Prospects to bypass nonlocal phenomena in metals using phonon-polaritons

TL;DR

The paper addresses whether nonlocal electron response in metals imposes limits on nanophotonic confinement for polaritons. It introduces hyperbolic image phonon-polaritons (HIPs) in thin hBN on Au and combines s-SNOM measurements with theory to map their dispersion. Experimentally, HIPs reach extremely large effective indices and reveal a dispersion blueshift that is explained by a 2 nm interfacial layer identified by TEM/EELS as carbon-oxygen rich. When this layer is included, the data show no measurable nonclassical damping as HIP phase velocities approach the Au Fermi velocity, suggesting HIPs can bypass the traditional velocity barrier and enable ultra-confined, local polaritons in vdW metal hybrids.

Abstract

Electromagnetic design relies on an accurate understanding of light-matter interactions, yet often overlooks electronic length scales. Under extreme confinement, this omission can lead to nonclassical effects, such as nonlocal response. Here, we use mid-infrared phonon-polaritons in hexagonal boron nitride (hBN) screened by monocrystalline gold flakes to push the limits of nanolight confinement unobstructed by nonlocal phenomena, even when the polariton phase velocity approaches the Fermi velocities of electrons in gold. We employ near-field imaging to probe polaritons in nanometre-thin crystals of hBN on gold and extract their complex propagation constant, observing effective indices exceeding 90. We further show the importance of sample characterisation by revealing a thin low-index interfacial layer naturally forming on monocrystalline gold. Our experiments address a fundamental limitation posed by nonlocal effects in van der Waals heterostructures and outline a pathway to bypass their impact in high-confinement regimes.

Figures (5)

• Figure 1: Prospects for extreme confinement and slow-down of HIP modes. Effect of hBN thickness on HIP phase velocity (red lines) and spacer thickness on AGP phase velocity (blue lines) at a frequency of 1500 cm$^{-1}$. Graphene is modelled with Fermi level $E_F=0.5$ eV and damping $\hbar\gamma=10$ meV. Horizontal grey dotted lines indicate possible nonlocal couplings to slow matter excitations. For AGPs, the phase velocity is influenced by the combined Fermi velocities of graphene and Au, leading to significant discrepancies between local and nonlocal theories -- the phase velocity cannot bypass the Fermi velocity barrier. For HIPs, the Fermi velocity of Au does not induce notable deviations, and the mode can be slowed beyond the intuitive phase velocity barrier. At an hBN thickness of 1 nm (corresponding to three atomic layers), the HIP phase velocity is approaching the phase velocity of plasmons associated with Shockley--Tamm surface states in Au yet is still far from the sound velocities causing spatial dispersion in hBN. At large thicknesses, the phase velocity is naturally bounded by the speed of light in the medium.
• Figure 2: Energy density distribution.a,b, Local (a) and nonlocal (b) energy density $U$ (multiplied by the spacing distance $d$) as a function of $d$ and position along the HIP-supporting heterostructure (schematic on the left), at a frequency of 1500 cm$^{-1}$. Energy density is calculated and normalised as described in the Supplementary information. c, Integrated energy density within the hBN (red), air (green), and Au (blue) regions, as percentage of the total integrated energy density in the full structure, plotted as a function of $d$. Results are calculated within both local (dashed) and nonlocal (solid) metal formalisms. d,e,f, same as (a), (b), (c), respectively, but for the AGP-supporting heterostructure depicted on the left. Graphene conductivity is always described through its nonlocal response. In all panels, dashed lines are added highlighting the hBN monolayer limit and the Fermi velocity of Au.
• Figure 3: Experimental setup and near-field imaging.a, Experimental heterostructure: monocrystalline Au flake with an hBN flake on top, probed by a metallic AFM tip. Inset to a, close-up of the hBN/Au interface displaying interference fringes probed by s-SNOM with a in-plane wave vector $q=2\pi/\lambda_\mathrm{HIP}$b, AFM measurement revealing terraces on the Au surface. Inset to b, surface terrace in the top left corner of the main image (scale bars, 250 nm). c, Spatial plot of the s-SNOM measurement of a sample at a frequency of 1480 cm$^{-1}$, where the field is saturated over the Au area. (scale bar, 250 nm). d, Line scans extracted from c and at frequency increments of 10 cm$^{-1}$ between 1460 and 1500 cm$^{-1}$. The line scans were all normalised and offset for ease of comparison. e, Normalised and offset Fourier spectrum and fit of the tip-launched part of the near-field signal in d. f,g, Experimental and theoretical dispersion relation, $q_0$ versus $\mathrm{Re}(q)$ (f) and $\mathrm{Im}(q)$ (g).
• Figure 4: Observation of interfacial layer.a, cross-sectional high-resolution TEM image of the hBN/Au interface where an interfacial layer is present (scale bar, 1 nm). b, EELS spectra of the interfacial layer with clear peaks at the carbon and oxygen K-edges.
• Figure 5: Systematic measurement of the dispersion.a,b,c, Measured (markers) dispersion of $\mathrm{Re}(q)$ (a), $\mathrm{Im}(q)$ (b), and the phase velocity (c) as a function of hBN thickness and HIP frequency. Classical theory (dashed lines) deviate considerably from our observations but are well accounted for when adding an interfacial layer (solid lines) in the classical theory.