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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 graphite (up to N≈7) the dominant flexural mode specific heat (due to its N-1 dependence) gives rise to a strong layer number-dependence on the pulsed laser ablation threshold energy density, while for 3D regime (N>>7) the ablation threshold saturates due to dominant acoustic mode specific heat. As a result, several energy density windows exist between the minimum energy densities that are required for ablating single, bi, or more layers of graphene, allowing layer number selectivity.


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