Transport in curved nanoribbons in a magnetic field

We study the low-field and ballistic electronic transport in curved nanoribbons subject to static and uniform magnetic fields, where the curved nanoribbon is placed between two leads that inject scattering states. The method we present is based on a tight-binding form of the time-independent two-dimensional Schrödinger equation in curvilinear coordinates, with electric scalar and magnetic vector potentials included, and it enables a numerical description of transport in arbitrarily shaped curved nanostructures. A description of transport in terms of the scattering-state basis in the presence of magnetic field, together with curvature and possibly misaligned contacts, requires the use of a local Landau gauge. Based on the use of a stabilized transfer matrix method, we compute the conductance and normalized electronic density at the Fermi level for several curved nanoribbons in cylindrical and toroidal geometry, with and without the magnetic field. The magnetic field determines the number of injected propagating modes by affecting the Landau-level energies in the contacts, while a complex interplay between the magnetic field and the nanoribbon shape (both its curvature and helicity) determines the transmission of injected modes.