Anees P
Materials Physics Division, Indira Gandhi Centre for Atomic Research, Kalpakkam 603102, Tamil Nadu, India.
J Phys Condens Matter. 2020 May 15;32(33). doi: 10.1088/1361-648X/ab8761.
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 (), and it can be expressed as>Ag2>B3g1>B3g2>>Ag1&>for Raman and IR active modes, respectively. The quasi-harmonicvalues 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.
采用光谱能量密度（SED）方法研究了单层黑磷烯（SLBP）的热力学稳定性和振动非谐性。在有限温度下，SLBP薄片由于热激发褶皱的形成而发生结构变形。通过计算有限温度声子色散来分析变形后的SLBP薄片的热稳定性，结果表明SLBP薄片在热力学上是稳定的，并且能够经受住褶皱转变。为了分析振动非谐性，提取了所有布里渊区中心光学声子模式的温度演化，包括实验中禁戒的红外和拉曼活性模式。模式分辨的声子谱显示模式频率随温度发生红移。强烈的非谐声子 - 声子耦合是观察到的声子模式红移的主要原因，热膨胀的贡献很小。此外，通过计算所有光学模式的一阶温度系数（）来分析它们的温度敏感性，对于拉曼和红外活性模式，分别可以表示为>Ag2>B3g1>B3g2>>Ag1&>。准谐值远小于SED和实验值；这证实了准谐方法是不够的，全面的非谐分析对于解释有限温度下SLBP的结构和动力学至关重要。
