Scattering matrix approach to the description of quantum electron transport

Abstract

We consider the scattering matrix approach to quantum electron transport in meso- and nano-conductors. This approach is an alternative to the more conventional kinetic equation and Green's function approaches, and often is more efficient for coherent conductors (especially for proving general relations) and typically more transparent. We provide a description of both time-averaged quantities (for example, current-voltage characteristics) and current fluctuations in time -- noise, as well as full counting statistics of charge transport in a finite time. In addition to normal conductors, we consider contacts with superconductors and Josephson junctions.

64 pages, 38 figures; minor changes

References in corpus (37)

• Electric Field Effect in Atomically Thin Carbon Films
• Chiral tunneling and the Klein paradox in graphene
• Andreev reflection and Klein tunneling in graphene
• Bipolar supercurrent in graphene
• Quantum-limited shot noise in graphene
• Selective transmission of Dirac electrons and ballistic magnetoresistance of \textit{n-p} junctions in graphene
• Specular Andreev reflection in graphene
• An On-Demand Coherent Single Electron Source
• Quantum supercurrent transistors in carbon nanotubes
• Josephson effect in ballistic graphene
• Quantum phase transition in a single-molecule quantum dot
• Josephson Current and Multiple Andreev Reflections in Graphene SNS Junctions
• Shot Noise in Ballistic Graphene
• Minimal excitation states of electrons in one-dimensional wires
• Low-frequency noise as a source of dephasing of a qubit
• Frequency-selective single photon detection using a double quantum dot
• Quantized conductance of a suspended graphene nanoconstriction
• Using a quantum dot as a high-frequency shot noise detector
• Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula
• Detection of non-Gaussian Fluctuations in a Quantum Point Contact
• Wave-packet Formalism of Full Counting Statistics
• Wide-band detection of the third moment of shot noise by a hysteretic Josephson junction
• Subharmonic gap structure in short ballistic graphene junctions
• Scattering Approach to Counting Statistics in Quantum Pumps
• Critical Josephson current in ballistic superconductor-graphene systems
• Allowed charge transfers between coherent conductors driven by a time-dependent scatterer
• Fredholm determinants and the statistics of charge transport
• Factorization of quantum charge transport for non-interacting fermions
• Energy entanglement in normal metal-superconducting forks
• Two-particle scattering matrix of two interacting mesoscopic conductors
• Phase transitions in full counting statistics for periodic pumping
• Critical currents in graphene Josephson junctions
• Continuously Tunable Charge in Andreev Quantum Dots
• N-particle scattering matrix for electrons interacting on a quantum dot
• Effects of Exchange Symmetry on Full Counting Statistics
• Measurement of high order current correlators
• Nanomechanical effects in an Andreev quantum dot

Cited by in corpus (36)

• Cooper Pair Splitting by means of Graphene Quantum Dots
• Electron Waiting Times in Mesoscopic Conductors
• Characterizing correlations with full counting statistics: classical Ising and quantum XY spin chains
• Spin Currents and Magnon Dynamics in Insulating Magnets
• Distributions of electron waiting times in quantum-coherent conductors
• Generic transport formula for a system driven by Markovian reservoirs
• Thermopower and thermal conductance of a superconducting quantum point contact
• Quantum thermodynamics with fast driving and strong coupling via the mesoscopic leads approach
• Majorana bound states in a superconducting Rashba nanowire in the presence of antiferromagnetic order
• Hybrid normal-superconducting Aharonov-Bohm quantum thermal device
• Analytic approach to transport in superconducting junctions with arbitrary carrier density
• Direct observation of ballistic Andreev reflection
• Antiferromagnetic helix as an efficient spin polarizer: Interplay between electric field and higher ordered hopping
• Spin-flip reflection at the normal metal-spin superconductor interface
• Finite frequency backscattering current noise at a helical edge
• Probing the chirality of 1D Majorana edge states around a 2D nanoflake in a superconductor
• Controllable Andreev Bound States in Bilayer Graphene Josephson Junction from Short to Long Junction Limits
• Semi-classical theory of quantum stochastic resistors
• Current Correlations in a Quantum Dot Ring: A Role of Quantum Interference
• Projective versus weak measurement of charge in a mesoscopic conductor
• Entangling color centers via magnon-antimagnon pair creation
• Quantum thermocouples: nonlocal conversion and control of heat in nanostructures
• Levitons in correlated nano-scale systems
• Coherent current correlations in a double-dot Cooper pair splitter
• Integrable Aspects of Universal Quantum Transport in Chaotic Cavities
• Probing anyon statistics on a single-edge loop in the fractional quantum Hall regime
• Negative currents in Fabry-Pérot cavities are caused by interfering paths
• Periodic source of energy-entangled electrons in helical states coupled to a BCS superconductor
• Thermodynamic bound on current fluctuations in coherent conductors
• Confinement-induced zero-bias peaks in conventional superconductor hybrids
• Conductance matrix of multi terminal semiconductor devices with edge channels
• Two-parameter landscape of transport efficiency in mesoscopic networks: transitions from the Braess to normal regimes without a congestion relaxation
• Non-linear regime for enhanced performance of an Aharonov-Bohm heat engine
• Directional conductance of Andreev crystals in hybrid Josephson junction arrays
• Conductance matrix symmetries of multiterminal semiconductor-superconductor devices
• Scalable Machine Learning Models for Predicting Quantum Transport in Disordered 2D Hexagonal Materials