Superlattice Plasmon Modes: Mechanisms & Applications

• Superlattice plasmon modes are collective excitations in periodic structures that generate new resonance energies and dispersions absent in uniform systems.
• They arise through mechanisms such as electronic band reconstruction, plasmon hybridization, and periodic long-range interactions that control mode formation.
• Experimental studies, from graphene heterostructures to stacked plasmonic arrays, demonstrate unique dispersion features like Rayleigh anomaly locking and robust interface states for advanced photonic applications.

Across the cited literature, the term superlattice plasmon mode refers to a collective excitation whose existence, resonance energy, dispersion, or localization is set by a periodic superstructure rather than by an isolated plasmonic element or a uniform electron system. The superstructure may be a moiré pattern, a stack of plasmonic lattices, a periodic array of electron shells or strips, a supercell nanoparticle lattice, or a topological lattice of coupled interface states. In graphene/Ru(0001), for example, the moiré superlattice induces an extra low-energy mode that is absent in commensurate graphene/Ni(111), while in a stack of two plasmonic lattices the superlattice supports an odd hybrid mode positioned strictly on a Rayleigh anomaly; in a grating of 2D electron strips, the periodic array supports a new collective mode whose frequency depends on the strip period and gap through a logarithmic screening term (Politano et al., 2016, Fradkin et al., 2020, Muravev et al., 16 Aug 2025).

1. Structural settings in which superlattice plasmon modes arise

Superlattice plasmon modes appear in several structurally distinct settings. One class is based on electronic superlattices, where a periodic potential reconstructs the electronic bands. The moiré pattern of periodically rippled graphene on Ru(0001) creates a superlattice potential that modulates atomic positions, onsite energies, and hopping amplitudes, producing mini-bands, Dirac-cone replicas, and new saddle points in the density of states (Politano et al., 2016). Related graphene realizations include a one-dimensional superlattice potential $V(x)=V_0\cos(G_0x)$, a planar graphene superlattice formed by alternating gapless and gapped strips, and graphene nanoribbon arrays with periodically modulated chemical potential or number of layers (Brey et al., 2019, Ratnikov et al., 2016, Rodrigo et al., 2015).

A second class is based on periodic electromagnetic or plasmonic arrays. Examples include a stack of two identical plasmonic lattices, a one-dimensional periodic array of spherical two-dimensional electron gases intended as a model for fullerenes or metallic shells, and a one-dimensional grating of 2D electron strips in a GaAs/AlGaAs membrane (Fradkin et al., 2020, Balassis et al., 2014, Muravev et al., 16 Aug 2025). In these systems the superlattice is not primarily an electronic miniband structure; it is a periodic arrangement of resonant elements whose Coulomb or radiative coupling creates collective modes.

A third class is based on coupled interface states in topological or photonic superlattices. In a Tamm plasmon topological superlattice, the building blocks are Tamm photonic crystals of different topological character, and the relevant collective states are hybrid topological interface states called supermodes (Qiao et al., 2021). In one-dimensional plasmonic crystals made from patterned Au surfaces, single topological interface states are combined into an SSH-like superlattice, yielding superlattice bands and a superlattice interface state (Liu et al., 2022).

2. Microscopic mechanisms of mode formation

In moiré graphene/metal heterostructures, the extra low-energy mode is produced by band reconstruction. The superperiodic potential folds the Dirac bands into a mini-Brillouin zone and creates new van Hove singularities. In the calculated density of states these additional singularities appear around

$E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$

with $\lambda \approx 20.8a$ and $a=1.42$ Å, and the calculated optical conductivity shows a pronounced excitation peak at

$2|E_D| \approx 1.35\ \text{eV},$

matching the energy scale of the extra HREELS feature (Politano et al., 2016). The mode therefore originates in electron-hole inter-band transitions between superlattice-generated van Hove singularities rather than in the free-carrier dynamics of ordinary doped graphene.

In stacked plasmonic lattices, the mechanism is hybridization of localized surface plasmons through the lattice photon field. Each lattice supports lattice plasmon resonances, and when two identical lattices are stacked, the localized plasmons of the two layers hybridize into even and odd modes. Near a Rayleigh anomaly, the singular parts of the lattice sums cancel in the odd-mode denominator, allowing an exceptionally narrow resonance to lie exactly on the Rayleigh anomaly over a wide thickness range (Fradkin et al., 2020). The mode is therefore set by the interplay between particle polarizability, intralayer lattice response, and interlayer coupling.

In one-dimensional Coulomb-coupled superlattices, the relevant mechanism is periodic long-range interaction without tunneling. For the spherical two-dimensional electron-gas chain, Coulomb coupling between electrons on the same sphere and on different spheres is treated in RPA, while electron hopping between spheres is neglected (Balassis et al., 2014). For massive Dirac plasma superlattices, the plasmon band is obtained from the single-subsystem plasmon dressed by a superlattice form factor $S_d$, so that

$$\omega_{ds}^{(p,m,g)}=\omega_d^{(p,m,g)}\,S_d^{1/2}$$

in the long-wavelength limit (Sachdeva et al., 2015).

In topological plasmonic or Tamm superlattices, the microscopic object that hybridizes is not an individual nanoparticle plasmon but an interface state. The Tamm plasmon topological superlattice is described by an SSH-type tight-binding Hamiltonian with intra-dimer and inter-dimer couplings $t_1$ and $t_2$ (Qiao et al., 2021), while the one-dimensional plasmonic-crystal superlattice is described by coupled-mode equations with intracell and intercell couplings $K_1$ and $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$0, yielding the SSH-like dispersion

$E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$1

In both cases, the “superlattice plasmon mode” is a collective hybrid of many coupled interface states rather than a single localized resonance (Liu et al., 2022).

3. Dispersion, band folding, and damping

The dispersion of a superlattice plasmon mode may differ qualitatively from the ordinary plasmon of the corresponding uniform system. In graphene/Ni(111), the low-energy mode is the ordinary intraband plasmon of doped graphene, described by

$E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$2

which reduces to the standard $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$3 law in the long-wavelength limit (Politano et al., 2016). In graphene/Ru(0001), by contrast, the extra mode disperses only weakly, roughly from $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$4 eV at $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$5 to about $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$6 eV at larger momenta, and lies inside the particle-hole continuum, so that $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$7. It is therefore intrinsically damped even as $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$8 and is not a fully coherent plasmon in the same sense as the $E_D=\pm \frac{2\pi \hbar v_F}{\sqrt{3}\lambda},$9 intraband plasmon (Politano et al., 2016).

In the two-layer plasmonic lattice, the most unusual feature is Rayleigh-anomaly locking. The relevant condition is

$\lambda \approx 20.8a$0

and the paper shows that the odd hybridized resonance can remain exactly on the Rayleigh anomaly for thicknesses roughly from about $\lambda \approx 20.8a$1 nm up to about $\lambda \approx 20.8a$2 nm for the example period $\lambda \approx 20.8a$3 nm (Fradkin et al., 2020). The resonance energy is therefore set mainly by the in-plane period rather than by the interlayer spacing.

Superlattice periodicity also produces Bloch-like plasmon bands. In the spherical-shell chain, the one-dimensional translational symmetry is preserved in the plasmon spectrum, with periodicity $\lambda \approx 20.8a$4, and anisotropy in the Coulomb matrix elements causes anticrossing only when the superlattice direction is perpendicular to the quantization axis (Balassis et al., 2014). In graphene superlattices, the effect can be even stronger: in the planar graphene superlattice the quasi-one-dimensional plasmon is generally acoustic over much of the Brillouin zone, whereas in the quasi-two-dimensional regime the dispersion is anisotropic because $\lambda \approx 20.8a$5 (Ratnikov et al., 2016). In the non-local quantum treatment of a one-dimensional graphene superlattice $\lambda \approx 20.8a$6, a new energy scale $\lambda \approx 20.8a$7 appears, low-energy plasmons propagate perpendicularly to the superlattice axis, and along the superlattice direction they become damped by sub-band transitions (Brey et al., 2019).

4. Representative experimental manifestations

The clearest direct observation of a superlattice-induced extra mode is the HREELS spectrum of graphene/Ru(0001). Graphene/Ni(111) shows a single low-energy loss peak assigned to the ordinary intraband plasmon, whereas graphene/Ru(0001) shows two low-energy peaks: a lower-energy peak around $\lambda \approx 20.8a$8 eV and an extra peak near $\lambda \approx 20.8a$9 eV that is absent in graphene/Ni(111). As the scattering angle changes, the ordinary plasmon remains visible near specular conditions, but the extra mode emerges at larger momentum transfer and becomes dominant (Politano et al., 2016).

In the grating of 2D electron strips, the experimental signature is a strong resonant feature in normal-incidence transmission. The analytical theory gives the fundamental mode frequency

$a=1.42$0

so the mode depends on carrier density, effective mass, superlattice period $a=1.42$1, and gap width $a=1.42$2 through a logarithmic screening correction (Muravev et al., 16 Aug 2025). This distinguishes the resonance from the isolated-strip result, which scales primarily with $a=1.42$3.

Topological superlattice modes are observed by angle-resolved reflectance. In the Tamm plasmon topological superlattice, the measured supermode bandwidth decreases monotonically as the etching depth increases, from $a=1.42$4 THz at $a=1.42$5 nm to $a=1.42$6 THz at $a=1.42$7 nm, and the bands become nearly flat (Qiao et al., 2021). In one-dimensional plasmonic crystals, a boundary between trivial and nontrivial superlattices supports a superlattice interface state near $a=1.42$8 nm with localization length $a=1.42$9, larger than the single-interface-state value $2|E_D| \approx 1.35\ \text{eV},$0, and with smaller angular divergence (Liu et al., 2022).

A related but distinct realization is the supercell plasmonic nanoparticle array in which part of the square-lattice sites are left empty in a periodic pattern. The enlarged supercell folds the dispersive branches and creates additional band edges that support multi-mode lasing; the observed lasing modes were identified as the 74th $2|E_D| \approx 1.35\ \text{eV},$1-point mode and the 106th $2|E_D| \approx 1.35\ \text{eV},$2-point mode of the supercell (Heilmann et al., 2023).

5. Functional consequences and applications

Because superlattice plasmon modes are governed by periodicity, they provide unusually direct geometric control of resonance energy and bandwidth. In the two-layer plasmonic lattice, the period is the most stably reproduced experimental parameter, so the resonance energy can be chosen by fixing $2|E_D| \approx 1.35\ \text{eV},$3, while the thickness $2|E_D| \approx 1.35\ \text{eV},$4 can vary within a broad window without shifting the odd resonance away from the Rayleigh anomaly (Fradkin et al., 2020). The paper therefore points to sensing, light emission control, filtering, and lasing as practical settings in which the thickness-independent narrow resonance is useful.

In topological Tamm and plasmonic-crystal superlattices, the practical advantage comes from band flattening, localization control, and interface-state robustness. Increasing the etching depth in the Tamm system narrows the supermode bandwidth and yields nearly flat dispersion with strong localization regardless of excitation angle, implying very small group velocity and high local density of optical states; the stated applications include integrated photonic devices, optical sensing, selective thermal emitters, Tamm plasmon lasers, enhanced spontaneous emission, and stronger light–matter interaction (Qiao et al., 2021). In the one-dimensional plasmonic-crystal superlattice, the superlattice interface state has smaller angular divergence and longer localization length than its single-interface counterpart, making it desirable for robust signal transmission and high finesse cavity operation (Liu et al., 2022).

Graphene-based superlattices provide a different functionality: broad spectral and modal tunability. In graphene nanoribbon superlattices, the resonance energies depend on ribbon width $2|E_D| \approx 1.35\ \text{eV},$5, segment length $2|E_D| \approx 1.35\ \text{eV},$6, chemical potentials $2|E_D| \approx 1.35\ \text{eV},$7 and $2|E_D| \approx 1.35\ \text{eV},$8, number of layers, and interlayer separation $2|E_D| \approx 1.35\ \text{eV},$9, and the resulting spectra can contain multiple resonances whose energies lie between the isolated-component resonances (Rodrigo et al., 2015). In the 2D-electron-strip grating, the collective superlattice mode is proposed as a basis for resonant absorbers, filters, detectors, modulators, and magnetoplasmonic devices (Muravev et al., 16 Aug 2025). In supercell nanoparticle arrays, the extra superlattice band edges provide multiple low-loss feedback channels for multi-mode lasing (Heilmann et al., 2023).

6. Conceptual distinctions and modeling limits

A recurring issue is that a superlattice-induced excitation is not always an undamped plasmon in the conventional sense. The moiré-induced extra mode in graphene/Ru(0001) is generated by interband transitions between superlattice-created van Hove singularities, and the calculated loss peak lies inside the particle-hole continuum. The authors therefore stress that it is not a fully coherent plasmon like the ordinary $S_d$0 intraband mode and that it is also distinct from the high-energy $S_d$1-plasmon at $S_d$2–$S_d$3 eV (Politano et al., 2016).

A second distinction concerns the meaning of the word superlattice itself. The metal-proximity mode in a 2DEG under a finite metallic strip is a new collective branch with no transverse potential nodes and a dispersion

$S_d$4

but the paper explicitly states that it is not a superlattice plasmon in the sense of a periodic array and miniband formation (Muravev et al., 2019). By contrast, the one-dimensional graphene superlattice $S_d$5 requires a full non-local quantum response matrix to capture its low-energy damping and delocalized collective modes; semiclassical or local theories miss the $S_d$6 couplings that generate the new decay channels (Brey et al., 2019).

A third limit is the applicability of effective-medium descriptions. Metal–dielectric superlattices can behave as uniaxial plasmonic crystals and support Dyakonov-like oblique surface waves under the condition $S_d$7, but the same thinning of metallic layers that reduces loss and enlarges the angular existence range also increases spatial dispersion and can lead to the failure of the effective-medium approximation (Vukovic et al., 2011). This suggests that the category superlattice plasmon mode is physically heterogeneous: in some systems it denotes a weakly damped collective plasmon band, in others an intrinsically damped interband resonance, a topological interface supermode, or a hybrid surface wave whose existence is controlled by superlattice anisotropy.