The isolation of individual crystal planes from a large variety of exfoliating solids is one of the major progresses of material science in this century. These single-layer atomic crystals are stable under ambient conditions, exhibit high crystal quality, and they appear continuous on a macroscopic scale. Two-dimensional (2D) materials have diverse electronic properties, ranging from insulating hexagonal BN and semiconducting transition-metal dichalcogenides, to metallic graphene. Also their optical properties are exceptional. Their strong optical contrast is useful in microfabrication , the absorption of graphene is determined by the fine-structure constant , 2D transition-metal dichalcogenides are direct band semiconductors , while the bulk materials have an indirect band gap.
This richness in optical properties disguises very important subtleties in its physical description. Optical experiments have been interpreted by modelling these crystals as homogeneous slabs, with an effective thickness of the order of the interlayer spacing of the original exfoliating solid [1, 3, 4]. The reasons for this are at least two. The first, atomic force microscopes can indeed measure the thickness of these materials. This can be confused as an experimental confirmation of the slab model. The second, exfoliated 2D crystals can be single-layer or multi-layer and the slab model treats easily also multi-layer crystals.
In a recent paper  I fitted optical-contrast , ellipsometry  and absorption  experiments on graphene by modelling a 2D crystal as a zero-thickness interface with a complex surface conductivity and I compared the results with those for the slab model. A chi-squared test on the reported fits rejects the slab model at the 0.1% significance level or lower, while it is consistent with the surface-conductivity model. The paper shows how to extract from experimental data both the surface susceptibility (chi) and the surface conductivity (sigma) that emerge as the physical quantities useful to describe the optical response of single-layer 2D atomic crystals. For graphene I obtain, in the spectral range 450 nm - 750 nm, a chi = 8×10-10 ±3×10-10 m and a sigma =6.08×10-5 ±2×10-5 ohm-1 . While the experimental value of sigma has been reported several times , as far as I know, this is the first reliable experimental determination of chi. This result is very important because it correctly models the optical response these materials, relying on an accurate analysis of the experimental data. Once for all, it is shown that a single plane of atoms has no optical thickness, stressing once more how special 2D atomic crystals are.
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