Confinement due to spin-orbit interaction in quantum point contacts

One-dimensional systems with spin-orbit interaction have been hotly studied in recent years as both candidates for injectors and detectors of spin current, and for their role in the search for emergent Majorana fermions. I describe the properties of a quantum point contact (QPC) in the presence of the spin-orbit interaction and external magnetic field using scattering theory. It is shown that Dirac fermion states appear leading to confinement of particles in the constriction and resonances in the QPC conductance. The spacing of resonances can be tuned by the external magnetic field. Experimentally, the level spacing can be made narrow, transforming the QPC into a deep trap. This effect is directly analogous to surface and edge states in three- and two-dimensional topological insulators, and represents a manifestation of emergent Dirac physics in a one-dimensional channel.