A fermionic approach to tunneling through junctions of multiple quantum wires

Abstract

Junctions of multiple one-dimensional quantum wires of interacting electrons have received considerable theoretical attention as a basic constituent of quantum circuits. While results have been obtained on these models using bosonization and Density Matrix Renormalization Group (DMRG) methods, another powerful technique is based on direct perturbation theory in the bulk interactions, combined with the Renormalization Group (RG) and summed in the Random Phase Approximation (RPA). This technique has so far only been applied to the case where finite length interacting wires are attached to non-interacting Fermi liquid leads. We reformulate it in terms of the single-particle S-matrix, formally unifying treatments of junctions of different numbers of leads, and extend this method to cover the case of infinite length interacting leads obtaining results on 2-lead and 3-lead junctions in good agreement with previous bosonization and DMRG results.

24 pages, 5 figures; v2

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• Y-junction of Luttinger-liquid wires out of equilibrium
• Tunneling into and between helical edge states - fermionic approach
• Nano-welding of quantum spin-$1/2$ chains at minimal dissipation
• Enhancement in tunneling density of states in Luttinger liquid -- role of non-local interaction
• Conductance scaling of junctions of Luttinger-liquid wires out of equilibrium
• Tunneling into a Luttinger-liquid coupled to acoustic phonons out of equilibrium
• Resonant Multilead Point-Contact Tunneling: Boundary State Formulation
• Emergent chirality in multi-lead Luttinger-liquid junctions out of equilibrium
• Tunneling density of states in Luttinger Liquid in proximity to a superconductor: Effect of non-local interaction