Effect of a Geometric Potential on the Eigenfunction and Eigenvalue of the Energy of State in a Twisted Graphene Nanoribbon

Abstract

Abstract An expression is obtained for an effective geometric potential based on a coordinate system for a nanoribbon twisted in the form of a helicoid. The effective geometric potential for a Schrödinger equation is used to study a graphene nanoribbon of finite length with “armchair” edges under the action of an external electric field parallel to them. Solutions are calculated for the energy levels and wave functions of electrons in the vicinity of the Dirac point. It is shown there is only one state in the transverse direction.