Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers

Abstract

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 four-fold degenerate structural ground state, and a single energy scale E C (representing the * To whom correspondence should be addressed † Department of Physics. 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 B T m , and (ii) those having k B T 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 orderdisorder 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.

Controlled Sculpture of Black Phosphorus Nanoribbons

“…Further modeling of the nanosculpting effect would require a systematic study of electron-beam-induced disorder in BP 38 in addition to thermally induced defects. 39 …”

Polarization and valley switching in monolayer group-IV monochalcogenides

“…The energy curve for SnS has a minimum rather than a saddle point at Cmcm-ML, and therefore resembles a ferroelectric with first order phase transition, with the peculiarity that the Cmcm-ML structure is stable for all T > 0. Recently, based on Car-Parrinello molecular dynamics simulations, Mehboudi et al showed that monolayer monochalcogenides undergo an order-disorder phase transition [31]. Hence, since SnS and GeSe have four degenerate P nma-ML phases, we expect that the average total polarization goes to zero as temperature approaches T m .…”

Finite-temperature properties of nonmagnetic transition metals: Comparison of the performance of constraint-based semilocal and nonlocal functionals

“…vdW-DF-cx has already proven itself accurate and useful in a number of problems that involve both regions of sparse and dense electron distributions such as molecular dimers [16,40], layered materials [9,[41][42][43][44][45], semiconductors [9,46], molecular crystals [47,48], adsorption processes [21,49], as well as weak chemisorption, molecular switching, and molecular selfassembly [21,49,50]. The ACF foundation and the emphasis on conservation laws in the vdW-DF-cx construction further suggests a general-purpose nature [9] and motivates a comprehensive investigation of its performance also for regular dense matter.…”