Ballistic transport of electrons and composite fermions in narrow cross junctions

We describe the magnetotransport properties in cross junctions of narrow wires in the ballistic regime. The resistance is determined solely by the scattering from the geometry. It is unconventionally nonlocal and can be negative. These properties arise from the four-terminal nature of the resistance measurements. We consider the ballistic transmission under two circumstances: around zero magnetic field and in the vicinity of the half-filling of the lowest Landau level, where an electron and a composite fermion are the relevant particles, respectively. The electron trajectories are made random and chaotic by smooth corners in cross junctions. The magnetic field dependence of the negative bend resistance reflects the nature of the trajectories in the rounded junctions. For the composite fermion, nonuniform effective magnetic fields additionally modify the ballistic trajectories. We also investigate quantum ballistic transmission of quasiparticle excitations in the normalconductor-superconductor (NS) junctions. In hybrid NS systems, an electron (a hole) is reflected as a hole (an electron) from the NS interface. This Andreev reflection leads to a rich variety of behaviors in the composite structures.