Statistical mechanics of anisotropic 2D sheets

Atomically thin 2D sheets are now routinely produced and are used in a variety of electronic applications as well as in self-folding origami structures. The majority of 2D sheets, such as graphene, hexagonal boron nitride and the H phase of Transition Metal Dichalcogenides (TMDs), are isotropic. However, there also exist anisotropic 2D sheets, such as the T’ phase of TMDs. Note that in equilibrium most are in the isotropic H phase, however the T’ phase is stable for WTe₂. This motivated us to investigate the statistical mechanics of freely suspended anisotropic 2D sheets. Similar to isotropic sheets, thermal fluctuations effectively renormalize elastic constants for anisotropic sheets and make them scale dependent. Thermal fluctuations effectively increase flexural rigidities, while the in-plane elastic constants are reduced. We found 3 different universality classes (isotropic, orthorombic and monoclinic) that are characterized with different power-law exponents of the renormalized elastic constants. The T’ phase of TMDs falls in the orthorhombic universality class. Therefore, the elastic constants for WTe₂ are expected to scale differently than for other isotropic 2D sheets.