Effects of fermion flavor on exciton condensation in double-layer systems

We use a fermionic path-integral quantum Monte Carlo framework to study the effects of fermion flavor on the physical properties of dipolar exciton condensates in double-layer systems. We find that by including spin in the system the effective interlayer interaction strength is weakened, yet this has very little effect on the Kosterlitz-Thouless transition temperature. We further find that, to obtain the correct description of screening, it is necessary to account for correlation in both the interlayer and intralayer interactions. We show that while the excitonic binding cannot completely suppress screening by additional fermion flavors, their screening effectiveness is reduced by intralayer correlations leading to much higher transition temperatures than predicted with large-$N$ analysis.

Figure 1

(a) Superfluid fraction for spinless (black circles, $N_f=2$) and spin-1/2 (blue triangles, $N_f=4$) symmetric double-layer electron-hole condensate, calculated from PIMC simulations of 40 electron-hole pairs. Estimates of $T_{\text{KT}}$ are made where the superfluid fraction drops to $1/2$, and lines are a guide to the eye. We plot normalized histograms of topological winding distributions, which measure superfluid density, Eq. (2), for the (b) spinless and (c) spin-1/2 cases. $P_{00}$ represents the probability height of the (0,0) point in the histograms.

Figure 2

Radial pair correlation functions for (a) spinless, $N_f=2$, and (b) spin-1/2, $N_f=4$ cases. (c) Intralayer exchange-correlation hole for the same spin species, $g^{\uparrow \uparrow }\left({\mathbf{r}}_{ij}\right)$. (d) Intralayer correlation hole for opposite spin species, $g^{\uparrow \downarrow }\left({\mathbf{r}}_{ij}\right)$.

Figure 3

(a) Interlayer and intralayer polarizabilities for $N_f=2$ vs the perturbation wave vector normalized by the Fermi wave vector. (b) Interlayer and intralayer polarizabilities for $N_f=4$ normalized by the Fermi wave vector. (c) Sum of the interlayer and intralayer polarizabilities for $N_f=2$ and $N_f=4$ normalized by the Fermi wave vector. In each plot the polarizabilities are plotted against the Lindhard response function (shaded line) in two dimensions and have been normalized by the density of states at the Fermi energy in two dimensions, $N_0$.