Quantum signature of exciton condensation

Exciton condensation, a Bose-Einstein-like condensation of excitons, was recently reported in an electronic double layer (EDL) of graphene. We show that a universal quantum signature for exciton condensation can be used to both identity and quantify exciton condensation in molecular systems from direct calculations of the two-electron reduced density matrix. Computed large eigenvalues in the particle-hole reduced-density matrices of pentacene and hexacene EDLs reveal the beginnings of condensation, suggesting the potential for exciton condensation in smaller scale molecular EDLs.

Figure 1

(a) A schematic of the hydrogen-chain EDL shows the distance $\ell$ between hydrogen atoms in each chain and the distance $d$ between the two chains. (b) The largest eigenvalue of the modified particle-hole RDM is shown as a function of the parameter $d$ in Å for $\ell =6\AA$.

Figure 2

For the hydrogen-chain EDL, the particle-hole pairing in the eigenstate associated with the largest eigenvalue of the modified particle-hole RDM is shown. In (a), (b), and (c), the probability density of the hole is shown for the particle placed at the position of the red dot. Coordinates $z$ and $x$ are shown in atomic units (a.u.), where 1 a.u. = 0.529 Å.

Figure 3

(a) A schematic picture of the hexacene EDL is shown. (b) The largest eigenvalue of the modified particle-hole RDM of the hexacene EDL reaches a maximum of 1.8 around $d=2.5$ Å.

Figure 4

For the hexacene EDL, the particle-hole pairing in the eigenstate associated with the largest eigenvalue of the modified particle-hole RDM is shown. In each graph, the probability density of the hole is shown for the particle placed on the layer at $z=-2.36$ a.u. at the position of the red dot. In (a), (b), and (c), the red dot is center, right of center, and far right of center, respectively. Coordinates $z$ and $x$ are shown in atomic units (a.u.) where 1 a.u. = 0.529 Å.