Resonant multilead point-contact tunneling

Abstract

We analyze a model of resonant point-contact tunneling between multiple Luttinger-liquid leads. The model is a variant of the multichannel Kondo model and can be related to the quantum Brownian motion of a particle on lattices with $\ensuremath{\pi}$ flux through each plaquette (in the three-lead case, it is a honeycomb lattice with $\ensuremath{\pi}$ flux). By comparing the perturbative and instanton gas expansions, we find a duality property of the model. At the boundary, this duality exchanges Neumann and Dirichlet boundary conditions on the Tomonaga-Luttinger bosons, which describe the leads; in the bulk, it exchanges the ``momentum'' and ``winding'' modes of these bosons. Over a certain range of Luttinger-liquid parameter g, a nontrivial intermediate coupling fixed-point controls the low-energy physics. The finite conductance at this fixed point can be exactly computed for two special values of g. For larger values of g, there is a stable fixed point at strong coupling that has enhanced conductance resulting from an analogue of Andreev reflection at the point contact.