Resonant Multi-Lead Point-Contact Tunneling

Details Resonant Multi-Lead Point-Contact Tunneling Resonant Multi-Lead Point-Contact Tunneling

1997-10-29

arxiv.org/abs/cond-mat/9710305v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

18 pages, LaTeX, 5 figures, psfig

Scientific paper

We analyze a model of resonant point-contact tunneling between multiple Luttinger liquid leads. The model is a variant of the multi-channel Kondo model and can be related to the quantum Brownian motion of a particle on lattices with $\pi$-flux through each plaquette (in the 3-lead case, it is a honeycomb lattice with $\pi$-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 novel non-trivial 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 which has enhanced conductance resulting from an analogue of Andreev reflection at the point contact.

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