Finite temperature stability of single-layer black and blue phosphorus adsorbed on Au(1 1 1): A first-principles study

The finite-temperature stability of single-layer black (BP) and blue (bP) phosphorus deposited on a gold substrate is investigated using first-principles calculations. In contrast to previous studies, a density functional theory (DFT) treatment including van der Waals (vdW) corrections predicts that the thermo-structural properties do not lead to a phase transition from BP to bP. To account for entropic (i.e. finite temperature) effects on the stability of materials deposited on a substrate within a first-principles framework, we develop an algorithm to investigate phonons properties at the interface between the phosphorus layers and a metallic substrate. This approach greatly reduces the computational cost and makes it possible to use DFT to model vibrational properties of systems with hundreds of atoms, and especially those that can be separated into weakly interacting sub-systems. It also allows for the description of interfacial shear and breathing-like modes, which enter in the evaluation of finite temperature effects via the Helmholtz free energy. In contrast to the freestanding case, we find that bP is energetically more stable than BP adsorbed on Au(1 1 1) with an energy difference between these two phases equal to 46 meV/atom at room temperature.