Two-dimensional moiré phonon polaritons

TL;DR

The paper introduces a comprehensive framework for two-dimensional phonon polaritons in moiré systems, showing that moiré potentials create a new class of moiré PhPs with multiple flat bands and nano-patterned electromagnetic wavefunctions. By combining a lattice-based moiré PhP model with a macroscopic Huang-type theory and a continuum description, the authors demonstrate how long-wavelength light can excite near-field modes that exhibit subwavelength spatial structure dictated by the moiré lattice. They develop a mixed lattice-continuum approach and validate it with twisted bilayer hBN and MoTe$_2$, revealing that off-diagonal moiré couplings generate a proliferation of PhP branches whose detectability depends on phonon linewidth. The work establishes moiré superlattices as a versatile platform for engineering long-range light–matter interactions at the nanoscale and provides practical tools for predicting, analyzing, and potentially detecting these modes via near-field techniques. The continuum model offers efficient means to explore a range of twisting angles and materials, broadening the impact of moiré physics on nanophotonics and phononics."

Abstract

Phonon polaritons (PhPs) are hybrid light-matter modes. We investigate them in two-dimensional (2D) materials with twisted moiré structures, revealing that the moiré potential creates a new class of `moiré PhPs'. These exhibit a fundamental spectral reconstruction into multiple branches and, crucially, electromagnetic wavefunctions that are nano-patterned by the superlattice. Through numerical simulations based on realistic lattice models, we confirm the existence of these intriguing modes. The inherent nanoscale structuring produces a robust, spatially varying near-field response, establishing moiré superlattices as a platform for engineering light-matter interactions.

Figures (10)

• Figure 1: (a) A 2D polar sheet is positioned at $z=0$ in vacuum. The PhP exhibits characteristic 2D EM waves that decay along the $z$-axis, as illustrated by the purple coordinate system. The inset displays the long-wavelength ($\bm{q}=q\bm{e}_x$) LO and TO modes patterns in the $xy$-plane for a binary crystal. (b) The 2D PhP dispersion of the TM, TE modes near the light cone (LC) and resonance frequency $\omega_0$. For comparison, the LO, TO modes under the non-retarded approximation are also shown. In (b), we use $T/(2\omega_0c)=2.06\times10^{-4}$, obtained from the lattice model of monolayer hBN (SI Section 2.2).
• Figure 2: (a) The long-wavelength PhP dispersion of $2.65^{\circ}$ twisted bilayer hBN near $\nu_0=\omega_0/(2\pi)\approx 49.5$ THz ($q_0\approx 10^{-3}$ nm$^{-1}$), along the $\bar{\Gamma}-\bar{M}$ line, obtained by plotting the (normalized) spectrum $\ln(1+|\mathcal{L}(\bar{\bm{q}},\omega)|)$. Here a tiny linewidth $\delta/(2\pi)=10^{-3}$ THz is used to make each branch distinguishable. Many flat branches appear below the topmost dominant branch. (b) The detailed dispersion within the mini window $49.20$-$49.325$ THz.
• Figure 3: Field distributions of moiré PhPs in $2.65^{\circ}$ twisted bilayer hBN: in-plane ($z=0$ top row) and out-of-plane ($y=0$, bottom row) amplitudes $|\bm{E}_t|$ and $|E_z|$ along $\bar{\Gamma}-\bar{M}$ line at (a) $\bar{q}=0.01 \text{ nm}^{-1}$, $\nu=49.696$ THz; (b) $\bar{q}=0.01 \text{ nm}^{-1}$, $\nu=49.602$ THz; (c) $\bar{q}=0.01 \text{ nm}^{-1}$, $\nu=49.217$ THz; (d) $\bar{q}=0.05 \text{ nm}^{-1}$, $\nu=50.002$ THz. Fields are normalized to maxima of $1$. (a) and (c) indicate that, at a fixed $\bar{\bm{q}}$, the specific moiré pattern of EM waves is sensitive to the frequency. (a) and (d) are taken from the same branch.
• Figure 4: The local susceptibility as a function of frequency, calculated using linewidths (a) $\delta/(2\pi)=0.015$ THz ($0.5$ cm$^{-1}$) and (b) $\delta/(2\pi)=0.15$ THz ($5$ cm$^{-1}$). The red and blue curves denote the values at AA and AB points. The solid and dashed lines represent the real and imaginary parts. The black lines indicate their difference.
• Figure 5: TOC Graphic.