Junction of several weakly interacting quantum wires: a renormalization group study

Abstract

We study the conductance of three or more semi-infinite wires which meet at a junction. The electrons in the wires are taken to interact weakly with each other through a short-range density-density interaction, and they encounter a general scattering matrix at the junction. We derive the renormalization group equations satisfied by the S-matrix, and we identify its fixed points and their stabilities. The conductance between any pair of wires is then studied as a function of physical parameters such as temperature. We discuss the possibility of observing the effects of junctions in present day experiments, such as the four-terminal conductance of a quantum wire and crossed quantum wires.

RevTeX, 13 pages, including 4 eps figures

References in corpus (8)

• Bosonization and Strongly Correlated Systems
• Many-body spin related phenomena in ultra-low-disorder quantum wires
• Interacting electrons with spin in a one-dimensional wire connected to leads
• Spin-dependent transport in a quasiballistic quantum wire
• Nonequilibrium transport for crossed Luttinger liquids
• Transport through quasi-ballistic quantum wires: the role of contacts
• Transport and Coulomb drag for two interacting carbon nanotubes
• Conductance through contact barriers of a finite length quantum wire

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