Emergence of an excitonic collective mode in the dilute electron gas

Abstract

By comparing two expressions for the polarization function given in terms of two different local-field factors, G_+(q,iw) and G_s(q,iw), we have derived the kinetic-energy-fluctuation (or sixth-power) sum rule for the momentum distribution function n(p) in the three-dimensional electron gas. With use of this sum rule, together with the total-number (or second-power) and the kinetic-energy (or fourth-power) sum rules, we have obtained n(p) in the low-density electron gas at negative compressibility (namely, r_s>5.25 with r_s being the conventional density parameter) up to r_s ~ 22 by improving on the interpolation scheme due to Gori-Giorge and Ziesche proposed in 2002. The obtained results for n(p) combined with the improved form for G_s(q,w+i0^+) are employed to calculate the dynamical structure factor S(q,w) to reveal that a giant peak, even bigger than the plasmon peak, originating from an excitonic collective mode made of electron-hole pair excitations, emerges in the low-w region at q near 2p_F (p_F: the Fermi wave number). Connected with this mode, we have discovered a singular point in the retarded dielectric function at w=0 and q ~ 2p_F.