Two-Dimensional Disorder in Black Phosphorus and Monochalcogenide Monolayers

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

Research output: Contribution to journalArticlepeer-review


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 EC (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 Tc that is proportional to EC/kB. EC is tunable by chemical composition and it leads to a classification of these materials into two categories: (i) Those for which EC ≥ kBTm, and (ii) those having kBTm > EC ≥ 0, where Tm 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 EC > 0 belonging to class (ii) will undergo a two-dimensional transition prior to melting. EC/kB 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.

Original languageEnglish (US)
Pages (from-to)1704-1712
Number of pages9
JournalNano letters
Issue number3
StatePublished - Mar 9 2016


  • 2D atomic materials
  • black phosphorus
  • layered monochalcogenides
  • molecular dynamics
  • phase transitions
  • structural degeneracies

ASJC Scopus subject areas

  • Bioengineering
  • General Chemistry
  • General Materials Science
  • Condensed Matter Physics
  • Mechanical Engineering


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