Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers

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• 作者：Mehrshad Mehboudi ; Alex M. Dorio ; Wenjuan Zhu ; Arend van der Zande ; Hugh O. H. Churchill ; Alejandro A. Pacheco-Sanjuan ; Edmund O. Harriss ; Pradeep Kumar ; Salvador Barraza-Lopez
• 刊名：Nano Letters
• 出版年：2016
• 出版时间：March 9, 2016
• 年：2016
• 卷：16
• 期：3
• 页码：1704-1712
• 全文大小：800K
• ISSN：1530-6992

文摘

Ridged, orthorhombic two-dimensional atomic crystals with a bulk Pnma structure such as black phosphorus and monochalcogenide monolayers are an exciting and novel material platform for a host of applications. Key to their crystallinity, monolayers of these materials have a 4-fold degenerate structural ground state, and a single energy scale E_C (representing the elastic energy required to switch the longer lattice vector along the x- or y-direction) determines how disordered these monolayers are at finite temperature. Disorder arises when nearest neighboring atoms become gently reassigned as the system is thermally excited beyond a critical temperature T_c that is proportional to E_C/k_B. E_C is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which E_C ≥ k_BT_m, and (ii) those having k_BT_m > E_C ≥ 0, where T_m is a given material’s melting temperature. Black phosphorus and SiS monolayers belong to category (i): these materials do not display an intermediate order–disorder transition and melt directly. All other monochalcogenide monolayers with E_C > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. E_C/k_B is slightly larger than room temperature for GeS and GeSe, and smaller than 300 K for SnS and SnSe monolayers, so that these materials transition near room temperature. The onset of this generic atomistic phenomena is captured by a planar Potts model up to the order–disorder transition. The order–disorder phase transition in two dimensions described here is at the origin of the Cmcm phase being discussed within the context of bulk layered SnSe.