Electron-electron interaction in a two-dimensional electron gas: Bound states at low densities

If the bare interaction between two electrons is dressed in the two-dimensional electron gas by the response of the many-body environment, pairing may occur. Here, we study numerically the existence and character of bound states in the case where the dressing in the pair-interaction energy is described by the Overhauser geminal model [A. W. Overhauser, Can. J. Phys. 75, 683 (1995)]. The starting point of the model is the exchange correlation hole around a single electron. We constrain the hole by arguments based on the results for the exchange-correlation energy and the contact density of the pair-correlation function. We find a bound state with the energy minimized at a certain electron gas density. On the basis of the behavior of the binding energy we discuss recent experimental findings for the electron density dependence of the critical temperature in cuprate, Chevrel-phase, and Li-intercalated ${\mathrm{Li}}_x\mathrm{Zr}\mathrm{N}\mathrm{Cl}$ superconductors.

Figure 1

The shielding function $F\left(z\right)$ defined in the text, as a function of $z={\beta }^2{R}^2∕2$.

Figure 2

Binding energies $E_b\left(r_s\right)$ in the screened electron-electron potential of Eq. (5). The energies are solutions to Eq. (9) with the effective mass $\mu =0.5$.

Figure 3

The radial density $2\pi R{\mid \Psi \left(R\right)\mid }^2$ and the electron-electron screened potential for the optimal value of $r_s=13.9$.