Coulomb interactions and delocalization in quantum Hall constrictions

We study a geometry-dependent effect of long-range Coulomb interactions on quantum Hall (QH) tunneling junctions. In an X-shaped geometry, duality rel ates junctions with opening angles alpha and (pi-alpha). We prove that dual ity between weak tunneling and weak backscattering survives in the presence of long-range interactions, and that their effects are precisely cancelled in the self-dual geometry alpha = pi/2. Tunneling exponents as a function of alpha, the interaction strength chi, and the filling fraction nu are cal culated. We find that Coulomb interaction induces localization in narrow ch annels (large alpha), and delocalization for sharply pinched constrictions (small alpha). Consequently, an insulator-to-metal transition happens at an angle alpha(c)(chi, nu) less than or equal to pi/2. We discuss the implica tions of our results for tunneling experiments in OH-constriction and cleav ed-edge geometries.