subgap states in two dimensional spectroscopy of unconventional superconductors using graphene
- Tunneling spectroscopy and Josephson current of superconductor-ferromagnet hybrids on the surface of a 3D TI
- Phase-tunable electron transport assisted by odd-frequency Cooper pairs in topological Josephson junctions
- Greens function of semi-infinite Weyl semimetals
- Transport and spectral properties of magic angle twisted bilayer graphene junctions based on local orbital models
- Thermoelectric detection of Andreev states in unconventional superconductors
- Dirac point formation revealed by Andreev tunneling in superlattice-graphene/superconductor junctions
- Two-dimensional topological insulators in quantizing magnetic fields
- Thermoelectric processes of quantum normal-superconductor interfaces
- Diffusion on edges of insulating graphene with intravalley and intervalley scattering
- Supercurrent reversal in Josephson junctions based on bilayer graphene flakes
- Photoabsorption spectra and the X-ray edge problem in graphene
- Josephson coupling between superconducting islands on single and bilayer graphene
- Microscopic Green's function approach for generalized Dirac Hamiltonians
- A Green's function approach to Topological Insulator junctions with magnetic and superconducting regions
- Generic model for Cooper pair splitting
- Confinement-induced zero-bias peaks in conventional superconductor hybrids
- Tight-Binding Energy-Phase Calculation for Topological Josephson Junction Nanowire Architecture
- Long-range Cooper pair splitting by chiral Majorana edge states