Tight Binding Study of Multilayer Graphene With Arbitrary Stacking

It is well understood that the electronic properties of a crystal are greatly dependent on the band

structure at the Fermi level. The Dirac cones of graphene provide a basis for which much research

has been done in order to tune and analyze the electronic properties of the system at its Fermi level.

Traditionally, the semiconductor technique of doping has shown to be able to shift the Fermi level

away from the Dirac cones. We intend to do this without introducing any impurities but instead

through arbitrary stacking. We provide an analytical solution for finding the nonzero momentum

magnitudes that give energies at the Fermi level for arbitrarily stacked graphene, which introduce

rings around the Dirac points at the Fermi level, similar to semiconductor doping. Moreover, we

provide an analysis of inducing flat bands in an arbitrary stack, which provides consequences for

superconductivity.