LAUSR

We report a temperature-dependent Raman spectroscopy study of few-layer black phosphorus (BP) with varied incident polarization and sample thickness. The Raman-active modes A$_\text{g}^{1}$, B$_\text{2g}$, and A$_\text{g}^{2}$ exhibit a frequency downshift, while their linewidth tends to increase with increasing temperature. To understand the details of these phenomena, we perform first-principles density functional theory calculations on freestanding monolayer BP. The effect of thermal expansion is included by constraining the temperature dependent lattice constant. The temperature-induced shift of the phonon frequencies is carried out using \textit{ab initio} molecular dynamics simulations. The normal mode frequencies are calculated by identifying the peak positions from the magnitude of the Fourier transform of the total velocity autocorrelation. Anharmonicity induces a frequency shift for each individual mode and the three- and four-phonon process coefficients are extracted. These results are compared with those obtained from many-body perturbation theory, giving access to phonon lifetimes and the lattice thermal conductivity. We establish that the downshift phenomena are primarily due to phonon-phonon scattering while thermal expansion only has the indirect contribution of renormalizing the phonon-phonon scattering. Overall, the theoretical results are in excellent agreement with experiment, thus showing that controlling phonon scattering in BP could result in better thermoelectric devices or transistors that dissipate heat more effectively when confined to the nanoscale.