Scattering matrix approach to the description of quantum electron transport

2011/10/31 by G. B. Lesovik, Gordei B Lesovik, I. A. Sadovskyy +1
Engineering · Physics and Astronomy · #Advancements in Semiconductor Devices and Circuit Design #Computer science #Condensed matter physics #Current (fluid) #Electrical conductor #Electron #Electron scattering #Josephson effect #Materials science #Matrix (chemical analysis) #Molecular Junctions and Nanostructures #Noise (video) #Physics #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Scattering #Statistical physics #Superconductivity #cond-mat.mes-hall #cond-mat.stat-mech #cond-mat.supr-con #quant-ph

paper · pdf · doi:10.3367/ufne.0181.201110b.1041

published as UFN 181, 1041 (2011) [Phys. Usp. 54, 1007 (2011)] · 64 pages, 38 figures; minor changes

openalex publication_date 2011/10/31 · arxiv created 2015/04/07 · arxiv updated 2015/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Colloquium: Andreev reflection and Klein tunneling in graphene
• Nonlinearity in normal-metal–superconductor transport: Scattering-matrix approach
• Quantum transport in disordered wires: Equivalence of the one-dimensional σ model and the Dorokhov-Mello-Pereyra-Kumar equation
• Current correlations of an on-demand single-electron emitter
• Sub-Poissonian Shot Noise in Graphene
• Shot Noise in Ballistic Graphene
• Electron counting statistics and coherent states of electric current
• On the Mathematical Description of Light Nuclei by the Method of Resonating Group Structure
• Music therapy and the relationship between a mother and a toddler with a disability
• Zur Quantenmechanik der Sto�vorg�nge
• Subgap conductivity of a superconductor–normal-metal tunnel interface
• N-Particle Scattering Matrix for Electrons Interacting on a Quantum Dot
• An electronic Mach–Zehnder interferometer
• Statistical-Mechanical Theory of Irreversible Processes. I. General Theory and Simple Applications to Magnetic and Conduction Problems
• Scattering approach to counting statistics in quantum pumps
• Factorization of quantum charge transport for noninteracting fermions
• Significance of Electromagnetic Potentials in the Quantum Theory
• Theory of dirty superconductors
• Doubled shot noise in disordered normal-metal–superconductor junctions
• Thermal Agitation of Electric Charge in Conductors
• Electronic entanglement in the vicinity of a superconductor
• Noise in an ac biased junction: Nonstationary Aharonov-Bohm effect
• Numerical studies of localization in disordered systems
• Wideband Detection of the Third Moment of Shot Noise by a Hysteretic Josephson Junction
• Specular Andreev Reflection in Graphene
• Electric Field Effect in Atomically Thin Carbon Films
• Effects of Exchange Symmetry on Full Counting Statistics
• Ueber die Wärme‐Leitungsfähigkeit der Metalle
• Shot Noise in Mesoscopic Conductors
• Reflectionless tunneling through a double-barrier NS junction
• Universal statistics of transport in disordered conductors
• Random-matrix theory of quantum transport
• What is the Thouless Energy for Ballistic Systems?
• Minimal Excitation States of Electrons in One-Dimensional Wires
• Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula
• Measurement of Counting Statistics of Electron Transport in a Tunnel Junction
• Josephson Currents through Junctions with Normal Metal Barriers
• Zitterbewegung, chirality, and minimal conductivity in graphene
• Electrical resistance of disordered one-dimensional lattices
• Tuning the Josephson current in carbon nanotubes with the Kondo effect
• (Mis-)handling gauge invariance in the theory of the quantum Hall effect. III. The instanton vacuum and chiral-edge physics
• Effects of Configuration Interaction on Intensities and Phase Shifts
• Possible new effects in superconductive tunnelling
• Giant Josephson current through a single bound state in a superconducting tunnel junction
• On the detection of finite-frequency current fluctuations
• Die ?beobachtbaren Gr��en? in der Theorie der Elementarteilchen