Calculation of the Nonlinear Susceptibility in van der Waals Crystals

The development of theoretical models for crystals has led to the evolution of computational methods with which much more thorough investigations than previously possible can be done, including studies of the nonlinear optical properties. There has recently been a rise in interest in 2-dimensional materials; unfortunately, measurements of the nonlinear susceptibility of these materials in the wavelength range of the order of hundreds of nanometers by traditional methods are difficult. Studies of second-harmonic generation (SHG) from the transition-metal dichalcogenides (TMDCs), MoS2 and MoSe2, have been reported; however, SHG from other typical van der Waals crystals such as GaSe and other transition metal monochalcogenides (TMMCs) has rarely been studied under the same conditions. In this study, the 211 (i = 2, j = 1, k = 1) elements in the susceptibility matrices of GaSe, InSe, MoS2 and WS2 were calculated and compared. A tendency for the SHG intensity to weaken as the wavelength increases from 500 nm to 1000 nm was observed for GaSe and InSe, and, apart from some periodic fluctuations, no clear increase could be seen for these two materials in the SHG response curve in the near infrared. By comparison, MoS2 and WS2 have obvious peaks in both the visible and infrared bands. Calculations of the SHG response show peaks at around 500 nm (for GaSe), 570 (for InSe), 660 nm, 980 nm (for MoS2) and 580 nm, 920 nm (for WS2). Moreover, similarities between the SHG curves for GaSe and InSe and for MoS2 and WS2 were revealed, which may be due to the similarities found for these two groups of crystals.