The electronic properties of graphene nanoribbons and the offset logarithm function

Graphene Nanoribbons (GN), being an important class of next-generation carbon materials, are of immense interest and find innumerable applications in diverse fields. A variation of the generalized Lambert W function, called the Offset Logarithm function, has been found to have important applications in fields such as physics, engineering and nanotechnology. We study the electronic properties of zigzag GN and use the generalized Lambert W function to study the eigenvalue equations of the massless Dirac equation applied to zigzag GN. We have studied the effects of nanoribbon width and determined the parameters that significantly affect the obtained solutions.