TRANSPORT THROUGH ASYMMETRIC TWO-LEAD JUNCTIONS OF LUTTINGER LIQUID WIRES
D.N. Aristov^a,b,c and P. Wölfle^b,d
aPetersburg Nuclear Physics Institute, Gatchina 188300, Russia
^bInstitute for Nanotechnology, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
E-mail: peter.woelfle@kit.edu
^cDepartment of Physics, St.Petersburg State University, Ulianovskaya 1, St.Petersburg 198504, Russia
^dInstitute for Condensed Matter Theory, and Center for Functional Nanostructures, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany

Received 20 April 2012; accepted 7 June 2012

We calculate the conductance of a system of two spinless Luttinger liquid wires with different interaction strengths g₁, g₂, connected through a short junction, within the scattering state formalism. Following earlier work we formulate the problem in current algebra language, and calculate the scale dependent contribution to the conductance in perturbation theory keeping the leading universal contributions to all orders in the interaction strength. From that we derive a renormalization group (RG) equation for the conductance. The analytical solution of the RG-equation is discussed in dependence on g₁, g₂. The regions of stability of the two fixed points corresponding to conductance G = 0 and G = 1 respectively, are determined.