Coulomb interactions and delocalization in quantum Hall constrictions

We study a geometry-dependent effect of long-range Coulomb interactions onquantum Hall (QH) tunneling junctions. In an X-shaped geometry, duality relatesjunctions with opening angles alpha and (pi - alpha). We prove that dualitybetween weak tunneling and weak backscattering survives in the presence of longrange interactions, and that their effects are precisely cancelled in the selfdual geometry alpha=pi/2. Tunneling exponents as a function of alpha, theinteraction strength chi, and the filling fraction nu are calculated. We findthat Coulomb interaction induces localization in narrow channels (large alpha),and delocalization for sharply pinched constrictions (small alpha).Consequently, an insulator to metal transition happens at an anglealpha_c(chi,nu) <=pi/2. We discuss the implications of our results fortunneling experiments in QH-constriction and cleaved-edge geometries.Comment: RevTeX 3.0, 13p., 5 figs with eps