Acoustic Graphene Plasmons

• Acoustic graphene plasmons (AGPs) are ultraconfined, linearly dispersing collective charge oscillations in graphene-based heterostructures, distinct from conventional plasmons.
• They arise from image charge effects and double-layer coupling, leading to a linear ω ∝ q dispersion that enhances field confinement dramatically.
• AGPs offer promising applications in nanophotonic devices, enabling Purcell enhancement, ultrasensitive sensing, and tunable quantum emitter control.

Acoustic graphene plasmons (AGPs) are ultraconfined, linearly dispersing collective charge oscillations emerging in graphene-based heterostructures where the Coulomb interaction is strongly modified by proximal metallic screening, band structure anisotropy, or vertical coupling between graphene layers. AGPs exhibit acoustic (ω ∝ q) dispersion at long wavelengths, with field confinement orders of magnitude below the free-space limit in both in-plane and vertical directions. Their existence, properties, and device applications are fundamentally distinct from standard graphene plasmons, which generally follow a non-acoustic (ω ∝ √q) scaling.

1. Physical Origins and Theoretical Models

1.1. Coupling-Induced Acoustic Dispersion

AGPs primarily arise from image charge effects when a graphene sheet is placed nanometers above a conducting substrate (e.g., metal, double graphene, or metal–insulator–graphene (MIG) geometry). Image charges in the substrate/or second graphene layer convert the long-range 1/q component of the 2D Coulomb potential into a constant at low q, resulting in a linear plasmon dispersion. For monolayer graphene separated by a distance d from a metal, the screened Coulomb interaction reads

$$V_d(q) = 2\pi e^2 \frac{1-e^{-2qd}}{q} \xrightarrow{qd \ll 1} 4\pi e^2 d,$$

which yields an RPA pole at

$$\omega_{\rm AGP}(q) \approx c_s q, \qquad c_s = v_F \sqrt{\frac{4\pi e^2 d n}{\hbar v_F}},$$

where n is carrier density and v_F the graphene Dirac velocity (Principi et al., 2011, Principi et al., 2018, Alonso-Gonzalez et al., 2016, Salasnich, 2021).

1.2. Double-Layer and Anisotropy Scenarios

In double-layer graphene with a thin interlayer dielectric of thickness g, symmetric (optical) and antisymmetric (acoustic) plasmonic branches arise, the latter exhibiting antisymmetric charge oscillations between layers and linear ω ∝ q dispersion at long wavelengths (Lee et al., 2020). Additionally, AGPs may emerge in free-standing doped graphene along crystal axes where the Fermi surface features strong velocity anisotropy; RPA calculations predict a second, acoustic branch from out-of-phase excitations of the two distinct velocity carrier populations (Pisarra et al., 2013).

1.3. Quantum and Nonlocal Effects

Ultimate field confinement, down to atomic scale, pushes AGP properties into the regime where nonlocal conductivity, surface-response, and quantum finite-size corrections in the metal substrate become non-negligible (Gonçalves et al., 2020, Echarri et al., 2019). Surface screening can be characterized via Feibelman d-parameters, inducing resolvable shifts (Δq/q) in AGP dispersion for single-layer and few-layer metal substrates, with the largest impact at vanishing spacer thickness (Gonçalves et al., 2020, Echarri et al., 2019).

2. Analytical Formulation: Dispersion, Confinement, and Mode Structure

2.1. Dispersion Relations

Representative AGP systems and their characteristic dispersion laws:

System	Dispersion, ω(q)	Key Parameter
Graphene/metal (MIG)	ω(q) = v_p q	v_p ∝ √(E_F d)
Double-layer graphene	ω_-(q) ≈ v_a q	v_a ∝ gap g, conductivity σ
Free graphene (anisotropy)	ω(q) = v_s q (acoustic)	v_s < v_{F1}, v_{F2}

For the MIG case, field matching at the interfaces plus graphene sheet conductivity yields (in local Drude approximation):

$$q(\omega) = \frac{i \omega \epsilon_0 (\epsilon_1 + \epsilon_2)}{\sigma(\omega)}, \quad \omega = v_p q$$

where σ(ω) is graphene’s conductivity, and the effective mode velocity v_p can reach values as low as 0.01c, compressing λ_p to λ_0/100 or below (Menabde et al., 2020, Principi et al., 2018, Alonso-Gonzalez et al., 2016, Epstein et al., 2020).

2.2. Confinement Metrics

AGPs demonstrate extreme electromagnetic mode compression, measured by lateral confinement index n_eff = q/k_0, vertical mode length ℓ_z = 1/q, and effective mode volumes V_eff ≪ λ_0^3. Monoatomic spacers yield n_eff ≳ 10^3, with vertical fields localized to sub-nanometer gaps (Lee et al., 2020, Chen et al., 2018, Gonçalves et al., 2020). AGP nanoresonators achieve mode volumes down to 5×10^{-10} λ_0^3 (for a few-nm dielectric gap) (Epstein et al., 2020, Gruber et al., 2 Dec 2025).

3. Excitation Mechanisms and Coupling Strategies

3.1. Near-Field and Far-Field Coupling

Excitation of AGPs generally requires momentum matching due to their large q. Efficient coupling strategies include:

• Nano-emitters or dipole arrays positioned at controlled symmetry points to selectively launch optical or acoustic modes; vertical dipoles in the mid-plane maximize acoustic content (χ ≈ +1) (Lee et al., 2020).
• Magnetic-resonance patch antennas (e.g., Ag nanocubes atop graphene/hBN/metal) provide direct far-field coupling via localized magnetic dipoles, obviating the need for patterning or gratings (Epstein et al., 2020).
• Grating-coupled arrays (metal ribbon array or dielectric patterning) convert free-space photons to AGPs, phase-matched at k_{AGP} = 2π/P, P being the array period (Menabde et al., 2020).
• Broadband focusing by electrical current: application of DC bias induces angular tailoring and nonreciprocal Doppler shifted AGP spectra (Sammon et al., 2021).

3.2. Purcell Enhancement and Strong Coupling

AGP cavities allow for Purcell enhancement of spontaneous emission by up to six orders of magnitude in the mid-IR, with quantum efficiencies exceeding 90% in optimized geometries (Gruber et al., 2 Dec 2025). Multipolar (E2, E3), two-photon, and entangled-photon emission are all significantly boosted, offering on-chip, voltage-tunable, quantum light sources (Gruber et al., 2 Dec 2025).

4. Device Platforms, Tunability, and Applications

4.1. Nanopatterned and Layered AGP Devices

Key device structures include:

• Nanometric AGP cavities defined by metallic nanocubes over graphene/hBN/metal (Epstein et al., 2020, Gruber et al., 2 Dec 2025).
• Patterned double-layer graphene with monoatomic hBN spacers for maximum confinement (Lee et al., 2020).
• Metal–insulator–graphene planar stacks, supporting propagating, resonant, and topological AGPs (Menabde et al., 2020, Rappoport et al., 2021, Soares et al., 30 Nov 2025).
• Heterostructures with transition-metal dichalcogenides (TMDs) for strong plasmon–phonon hybridization and ultrasensitive environmental sensing (Lavora et al., 21 Jun 2024).

4.2. Electrical and Structural Tunability

The AGP modal frequency is set by graphene Fermi energy, interlayer/gap thickness, and the environment. Electrostatic gating provides real-time control of resonance position and field enhancement (Epstein et al., 2020, Gruber et al., 2 Dec 2025). Spacer thickness and vertical component engineering—down to monoatomic limits—allow access to quantum/surface nonlocal effects (Lee et al., 2020, Gonçalves et al., 2020, Echarri et al., 2019).

4.3. Technological Applications

AGPs enable:

• Active and reconfigurable mid-IR metasurfaces (Lee et al., 2020, Menabde et al., 2020).
• Ultrasensitive vibrational/chemical sensing with mode volume below 10^{-4}λ_0^3 and refractive index figure of merit (FOM) exceeding conventional metal antennas (Chen et al., 2018).
• Electrically tunable quantum emitters, sources of ultrafast photons, and entangled pairs at mid-IR and telecom wavelengths (Gruber et al., 2 Dec 2025).
• Nonlinear optical elements, photodetectors, modulators, deep-subwavelength THz components (Alonso-Gonzalez et al., 2016, Menabde et al., 2020).
• Probing of quantum metal surface response and dielectric properties with Ångström precision (Gonçalves et al., 2020).

5. Hybridization, Coupling, and Topological Effects

5.1. Plasmon–Phonon Interaction

AGPs efficiently hybridize with optical phonons in graphene or TMD substrates, yielding avoided crossing gaps and bidirectional energy flow between lattice and electrons (Nazarov et al., 2013, Lavora et al., 21 Jun 2024). The coupling strength is greatly enhanced by metallic screening, entering the ultrastrong-coupling regime, and can be used to control vibrational processes or lattice cooling (Lavora et al., 21 Jun 2024).

5.2. Topological AGPs and Plasmonic Crystals

Patterned AGP systems (e.g., periodic arrays of nanorods or Fermi level modulation) realize analogues of the Su-Schrieffer-Heeger (SSH) model and support topologically nontrivial plasmonic bands and interface states protected by Zak phase quantization (Rappoport et al., 2021, Soares et al., 30 Nov 2025). The plasmonic band structure can be engineered via lateral patterning or periodic gating, and edge states are directly observable via far-field or near-field probing.

6. Quantum Effects, Ultimate Confinement, and Experimental Signatures

6.1. Quantum and Nonlocal Corrections

In the sub-nanometer regime, quantum corrections to screening—quantified by Feibelman d-parameters—are significant. AGP dispersion becomes sensitive to the electronic structure of the underlying metal, offering a platform to measure surface response with unprecedented spatial accuracy (Gonçalves et al., 2020, Echarri et al., 2019).

6.2. Experimental Detection

Signature features of AGPs in experiments include:

• Linear (acoustic) plasmon dispersion ω ∝ q, in contrast to ω ∝ √q in unscreened systems (Alonso-Gonzalez et al., 2016, Menabde et al., 2020).
• Strongly reduced plasmon wavelength, e.g., λ_p ≈ λ_0/66 at THz frequencies (Alonso-Gonzalez et al., 2016).
• Ultra-confined near-fields visible with s-SNOM, photocurrent near-field microscopy, or electron energy-loss spectroscopy (EELS) (Menabde et al., 2020, Alonso-Gonzalez et al., 2016).
• Spectral focusing and nonreciprocity under DC current bias (Sammon et al., 2021).

Quality factors of AGPs in realistic platforms typically range from Q ≈ 10–100, with vertical and lateral field enhancement up to several orders of magnitude compared to free-space configurations (Lee et al., 2020, Principi et al., 2018, Gruber et al., 2 Dec 2025, Epstein et al., 2020).

7. Outlook

AGPs provide an expandable platform for the exploration of strong light–matter interaction at the atomic scale, topologically protected plasmonic phenomena, and tunable quantum optical devices. Ongoing work addresses ultimate confinement, ultrastrong coupling regimes, and integration with quantum emitters and novel 2D heterostructures. The interplay of screening, quantum surface effects, and device engineering defines the operational landscape and performance limits of AGP-based technologies.

Key references: (Lee et al., 2020, Principi et al., 2011, Principi et al., 2018, Menabde et al., 2020, Epstein et al., 2020, Gruber et al., 2 Dec 2025, Echarri et al., 2019, Gonçalves et al., 2020, Menabde et al., 2020, Soares et al., 30 Nov 2025, Lavora et al., 21 Jun 2024, Rappoport et al., 2021, Nazarov et al., 2013, Alonso-Gonzalez et al., 2016, Pisarra et al., 2013).