Issue
EPL
Volume 82, Number 2, April 2008
Article Number 27001
Number of page(s) 6
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
DOI http://dx.doi.org/10.1209/0295-5075/82/27001
Published online 18 March 2008
EPL, 82 (2008) 27001
DOI: 10.1209/0295-5075/82/27001

Transport of interacting electrons through a potential barrier: Nonperturbative RG approach

D. N. Aristov1, 2 and P. Wölfle1, 2, 3

1  Institut für Theorie der Kondensierten Materie, Universität Karlsruhe - 76128 Karlsruhe, Germany, EU
2  Center for Functional Nanostructures, Universität Karlsruhe - 76128 Karlsruhe, Germany, EU
3  Institut für Nanotechnologie, Forschungszentrum Karlsruhe - 76021 Karlsruhe, Germany, EU


received 18 December 2007; accepted in final form 15 February 2008; published April 2008
published online 18 March 2008

Abstract
We calculate the linear response conductance of electrons in a Luttinger liquid with arbitrary interaction g2, and subject to a potential barrier of arbitrary strength, as a function of temperature. We first map the Hamiltonian in the basis of scattering states into an effective low-energy Hamiltonian in current algebra form. Analyzing the perturbation theory in the fermionic representation the diagrams contributing to the renormalization group (RG) $\beta $-function are identified. A universal part of the $\beta $-function is given by a ladder series and summed to all orders in g2. First non-universal corrections beyond the ladder series are discussed. The RG-equation for the temperature-dependent conductance is solved analytically. Our result agrees with known limiting cases.

PACS
71.10.Pm - Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.).
73.63.Nm - Electronic transport in nanoscale materials and structures: Quantum wires.
71.10.-w - Theories and models of many-electron systems.

© EPLA 2008