Graphene Islands as a Platform for Band-Structure Engineering

Multilayer graphenes have emerged as a versatile avenue towards exploring novel electronic phases of matter. Recently, nanoscale multilayer graphene islands have been realized experimentally, where the island is less than 50 nm in diameter and distinct in layer configuration from the contact portion of the same graphene sheets, the latter of which act as leads for transport probes. Here, we theoretically investigate how the proximity between these islands and their chemically identical environment modifies the electronic structure. Within the tight-binding approximation, we find that the proximity effect is enhanced by the closely matched momenta between both parts, creating an unusually strong band renormalization which persists as the island size is increased, and only limited by the coherence length. An effective single-unit-cell Hamiltonian to capture these modifications is derived, expressed in terms of interlayer hopping parameters that scale with the relative island area. We predict a substantially altered low-energy density of states for 3- and 4-layer graphene islands, demonstrating the tunability of the electronic structure by spatial size.