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Selectively creating regions of spatially varying thickness may enable the utilization of the electronic properties of N-layer (N=1 or more) graphene and other similar layered materials (e.g., topological insulators or layered superconductors) for novel devices and functionalities on a single chip. The ablation threshold energy density increases dramatically for decreasing layer numbers of graphene originating from the dimensional crossover of the specific heat. For the 2D regime of graphitedoi:10.1063/1.3584204 fatcat:cbhi4tfl4vhdnga7tbqtqnfx4a