Effect of strong phonon–phonon coupling on the temperature dependent structural stability and frequency shift of 2D hexagonal boron nitride

The temperature dependent structural stability, frequency shift and linewidth of 2D hexagonal boron nitride (h-BN) are studied using a combination of lattice dynamics (LD) and molecular dynamics (MD) simulations. The in-plane lattice parameter shows a negative thermal expansion in the whole computed temperature range (0–2000 K). When the in-plane lattice parameter falls below the equilibrium value, the quasi-harmonic bending (ZA) mode frequency becomes imaginary along the Γ–M direction in the Brillouin zone, leading to a structural instability of the 2D sheet. The ZA mode is seen to be stabilized in the dispersion obtained from MD simulations, due to the automatic incorporation of higher order phonon scattering processes in MD, which are absent in a quasi-harmonic dispersion. The mode resolved phonon spectra computed with a quasi-harmonic method predict a blueshift of the longitudinal and transverse (LO/TO) optic mode frequencies with an increase in temperature. On the other hand, both canonical (NVT) and isobaric–isothermal (NPT) ensembles predict a redshift with an increase in temperature, which is more prominent in the NVT ensemble. The strong phonon–phonon coupling dominates over the thermal contraction effect and leads to a redshift in LO/TO mode frequency in the NPT ensemble simulations. The out-of-plane (ZO) optic mode quasi-harmonic frequencies are redshifted due to a membrane effect. The phonon–phonon coupling effects in the NVT and NPT ensemble simulations lead to a further reduction in the ZO mode frequencies. The linewidth of the LO/TO and ZO mode frequencies increases in a monotonic fashion. The temperature dependence of acoustic modes is also analyzed. The quasi-harmonic calculations predict a redshift of ZA mode, and at the same time the TA (transverse acoustic) and LA (longitudinal acoustic) mode frequencies are blueshifted. The strong phonon–phonon coupling in MD simulations causes a redshift of the LA and TA mode frequencies, while the ZA mode frequencies are blueshifted with an increase in temperature.