Stability of trions in coupled quantum wells modeled by two-dimensional bilayers

We report variational and diffusion quantum Monte Carlo calculations of the binding energies of isolated indirect trions and biexcitons in ideal two-dimensional bilayer systems within the effective-mass approximation, and with a Coulomb $1/r$ interaction between charge carriers. The critical layer separation at which trions become unbound has been studied for various electron-hole mass ratios, and found to be over an order of magnitude larger than the critical layer separation for biexcitons.

Figure 1

Schematic arrangement of two electrons (light green) and a hole (red) for a negative trion in a coupled quantum well, showing the definition of the interparticle distances. The two electrons are in a spin singlet state and hence act as distinguishable particles in the spatial wave function. The electrons and hole move in two dimensions in spatially separated layers.

Figure 2

Negative-trion binding energy as a function of interlayer spacing $d$ and electron-hole mass ratio $\sigma$, in excitonic units. The inset shows the edge of the region of stability for negative trions in greater detail.

Figure 3

(a) Electron-electron $\left[g_{{\text{X}}^{-}}^{\text{ee}}\left(r\right)\right]$ and (b) electron-hole $\left[g_{{\text{X}}^{-}}^{\text{eh}}\left(r\right)\right]$ pair-distribution functions for indirect negative trions in bilayers with different separations $d$ and electron-hole mass ratios $\sigma$. The $x$ axis shows the in-plane separation.