Observation of quantum states without a semiclassical equivalence bound by a magnetic field gradient

Resonant transmission through electronic quantum states that exist at the zero points of a magnetic field gradient inside a ballistic quantum wire is reported. Since the semiclassical motion along such a line of zero magnetic field takes place in the form of unidirectional snake trajectories, these states have no classical equivalence. The existence of such quantum states has been predicted more than a decade ago by theoretical considerations. We further show how their properties depend on the amplitude of the magnetic field profile as well as on the Fermi energy.