Thermodynamic stability and vibrational anharmonicity of black phosphorene—beyond quasi-harmonic analysis

Abstract

Thermodynamic stability and vibrational anharmonicity of single layer black phosphorene (SLBP) are studied using a spectral energy density (SED) method. At finite temperatures, SLBP sheet undergoes structural deformation due to the formation of thermally excited ripples. Thermal stability of deformed SLBP sheet is analyzed by computing finite temperature phonon dispersion, which shows that SLBP sheet is thermodynamically stable and survives the crumpling transition. To analyze the vibrational anharmonicity, temperature evolution of all zone center optic phonon modes are extracted, including experimentally forbidden IR and Raman active modes. Mode resolved phonon spectra exhibits red-shift in mode frequencies with temperature. The strong anharmonic phonon–phonon coupling is the predominant reason for the observed red-shift of phonon modes, the contribution of thermal expansion is marginal. Further, temperature sensitivity of all optic modes are analyzed by computing their first order temperature co-efficient (χ), and it can be expressed as B 2g > > > > B 1g > & B 2u > B 1u for Raman and IR active modes, respectively. The quasi-harmonic χ values are much smaller than the SED and experimental values; which substantiate that quasi-harmonic methods are inadequate, and a full anharmonic analysis is essential to explain structure and dynamics of SLBP at finite temperatures.