Negative compressibility in graphene-terminated black phosphorus heterostructures

Negative compressibility is a many-body effect wherein strong correlations give rise to an enhanced gate capacitance in two-dimensional (2D) electronic systems. We observe capacitance enhancement in a newly emerged 2D layered material, atomically thin black phosphorus (BP). The encapsulation of BP by hexagonal boron nitride sheets with few-layer graphene as a terminal ensures ultraclean heterostructure interfaces, allowing us to observe negative compressibility at low hole carrier concentrations. We explain the negative compressibility based on the Coulomb correlation among in-plane charges and their image charges in a gate electrode in the framework of Debye screening.