  Carbon nanoscrolls are material structures that have been shown to exhibit
excellent performances in electric capacity and carrier mobility. They also
represent a prime realization of radial superlattices whose geometric shape is
expected to modulate the electronic and magnetic properties. Here, we show that
these nanostructures display the Aharonov-Bohm effect even if they do not
possess the closed cylindrical geometry of carbon nanotubes. Using a
combination of density functional theory calculations and low-energy continuum
models, we determine the electronic states in a simple two-winding carbon
nanoscroll, and indeed show oscillations of the energy levels in the presence
of an axial magnetic field. We prove that these oscillations, and hence the
occurrence of the Aharonov-Bohm effect, are entirely due to electronic
tunneling between the two windings of the spiral-shaped scroll. We also show
that the open geometry of the scroll leads to the occurrence of one-dimensional
conducting channels. Our study establishes the occurrence of the Aharonov-Bohm
effect as a generic property of radial superlattices, including the recently
synthesized high-order van der Waals superlattices.
