Transport of interacting electrons through a potential barrier: Nonperturbative RG approachD. 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
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.
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.
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