Shaping electron wave functions in a carbon nanotube with a parallel magnetic field

Transport through any electronic system is determined by the properties of its electronic states which serve as transport channels; their amplitude at the contacts is essential to the coupling to external leads. A magnetic field – through its vector potential – usually causes measurable changes in the electron wave function only in the direction transverse to the field. Here we demonstrate experimentally and theoretically that in carbon nanotube quantum dots, combining cylindrical topology and bipartite hexagonal lattice, a magnetic field along the nanotube axis impacts also the longitudinal profile of the electronic states. They can be tuned all the way from “half-wave resonator” shape, with nodes at both ends, to “quarter-wave resonator” shape, with an antinode at one end. This in turn causes a distinct dependence of the nonlinear conductance on the magnetic field. Our results shed new light on the impact of magnetic fields on quantum systems with nontrivial lattices and topology.