Strongly Coupled Exciton--Hyperbolic-phonon-polariton Hybridized States in hBN-encapsulated Biased Bilayer Graphene

TL;DR

This work addresses strong light–matter coupling in the mid-infrared by coupling electrically tunable excitons in biased bilayer graphene to hyperbolic-phonon-polaritons in hBN. Using an air/hBN/BBLG/hBN/air transmission-line analysis, the authors derive closed-form dispersion relations for hybridized exciton–HPhP states and reveal symmetry-driven selection rules that control which modes hybridize. They demonstrate multiple strongly coupled hybridized states in both symmetric and asymmetric hBN configurations, with even modes showing pronounced anticrossings near main exciton resonances and high-momentum modes decoupled by effective boundary conditions. The results establish a tunable MIR platform for engineering strongly coupled quasiparticles in biased graphene, with potential extensions to other layered graphene systems such as rhombohedral trilayer graphene, enabling controlled light–matter interactions in the long-wavelength regime.

Abstract

Excitons in biased bilayer graphene are electrically tunable optical excitations residing in the mid-infrared (MIR) spectral range, where intrinsic optical transitions are typically scarce. Such a tunable material system with an excitonic response offer a rare platform for exploring light-matter interactions and optical hybridization of quasiparticles residing in the long wavelength spectrum. In this work, we demonstrate that when the bilayer is encapsulated in hexagonal-boron-nitride (hBN)-a material supporting optical phonons and hyperbolic-phonon-polaritons (HPhPs) in the MIR-the excitons can be tuned into resonance with the HPhP modes. We find that the overlap in energy and momentum of the two MIR quasiparticles facilitate the formation of multiple strongly coupled hybridized exciton-HPhP states. Using an electromagnetic transmission line model, we derive the dispersion relations of the hybridized states and show that they are highly affected and can be manipulated by the symmetry of the system, determining the hybridization selection rules. Our results establish a general tunable MIR platform for engineering strongly coupled quasiparticle states in biased graphene systems, opening new directions for studying and controlling light-matter interactions in the long-wavelength regime.

Figures (5)

• Figure 1: Conductivity of BBLG for (a) $V=58\,\mathrm{meV}$ and (b) $V=115\,\mathrm{meV}$, with the in-plane and out-of-plane permittivity of hBN. The main (marked with arrows) and additional exciton energies (dashed black lines) are inside the band limits (dashed green lines). The configuration of BBLG encapsulated by hBN is illustrated as an inset.
• Figure 2: Hybridization of BBLG excitons and hBN HPhPs for the symmetric structure, with $\frac{d}{2}=50\,\mathrm{nm}$. The dispersion relation of the hybridized polariton in the symmetric case for BBLG with $V=115\,\mathrm{meV}$ (a) and $V=58\,\mathrm{meV}$ (b), calculated from Eq. \ref{['Eq hybrid sym even']} (dashed red lines) and Eq. \ref{['Eq hybrid sym odd']} (dashed blue lines), and simulated using TMM (colormap). Even modes of HPhP (green lines), calculated from Eq. \ref{['Eq HPhP']}, and exciton energies of BBLG (dashed black lines) are also plotted. The modal orders $L$ are marked in the figure. The even hybridized modes present an anticrossing behavior between even modes of HPhPs and the excitonic resonances of BBLG while the odd hybridized modes have the dispersion relation of odd HPhPs. The configuration is illustrated above the figure.
• Figure 3: Hybridization of BBLG excitons and hBN HPhP for the asymmetric structure in the upper Reststrahlen band, with $d_1=10\,\mathrm{nm}$ and $d_2=200\,\mathrm{nm}$. (a) The dispersion relation of the hybridized polariton for BBLG with $V=115\,\mathrm{meV}$ simulated using TMM (colormap) showing two sets of modes. (b) Zoom in on the low momentum modes of panel (a) together with the dispersion relation calculated from Eq. \ref{['Eq hybrid asym low']} (dashed red lines). Modes of HPhP for hBN with thickness of $d_1+d_2$ (green lines) and exciton energies of BBLG (dashed black lines) are also plotted. (c) Zoom out to the high momentum modes of panel (a) together with the dispersion relation calculated from Eq. \ref{['Eq hybrid asym high']} (dashed red lines). Odd modes of HPhP for hBN with thickness of $2d_1$ (blue lines) and exciton energies of BBLG (dashed black lines) are also plotted. The low momentum hybridized modes present an anticrossing behavior while the high momentum hybridized modes cross the main excitonic resonances. The configuration is illustrated as inset.
• Figure 4: Hybridization of BBLG excitons and hBN HPhP for the asymmetric structure in the lower Reststrahlen band, with $d_1=10\,\mathrm{nm}$ and $d_2=200\,\mathrm{nm}$. (a) The dispersion relation of the hybridized polariton for BBLG with $V=58\,\mathrm{meV}$ simulated using TMM (colormap) showing two sets of modes. (b) Zoom in on the low momentum modes of panel (a) together with the dispersion relation calculated from Eq. \ref{['Eq hybrid asym low']} (dashed red lines). Modes of HPhP for hBN with thickness of $d_1+d_2$ (green lines) and exciton energies of BBLG (dashed black lines) are also plotted. (c) Zoom out to the high momentum modes of panel (a) together with the dispersion relation calculated from Eq. \ref{['Eq hybrid asym high']} (dashed red lines). Odd modes of HPhP for hBN with thickness of $2d_1$ (blue lines) and exciton energies of BBLG (dashed black lines) are also plotted. The low momentum hybridized modes present an anticrossing behavior while the high momentum hybridized modes cross the main excitonic resonances.
• Figure 5: $d_\sigma$ for (a) $V=58\,\mathrm{meV}$ and (b) $V=115\,\mathrm{meV}$.