Pressure induced evolution of band structure in black phosphorus studied by $^{31}$P-NMR

Two-dimensional layered semiconductor black phosphorus (BP), a promising pressure-induced Dirac system as predicted by band structure calculations, has been studied by $^{31}\mathrm{P}$ nuclear magnetic resonance. Band calculations have been also carried out to estimate the density of states $D(E)$. The temperature and pressure dependences of the nuclear spin lattice relaxation rate $1/{T}_{1}$ in the semiconducting phase are well reproduced using the derived $D(E)$, and the resultant pressure dependence of the semiconducting gap is in good accordance with previous reports, giving a good confirmation that the band calculation on BP is fairly reliable. The present analysis of $1/{T}_{1}$ data with complemental theoretical calculations allows us to extract essential information, such as the pressure dependences of $D(E)$ and the chemical potential, as well as to decompose the observed $1/{T}_{1}$ into intrinsic and extrinsic contributions. An abrupt increase in $1/{T}_{1}$ at $P=1.63\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ indicates that the semiconducting gap closes, resulting in the enhancement of conductivity.