Buckling on stanene: the role played by spin-orbit coupling and pseudo Jahn-Teller effect

Abstract

ABSTRACTTwo-dimensional group IV layers beyond graphene, as silicene, germanene and the Sn-based stanene, have been recently synthesized by molecular beam epitaxy. Density Functional Theyory (DFT) calculations predict low-buckled structures for these 2D nanosheets, with a hexagonal honeycomb conformation, typical of the graphene-like surfaces. The buckling parameter δ increases from Si to Sn-based layers, with a maximum predicted of 0.92 Å for stanene. High-buckled structures for these materials resulted to be unstable. We have previously shown that for silicene and germanene, the origin of the buckled structure resides on the pseudo Jahn-Teller puckering distortion, resulting from non-adiabatic effects. It has been shown that hexagermabenzene, the single hexagonal unit of germanene, is subject to a strong vibronic coupling whose origin is the pseudo Jahn-Teller effect. This coupling resulted to be around ten times larger than the one obtained for hexasilabenzene. For stanene, an additional effect needs to be considered to understand the origin of buckling: the spin-orbit coupling (SOC). This SOC contributes to open an electronic band gap, enabling the use of these layers as nanoelectronic components. In this work, we present an analysis based on DFT in the Zeroth-Order Regular Approximation (ZORA) for both scalar relativistic and spin-orbit versions that quantify the influence of the spin-orbit coupling in the puckering of Sn6H6. Also, under the linear vibronic coupling model between the ground and the lowest excited states, we present the pseudo Jahn-Teller contribution. The scalar ZORA approximation is used to perform time-dependent DFT calculations to incorporate the low-energy excitations contributions. Our model leads to the determination of the coupling constants and predicts simultaneously the Adiabatic Potential Energy Surface behavior for the ground and excited states around the maximum symmetry point. These values allow us to compare the Jahn-Teller relevance in buckling with the other group IV layers.