Scattering approach to quantum transport and many body effects

Journal Article · Tue Dec 21 00:00:00 EST 2010 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.3536609· OSTI ID:21510068

Pichard, Jean-Louis ^[1]; Freyn, Axel ^[1]

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1. Service de Physique de l'Etat Condense, (CNRS URA 2464), IRAMIS/SPEC, CEA Saclay, 91191 Gif sur Yvette cedex (France)

We review a series of works discussing how the scattering approach to quantum transport developed by Landauer and Buttiker for one body elastic scatterers can be extended to the case where electron-electron interactions act inside the scattering region and give rise to many body scattering. Firstly, we give an exact numerical result showing that at zero temperature a many body scatterer behaves as an effective one body scatterer, with an interaction dependent transmission. Secondly, we underline that this effective scatterer depends on the presence of external scatterers put in its vicinity. The implications of this non local scattering are illustrated studying the conductance of a quantum point contact where electrons interact with a scanning gate microscope. Thirdly, using the numerical renormalization group developed by Wilson for the Kondo problem, we study a double dot spinless model with an inter-dot interaction U and inter-dot hopping t{sub d}, coupled to leads by hopping terms t{sub c}. We show that the quantum conductance as a function of t{sub d} is given by a universal function, independently of the values of U and t{sub c}, if one measures t{sub d} in units of a characteristic scale {tau}(U,t{sub c}). Mapping the double dot system without spin onto a single dot Anderson model with spin and magnetic field, we show that {tau}(U,t{sub c}) 2T{sub K}, where T{sub K} is the Kondo temperature of the Anderson model.

• OSTI ID: 21510068
• Journal Information: AIP Conference Proceedings, Vol. 1319, Issue 1; Conference: 4. Mexican meeting on experimental and theoretical physics, Mexico City (Mexico), 19-23 Jul 2010; Other Information: DOI: 10.1063/1.3536609; (c) 2010 American Institute of Physics; ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
ELECTRIC CONTACTS
ELECTRON-ELECTRON COLLISIONS
ELECTRON-ELECTRON COUPLING
ELECTRON-ELECTRON INTERACTIONS
ELECTRONS
GREEN FUNCTION
KONDO EFFECT
MAGNETIC FIELDS
MANY-BODY PROBLEM
MICROSCOPES
QUANTUM MECHANICS
RENORMALIZATION
SCATTERING
SIMULATION
SPIN
TRANSMISSION
ANGULAR MOMENTUM
COLLISIONS
COUPLING
ELECTRICAL EQUIPMENT
ELECTRON COLLISIONS
ELEMENTARY PARTICLES
EQUIPMENT
FERMIONS
FUNCTIONS
INTERACTIONS
LEPTON-LEPTON INTERACTIONS
LEPTONS
MECHANICS
PARTICLE INTERACTIONS
PARTICLE PROPERTIES