Ground state properties of electron-hole bilayer: Mass-asymmetric effect

We study the effects of mass asymmetry on the ground state properties of an electron-hole bilayer (EHBL) system at $T=0$ by using the quantum Monte Carlo method. Particularly, we use the variational Monte Carlo method to calculate the pair-correlation function $g\left(r\right)$ and the condensation fraction $c$ at a fixed density for different values of interplaner distance $d$ and extract the phases of the EHBL system. We use a single trial wave function that can describe fluid, excitonic, and biexcitonic phases. We find that the excitonic fluid phase is stable in the region of $d\ge 0.25\mathrm{a}.\mathrm{u}.$ and a transition from the excitonic fluid phase to the biexcitonic fluid phase at $d=0.24\mathrm{a}.\mathrm{u}.$

Figure 1

VMC expectation values of $c\left(r\right)$ for the EHBL bilayer at $d=9$, 5, 2, 0.3, 0.2, and 0.05 a.u. for $r_s=5\mathrm{a}.\mathrm{u}.$ and $m_h=7\times m_e$.

Figure 2

Intralayer PCF, (a) $g_{e^{\uparrow }{e}^{\downarrow }}$, (b) $g_{h^{\uparrow }{h}^{\downarrow }}$, (c) $g_{e^{\uparrow }{e}^{\uparrow }}$, and (d) $g_{h^{\uparrow }{h}^{\uparrow }}$ and interlayer PCF, (e) $g_{e^{\uparrow }{h}^{\uparrow }}$ and (f) $g_{e^{\uparrow }{h}^{\downarrow }}$ for $d=5$, 0.5, 0.3, 0.2, and 0.05 a.u. at $r_s=5\mathrm{a}.\mathrm{u}.$ Up- $(\uparrow )$ and down- $(\downarrow )$ arrows represent up-spin and down-spin charge carriers, respectively. The legends are displayed in (c). The inset shows the zoomed view of the same data near the origin.

Figure 3

The same- and opposite-spin $e-h$ PCFs are shown as black-thick lines and green-thin lines (overlapped on the black-thick lines), respectively. The PCFs corresponding to the lower value at $r=0\mathrm{a}.\mathrm{u}.$ is for $d=0.2$ and that for the higher value is for $d=0.05\mathrm{a}.\mathrm{u}.$ The inset shows the zoomed view of the same data near the origin.