Fig. 2: Illustration of the alignment of electron pairs.
From: Electronic pair alignment and roton feature in the warm dense electron gas
Let the green bead be a fixed reference particle. Without an external perturbation [ϕext, dark grey sinusoidal line], the system is disordered on average in the WDM regime, see the blue beads. In order to follow ϕext, the particles have to re-align themselves to the minima of the latter, see blue arrow + red bead. In the process, they change the potential energy of the green reference particle by an amount of ΔW, see Eq. (3). In the regime of electronic pair alignment, λ ~ d, the energy shift ΔW is substantially negative. In other words, a density fluctuation with a corresponding q = 2π/λ contains comparably less energy due to its alignment to the potential energy landscape of the system (shaded green area). The random phase approximation (RPA) substantially underestimates this effect and, therefore, does not capture this correlation-induced red-shift.
