Anisotropic Ripple Deformation in Phosphorene

TL;DR

This study reveals a highly anisotropic ripple pattern in phosphorene, where deformation occurs only along the zigzag direction due to its puckered structure, impacting its electronic properties and potential device applications.

Contribution

First-principles calculations uncover a novel anisotropic ripple mode in phosphorene, supported by an analytical elasticity model, advancing understanding of its structural and electronic behavior.

Findings

Ripple deformation occurs only along zigzag direction up to 10% strain.

The anisotropic ripple pattern is due to phosphorene's puckered structure.

Analytical model explains ripple behavior under arbitrary strain.

Abstract

Two-dimensional materials tend to become crumpled according to the Mermin-Wagner theorem, and the resulting ripple deformation may significantly influence electronic properties as observed in graphene and MoS2. Here we unveil by first-principles calculations a new, highly anisotropic ripple pattern in phosphorene, a monolayer black phosphorus, where compression induced ripple deformation occurs only along the zigzag direction in the strain range up to 10%, but not the armchair direction. This direction-selective ripple deformation mode in phosphorene stems from its puckered structure with coupled hinge-like bonding configurations and the resulting anisotropic Poisson ratio. We also construct an analytical model using classical elasticity theory for ripple deformation in phosphorene under arbitrary strain. The present results offer new insights into the mechanisms governing the structural and electronic properties of phosphorene crucial to its device applications.