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. Thermal stability of SLBP sheet is analyzed by computing phonon dispersion at 300 K, which shows that SLBP sheet is dynamically stable at finite temperature and survives the crumpling transition. Temperature evolution of all zone center optic phonon modes are extracted, including experimentally forbidden IR and Raman active modes. Mode resolved phonon frequencies of optic modes shows significant deviation from quasi-harmonic prediction, which is ascribed to the effects of inclusion of higher order phonon-phonon scattering processes. Further, temperature sensitivity of each mode is analyzed by computing their first order temperature co-efficient (\c{hi}). The quasi-harmonic \c{hi} values are one order magnitude smaller than the SED and experimental values; which again substantiate that quasi-harmonic methods are inadequate, and a full anaharmonic analysis is essential to explain structure and dynamics of SLBP at finite temperatures.