Simulating critical anion chemistry with indirect excitons

We study the effect of geometric constraints on the formation of indirect excitonic complexes with excess charge by considering the problem of two identical electrons moving in half-space subject to mutual Coulomb repulsion and the Coulomb attraction to a heavy hole of charge $Z$ residing on a flat impenetrable surface. We find that $Z=1$ is the critical charge necessary for binding, as compared to $Z_c\approx 0.911$ in the unconstrained system. This suggests that interlayer electron-hole systems may serve as a flexible and experimentally accessible platform to study electronic behavior close to the critical nuclear charge necessary for binding.

Figure 1

Schematic depiction of the arrangement considered.

Figure 2

Variational estimates of the binding energy $\mathrm{\Delta }E$ as a function of $Z$, both from the pure Chandrasekhar ansatz (10) and its slight extension with explicit angular correlation, (30), together with the asymptotics close to the stability edge $Z=1$, (27). The existence of a bound state for $Z<1$ is excluded in the singlet sector by the lack of appropriate excited states for the hydrogen anion. ${\tilde{E}}_0$ is the atomic-like energy unit defined in (1).

Figure 3

Optimal values of the variational parameters $\alpha ,\beta ,\lambda$ in the extended Chandrasekhar ansatz (30). The asymptotic behavior is described by (28) and (29). Note that while $\alpha$ and $\beta$ are measured in units of the inverse effective Bohr radius ${\tilde{a}}_0$ defined before (1), $\lambda$ is dimensionless.

Figure 4

Behavior of the optimal value of the variational parameter $\alpha$ determining the effective inverse Bohr radius of the further electron, as a function of $Z$. A crossover from the asymptotic regime of a weakly bound ion described by (28) to the quasineutral regime around $Z=2$ is observed.

Figure 5

Chandrasekhar radial probability density of finding an electron at distance $r$ from the hole, integrated over angles. Close to neutrality, it possesses a single maximum: for lower $Z$, a second maximum appears whose position wanders off to infinity as $Z\to 1$. The number of maxima can be employed to characterize the system as atom-like and/or anion-like. ${\tilde{a}}_0$ is the Bohr radius corresponding to electrons with the appropriate effective mass and the dielectric constant of the material, equal to unity in the pseudoatomic units $\hslash =1,m_e=1$ used in the text.