Riemann Surfaces of Carbon as Graphene Nanosolenoids

Traditional inductors in modern electronics consume excessive areas in the integrated circuits. Carbon nanostructures can offer efficient alternatives if the recognized high electrical conductivity of graphene can be properly organized in space to yield a current-generated magnetic field that is both strong and confined. Here we report on an extraordinary inductor nanostructure naturally occurring as a screw dislocation in graphitic carbons. Its elegant helicoid topology, resembling a Riemann surface, ensures full covalent connectivity of all graphene layers, joined in a single layer wound around the dislocation line. If voltage is applied, electrical currents flow helically and thus give rise to a very large (∼1 T at normal operational voltage) magnetic field and bring about superior (per mass or volume) inductance, both owing to unique winding density. Such a solenoid of small diameter behaves as a quantum conductor whose current distribution between the core and exterior varies with applied voltage, resulting in nonlinear inductance.