Compressibility and Spin/Valley Susceptibility of Electron Gas in Doped Two-Dimensional Semiconductors*

Due to the exchange interaction, the two-dimensional electron gas (2DEG) can have negative electronic compressibility and undergo a ferromagnetic transition below a critical density, which depends on the screening environment. In a uniform dielectric, the screening is simply characterized by the dielectric constant, which renormalizes the energy and electron density scale. However, in a 2D material or its heterostructure, the screening is characterized by a quasi-2D form with a intrinsic length scale called the 2D polarizability, resulting in different compressibility and spin/valley susceptibility for the 2DEG in doped 2D materials. With input from first-principles calculation, we calculate the total energy of the electron gas in such doped 2D semiconductor as a function of the carrier density and spin/valley polarization within the random-phase approximation. We find negative electronic compressibility and enhanced spin/valley susceptibility at low carrier density, which appear stronger in material with lower 2D polarizability and effective mass.