Black phosphorene exhibiting negative thermal expansion and negative linear compressibility

Positive expansion on heating, and positive contraction on hydrostatic compression are our general understanding. Actually, the abnormal negative thermal expansion (NTE) or negative linear compressibility (NLC) behavior is permissible, but exists in very few materials. Interestingly, we find that the NTE and NLC behaviors can coexist in the low-dimensional black phosphorene using first-principles calculations. In the temperature-field, the volume-NTE of black phosphorene can be exhibited below about 200 K, while the axial-NTE exists in the whole studied temperature range. In the hydrostatic pressure-field, the NLC behavior can occur along a zigzag direction or armchair direction in different pressure ranges. The phonon abnormality in black phosphorene is detected. It is found that acoustic phonons, especially the lowest-frequency TA_z mode, play a very important role. The re-entrant honeycomb network in black phosphorene, as the specific topology, will facilitate the occurrence of NTE and NLC behaviors. This work can provide some foundations and clues for exploring the abnormal properties in other 2D materials.