Figure 1

(a) Interlayer excitons arise when one stacks an electron and a hole layer in a heterostructure, separated by an insulator. The Coulomb attraction between the negative electrons and positive holes creates bound electron-hole pairs, commonly referred to as “interlayer excitons.” (b) In the presence of strong electron-electron interactions the electrons localize and only the spin degree of freedom remains. An exciton can now be viewed as the bound state of a double occupied and an empty site (a doublon-holon pair). The remaining electrons are not paired into excitons and contribute to the magnetic behavior.Reuse & Permissions

Figure 2

The absorptive part of the dynamical magnetic susceptibility ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ in a Mott insulating bilayer (a) doped to become an exciton condensate [(b), (c)]. (a) The spectrum of a Mott insulating bilayer with the same gap as the exciton condensates of (b) and (c). The gap determined by the interlayer Heisenberg coupling $J_{\perp }$ is taken to be so small that it is barely visible. The bandwidth of the triplon mode is of the order $Jz$. (b) In the presence of the exciton condensate, the magnetic excitation spectrum consists of propagating triplets with a gap in their spectrum as (a). Instead of the small $\mathcal{O}\left(Jz\right)$ bandwidth, the triplet has now an enhanced bandwidth $\mathcal{O}\left(z{t}_{ex}{\rho }_{SF}\right)$, proportional to the superfluid density. The enhancement can be understood as a result of the condensation of the interlayer excitons, whereby the exciton-spin interaction is transformed into a mechanism that promotes the propagation of the free triplets [see Eqs. (7) and (8)]. This result is computed using a linear spin wave approximation, using model parameters $t_{ex}=2,J=0.125,\alpha =0.04$, and $\rho =0.15$. (c) The same result as in (b), but now with a higher exciton density $\rho =0.27$. The triplet mode bandwidth is seen to scale with the exciton superfluid density.Reuse & Permissions

Figure 3

The absorptive part of the dynamical magnetic susceptibility ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ in the weak-coupling limit of both the exciton binding energy and electron-electron interactions. (a) The magnetic susceptibility is also in the exciton condensate phase dominated by the Lindhard continuum. This is qualitatively different from the triplons found in the strong-coupling limit of Fig. 2. Model parameters are ${\xi }_{1\mathbf{k}}=-zt{\gamma }_{\mathbf{k}}-\mu =-{\xi }_{2\mathbf{k}}$, $t_{\perp }=0.05zt$, $\mu =-0.8zt$, and $\Delta \overline{W}=t$. (b) For comparison we computed the ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ in an electron-hole bilayer without exciton condensation.Reuse & Permissions