Excitonic superfluidity and screening in electron-hole bilayer systems

Superfluidity in electron-hole bilayers in graphene and GaAs has been predicted theoretically many times but not yet definitively observed. A key controversy is the correct approximation for the screening of the Coulomb interaction for the pairing. Mean-field theories using different approximations for the screening lead to diametrically contradictory predictions for superfluidity. We test these different approximations against diffusion quantum Monte Carlo results and find good agreement with the mean-field theory that uses screening in the superfluid state, but large discrepancies with other approximations for screening. This mean-field theory predicts no superfluidity in existing devices, provides pointers for new devices to generate the superfluidity, and, very importantly, it permits calculations for complicated lattices at finite temperatures, impractical in Monte Carlo.

Figure 1

(a) Superfluid-normal phase diagram at zero temperature. Axes are layer separation $d$ and interparticle spacing $r_s$. Condensate fraction phase boundary $c=0$ for DQMC taken from Ref. [20] (dashed black curve with filled circles), and for superfluid state screened interaction (SS) (solid red line). (b) Condensate fraction $c=0.25$ contour line for DQMC, for screened interaction in the superfluid state (SS), for unscreened (US) (dotted green line), and for screened in the normal state (NS) (dash-dotted blue line).

Figure 2

Condensate fraction $c$ as a function of $r_s$ for barrier thickness $d$ as labeled. DQMC (Ref. [20]) (dashed black curve with filled circles); unscreened (US) (dotted green line); screened in superfluid state (SS) (solid red line); screened in normal state (NS) (dash-dotted blue line).

Figure 3

Superfluid gap ${\Delta }_{\max }$ at $T=0$ as a function of $r_s$, calculated for a Coulomb electron-hole pairing interaction which is unscreened (US) ${\Delta }_{\max }^{\left(\mathrm{US}\right)}$ (dotted green line); screened in the superfluid state (SS) ${\Delta }_{\max }^{\left(\mathrm{SS}\right)}$ (solid red line); screened in the normal state (NS) ${\Delta }_{\max }^{\left(\mathrm{NS}\right)}$ (dash-dotted blue line).