Electron correlations in a multivalley electron gas and Fermion-boson conversion

The correlation energy εc, the chemical-potential shift due to the correlation, μc, the compressibility {κ}, and the renormalization factor at the Fermi surface, zF, are calculated for the paramagnetic valley-unpolarized state of the multivalley electron gas that may be realized in a doped multivalley semiconductor or multivalley semimetal. The calculations are based on an improved version of the effective-potential expansion method, which is known to give accurate εc, μc, {κ}, and zF for a single-valley electron gas at metallic densities. The valley degeneracy is found to be a good parameter to connect the total energies of the electron gas of both paramagnetic and ferromagnetic states with that of the charged-boson system. Based on this connection, the possibility of a valley-polarized state is discussed.