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 $-0.574447(E_{h}a_{0}^{3/4}m*^{3/4})n^{1/4}$, with $E_h$ being the Hartree energy, $a_0$ 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. The formalism is verified using both Quantum Monte Carlo and density-functional theory calculations.