Chiral Cavity Control of the Interlayer Exciton Energy Spectrum

TL;DR

Interlayer excitons in two-dimensional heterostructures can have their energy spectra manipulated by light-matter coupling in a time-reversal-symmetry-breaking chiral cavity. The authors derive an effective Hamiltonian with a cavity-induced term that depends on angular momentum and a dimensionless coupling $\alpha = \frac{1}{2}\left(\frac{g}{\Sigma \omega_c a^*}\right)^2$, and show the cavity breaks TRS and reorders the bound-state spectrum. As a result, the ground state can transition from an $s$-orbital ($\ell=0$) to a $p$-orbital ($\ell=-1$) with increasing $\alpha$ or interlayer separation $d$, delineated by a phase boundary $\alpha_c(d)$. This angular-momentum control enables potentially tunable single-photon emission and engineered excitonic devices in realistic device geometries, with energies expressed in $Ry^*$ and lengths in $a_B^*$ and applicable to interlayer separations typical of hBN-capped TMD stacks.

Abstract

Heterostructures of two-dimensional materials offer a versatile platform to study light-matter interactions of electron and hole gases. By separating electron and hole layers with an insulator long-lived electron-hole bound states known as interlayer excitons can form. We predict that by placing an interlayer exciton in a time-reversal-symmetry-breaking chiral cavity the energy spectrum of an interlayer exciton can be reordered. As a consequence of this reordering the ground state of the interlayer exciton can be driven from an s-orbital to a p-orbital, effectively changing the symmetry of the electron-hole pair. We present a phase diagram showing the couplings and separations required for a p-orbital excitonic ground state where we predict that larger interlayer separations require higher cavity couplings. We expect these results to be relevant for angular-momentum-tunable, single photon emission physics.

Figures (3)

• Figure 1: a) Heterostructure in a chiral cavity (gray disks). A device consisting of two H-phase TMD monolayers with interlayer separation d and cavity coupling $\alpha$: an electron (blue) and a hole (red) monolayer separated by insulating hBN (light gray). The TMD bilayer is surrounded by more hBN and encapsuled by two graphene gates (dark gray slabs). In experiment the voltage difference between the gates and TMDs allow for independent control of charge carriers in the TMDs. The cavity hosts purely left- or right-handed photons. b) Chiral cavity coupling can drive the ground state of an exciton from an isotropic s-orbital to an anisotropic p-orbital.
• Figure 2: a) First few energy levels of the indirect exciton in the absence of a cavity. The interlayer separation breaks the degeneracy between states with and without angular momentum. Angular momentum states and their time-reversed version remain degenerate. The table in a) is the legend used in a), b) and c). b) and c): effects of variation of $\alpha$ at $d = 0.5 \; a_B^*$ and interlayer separation $d$ at $\alpha = 5$ on the same same levels as a), respectively. The effects of decreasing $\alpha$ are similar to the effects of increasing $d$.
• Figure 3: a) Ground State Phase Diagram: as the separation of the layers increases, a higher cavity coupling is needed. The shaded region (blue) indicates parameters where the ground state is a p-orbital. The range of interlayer separations corresponds to typical experimental devices. b) Energies of lowest orbitals along phase boundary from a). Lowest $L = 0$ and lowest $L = -1$ energy levels are degenerate. There are no energy crossings nor are there any degeneracies other than the ground state.