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

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: 15 February 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) -function are identified. A universal part of the -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.