Odd property

Nano Lett. http://doi.org/mvg (2013)

Physical properties and symmetry are intricately linked. For example, crystals that lack inversion symmetry can 'convert' incoming laser light into radiation with twice the original frequency — a nonlinear optical effect known as second-harmonic generation. The phenomenon is absent for centrosymmetric structures.

Yilei Li and colleagues have now explored second-harmonic generation in two types of layered materials: hexagonal boron nitride (hBN) and molybdenum disulphide (MoS₂). For each compound, stacks built of an odd number of layers — including the case of just a single layer — are non-centrosymmetric; those having an even number of sheets are centrosymmetric. Accordingly, Li et al. saw strong second-harmonic signals for stacks of an odd number of layers. For hBN, the intensity is nearly constant, whereas for MoS₂, the second-harmonic response decreases with increasing (odd) number of layers. This latter effect is attributed to increasing light absorption, which in turn is a consequence of the electronic band structure's dependence on the number of layers.

Hence second-harmonic generation provides a simple optical tool for characterizing the (parity of the) number of layers in hBN or MoS₂ stacks. Moreover, the measured intensity of the emitted radiation depends on the mutual orientation of the sample and the detector, enabling precise determination of the crystal's orientation.