Landauer-Type Transport Theory for Interacting Quantum Wires: Application to Carbon Nanotube Y Junctions

We propose a Landauerlike theory for nonlinear transport in networks of one-dimensional interacting quantum wires (Luttinger liquids). A concrete example of current experimental focus is given by carbon nanotube Y junctions. Our theory has three basic ingredients that allow one to explicitly solve this transport problem: (i) radiative boundary conditions to describe the coupling to external leads, (ii) the Kirchhoff node rule describing charge conservation, and (iii) density matching conditions at every node.

Figure 1

Schematic view of a Y junction. QWs extend from adiabatically contacted reservoirs with electrochemical potential ${\mu }_i$ at $x=-L$ to the node at $x=0$.

Figure 2

Nonlinear conductance $G_{11}(U)$ for $N=3$, ${\mu }_1=E_F+U$, ${\mu }_2={\mu }_3=E_F$, several temperatures and $g=1/2$.