Many-flavor electron gas approach to electron-hole drops

A many-flavor electron gas (MFEG) is analyzed, such as could be found in a multivalley semiconductor or semimetal. Using the rederived polarizability for the MFEG, an exact expression for the total energy of a uniform MFEG in the many-flavor approximation is found; the interacting energy per particle is shown to be −0.574 447(E_ha₀^3/4m^∗3/4)n^1/4, with E_h being the Hartree energy, a₀ being the Bohr radius, and m^∗ being the particle effective mass. The short characteristic length scale of the MFEG motivates a local-density approximation, allowing a gradient expansion in the energy density and the expansion scheme is applied to electron-hole drops, finding a new form for the density profile and its surface scaling properties.