High-pressure electronic structure and phase transitions in monoclinic InSe: X-ray diffraction, Raman spectroscopy, and density functional theory

Abstract

We have studied the crystal and electronic structure of monoclinic (MC) InSe under pressure finding a reversible phase transition to a ${\mathrm{Hg}}_{2}{\mathrm{Cl}}_{2}$-like tetragonal phase. The pressure evolution of the crystal structure was investigated by angle-dispersive x-ray diffraction and Raman spectroscopy in a diamond-anvil cell up to $30\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. From the diffraction experiments, we deduced that MC InSe becomes gradually more symmetric under pressure, transforming the crystal structure into a tetragonal one at $19.4\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$. This phase transition occurs without any volume change. Raman measurements under pressure confirmed the occurrence of a monoclinic-to-tetragonal transformation. The nondegenerate modes in the MC phase, especially the ${A}_{g}^{4}$ modes, exhibit a negative pressure coefficient, converging with the ${B}_{g}^{1}$ modes, and becoming an $Eg$ mode in the tetragonal phase. The experimental results are interpreted through density-functional theory (DFT) electronic-structure and total-energy calculations, which showed that beyond $18\phantom{\rule{0.3em}{0ex}}\mathrm{GPa}$ the tetragonal phase is the most stable phase. It is also shown that along the continuous change from monoclinic to tetragonal InSe, there is a progressive decrease of the band gap and eventually, in the tetragonal phase, there occurs a small band overlap. However, the Raman-effect and optical-absorption measurements suggest that this overlap is probably due to the usual DFT band-gap underestimation. Tetragonal InSe is most likely a low-gap semiconductor. The bonding in the monoclinic phase and that in the tetragonal InSe phase are compared.