Transport through asymmetric two-lead junctions of Luttinger liquid wires

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.

[1]  P. Wölfle,et al.  Transport properties of a Y junction connecting Luttinger liquid wires , 2011 .

[2]  D. Aristov.  Constraints on conductances for Y-junctions of quantum wires , 2010, 1008.1645.

[3]  I. Gornyi,et al.  Tunneling into a Luttinger liquid revisited. , 2010, Physical review letters.

[4]  P. Woelfle,et al.  Conductance through a potential barrier embedded in a Luttinger liquid: Nonuniversal scaling at strong coupling , 2009, 0902.4170.

[5]  Thierry Giamarchi,et al.  Quantum physics in one dimension , 2004 .

[6]  A. Tsvelik,et al.  Bosonization and Strongly Correlated Systems , 1999, cond-mat/9909069.

[7]  H. Schulz,et al.  Interacting electrons with spin in a one-dimensional dirty wire connected to leads , 1996, cond-mat/9612173.

[8]  E. Fradkin,et al.  DISTINCT UNIVERSAL CONDUCTANCES IN TUNNELING TO QUANTUM HALL STATES : THE ROLE OF CONTACTS , 1997 .

[9]  Nagaosa,et al.  Tunneling through a barrier in a Tomonaga-Luttinger liquid connected to reservoirs. , 1996, Physical review. B, Condensed matter.

[10]  Weiss,et al.  Low-temperature nonequilibrium transport in a Luttinger liquid. , 1995, Physical review. B, Condensed matter.

[11]  Saleur,et al.  Exact nonequilibrium transport through point contacts in quantum wires and fractional quantum Hall devices. , 1995, Physical review. B, Condensed matter.

[12]  Matveev,et al.  Conduction of a weakly interacting one-dimensional electron gas through a single barrier. , 1994, Physical review. B, Condensed matter.

[13]  N. Nagaosa,et al.  Single-barrier problem and Anderson localization in a one-dimensional interacting electron system. , 1993, Physical review. B, Condensed matter.

[14]  Fisher,et al.  Transmission through barriers and resonant tunneling in an interacting one-dimensional electron gas. , 1992, Physical review. B, Condensed matter.