Nature of electron states and magneto-transport in a graphene geometry with a fractal distribution of holes

We consider an infinite graphene geometry where bonds and sites have been removed selectively to map it onto an effective Sierpinski gasket comprised of hexagons. We show that such a structure is capable of sustaining an infinite number of extended single particle states inspite of the absence of any translational order. When each basic hexagonal plaquette in the Sierpinski geometry is threaded by a magnetic flux, the spectrum exhibits bands of extended eigenstates. The bands persist for any arbitrary value of the flux but disappear again as the flux becomes equal to half the fundamental flux quantum. The localization- de-localization issues are discussed thoroughly along with the computation of two terminal magneto-transport of finite versions of the lattice. The numerical results corroborate our analytical findings.