Many-flavor electron gas approach to electron-hole drops
Abstract
A many-flavor electron gas (MFEG) is analyzed, such as could be found in a multi-valley semiconductor or semimetal. Using the re-derived 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 -0.574447Eh a03/4 m*3/4 n1/4 with Eh being the Hartree energy, a0 Bohr radius, and m* 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.
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