Interband Plasmon Resonances

• Interband plasmon resonances are collective oscillations arising from coherent interband polarization enabled by pronounced joint density of states features and a finite Berry connection.
• They exhibit a universal gapped dispersion with near-flat response at high momenta, as demonstrated in systems like twisted double-bilayer graphene using RPA dielectric formalism.
• These robust excitations allow for tunable optoelectronic and nanophotonic applications through precise control of twist angle, electric field, and carrier doping.

Interband plasmon resonances are collective charge oscillations arising from coherent interband polarization, distinct from conventional intraband (Drude-like) plasmons. These modes exist in a broad class of materials—including strongly correlated and moiré-engineered 2D systems, amorphous and crystalline semiconductors, p-block elements, topological materials, and nanostructures—whenever strong optical or electronic transitions occur between two (or more) bands separated by a finite energy gap. The physical realization and principal characteristics of such resonances are determined by the joint density of states (JDOS) between the participating bands, the Berry connection (where applicable), and the symmetry and topology of the underlying band structure. Recent research has established interband plasmons as tunable, long-lived, and robust excitations with highly nontrivial dispersion and direct impact on optoelectronic device concepts.

1. Physical Origin: Joint Density of States and Berry Connection

The essential precondition for an interband plasmon is a pronounced feature in the JDOS for transitions at a given excitation energy $\omega_0$, typically associated with Van Hove singularities (VHS) in 2D materials. The oscillator strength and ability of these transitions to support collective oscillations are further enhanced by a finite interband Berry connection.

In the paradigmatic case of twisted double-bilayer graphene (TDBG), the electronic structure near the Fermi level consists of flat conduction and valence bands separated by energy $\Delta_0$—the energy difference between corresponding VHS points in each band (Chakraborty et al., 2022). The joint density of states diverges logarithmically at the VHS energy according to

$J(\omega) \approx J_0\,\ln|\omega-\Delta_0/\hbar|$

providing an abundant phase space for resonant interband transitions. A nonzero Berry connection

$$\mathcal{R}^{mn}_k = \langle m,k | i\nabla_k | n,k\rangle$$

ensures that the interband velocity matrix element does not vanish, which is necessary for the formation of a collective mode. The resulting interband matrix element in the density-density response, $h(q)\sim q^2$ for small $q$, directly involves the Berry connection.

The general prerequisite for gapped interband plasmons in any 2D system is therefore:

• a VHS (or equivalent electronic singularity) in the JDOS for two bands at an energy $\Delta_0$; and
• a finite Berry connection between the respective Bloch states, granting nonzero oscillator strength to vertical (interband) transitions.

2. Theoretical Formalism and Universal Dispersion

The interband plasmon resonance manifests as a pole in the loss function

$$\mathcal{L}(q,\omega) = -\Im\left[\frac{1}{\varepsilon(q,\omega)}\right]$$

arising from zeros of the real part of the RPA dielectric function for excitation energies lying outside the single-particle continuum. The general RPA expression is:

$\varepsilon(q,\omega) = 1 - V_q\Pi(q,\omega)$

where $V_q$ is the Coulomb kernel and $\Pi(q,\omega)$ the noninteracting polarization, including both intra- and interband contributions. For interband plasmons specifically, the interband part of the Lindhard function is essential:

$$\Pi_{\text{inter}}(q,\omega) = g \sum_{\mathbf{k},m\ne n} [f_{n,\mathbf{k+q}}-f_{m,\mathbf{k}}] |\langle n,\mathbf{k+q}|m,\mathbf{k}\rangle|^2 / (\hbar\omega + i0^+ + E_{m,\mathbf{k}}-E_{n,\mathbf{k+q}})$$

For TDBG and other flat-band systems with a VHS at $\Delta_0$, the plasmon condition leads to a universal gapped dispersion:

$$\omega_{\text{inter}}(q) \approx \Delta_0\,\sqrt{1 + \frac{g e^2}{\kappa \varepsilon_0 \Delta_0}\,\frac{h(q)}{q}}$$

and, in the long-wavelength limit where $h(q) \simeq A q^2$,

$$\omega_{\text{inter}}(q\rightarrow 0) \approx \Delta_0\left[1+\frac{g e^2 A}{2\kappa \varepsilon_0 \Delta_0}\,q\right]$$

This result is universal for all 2D materials with strong VHS-driven JDOS and nonvanishing Berry connection, indicating that the plasmon gap is pinned exactly at the VHS energy separation, $\hbar\omega_{\text{gap}} = \Delta_0$ (Chakraborty et al., 2022).

3. Dispersion Flattening, Lifetimes, and Moiré Control

At higher momenta ($q$), the behavior of $h(q)$ typically transitions from quadratic to linear, causing the plasmon dispersion to saturate and flatten:

• For $q \gtrsim 30\,\mu\text{m}^{-1}$ in TDBG, $h(q)$ becomes linear in $q$, and $\omega_{\text{inter}}(q)$ becomes nearly independent of momentum.
• The resulting "slow" plasmon exhibits minimal group velocity and is exceptionally long-lived, as it exists outside the electron–hole continuum ($\Im\Pi=0$), and thus is undamped except when it enters the continuum at very large $q$.

This flattening and long lifetime can be traced to enhanced interband screening due to the moiré miniband structure (in twisted systems), and the spectral isolation of the collective mode. The flatness also implies low light–plasmon phase velocity mismatch, beneficial for light–matter coupling and nanophotonic applications.

4. Material Platforms, Tuning Parameters, and Experimental Realizations

Twist-Angle, Electric Field, and Carrier Doping (TDBG)

The interband plasmon gap and dispersion in TDBG are highly tunable:

• Twist angle $\theta$: As $\theta$ increases from the "magic angle" towards $\sim1.3^\circ$, the flat-band bandwidth and $\Delta_0$ increase, leading to a higher plasmon gap; beyond $\theta_c\approx1.2^\circ$ the system becomes insulating at neutrality.
• Perpendicular field $\Delta$ (vertical electric field): Drives a metal-insulator transition; for $\Delta < \Delta_c$ an intraband plasmon emerges, for $\Delta > \Delta_c$ only gapped interband modes survive, with the gap tunable by up to 40% over $\Delta\in[0,20~\text{meV}]$.
• Carrier doping $\mu$: Enables switching between gapless intraband and gapped interband plasmonic regimes by moving the chemical potential through the band structure.

Material Universality

Interband plasmon resonances, governed by the above universal mechanisms, appear in:

• 2D materials with spin–orbit coupling (e.g., antimonene (Slotman et al., 2018));
• Patterned and nanostructured p-block semimetals (Bi, Sb, Ga) via strong interband oscillators (Toudert et al., 2016, Toudert et al., 2017);
• Amorphous and crystalline silicon for UV plasmonics driven by interband transitions (not carriers) (Toudert et al., 14 May 2025);
• Topological systems with inverted bands, supporting intrinsic plasmons due entirely to interband coherence (Zhang et al., 2017).

5. Comparison with Intraband Plasmons and Drude Physics

Distinct differences separate interband from conventional intraband plasmons:

• Energy Scale: Interband plasmons are gapped, with a threshold frequency set by the interband (often VHS-related) energy separation; intraband plasmons are gapless and scale with carrier density.
• Dispersion: Interband plasmons exhibit near-flat, universal dispersion set by band-structure singularities and Berry connection; intraband modes show $\sqrt{q}$ dependence at low $q$.
• Damping: Interband modes can be significantly longer-lived if they lie outside the e–h continuum; intraband modes are limited by Landau damping and disorder scattering.
• Oscillator Strength: Interband plasmons require finite Berry connection and sizable interband dipole matrix elements for collective response; intraband plasmons are driven by the Fermi surface electron density.

A typical case in 2D moiré systems is the coexistence of both modes—for instance, doping-dependent switching between Drude-like and VHS-controlled plasmonic resonances, tunable by external fields.

6. Applications, Experimental Signatures, and Device Concepts

Interband plasmon resonances offer new operational regimes for terahertz to mid-infrared optoelectronics:

• Spectrally Isolated, Tunable Modes: The gap and dispersion can be engineered with atomic-scale stacking, gating, and strain.
• Long-Lived, Flat Plasmons: Favorable for compact, high-$Q$ nanophotonic and quantum devices due to low loss and strong confinement.
• Selective Excitation: The well-separated energy scales enable wavelength-division multiplexing and filtering in nanoscale photonic circuitry.
• Sensing and Nonlinear Optics: Field enhancement at plasmonic hot-spots, particularly in amorphous silicon nanostructures, supports UV molecular detection and nonlinear conversion (Toudert et al., 14 May 2025).
• Mid-IR and THz Platforms: Intervalence plasmons in boron-doped diamond provide a path to tunable platforms for quantum photonics and sensing (Bhattacharya et al., 18 Mar 2024).

Experimental hallmarks include sharp peaks outside the e–h continuum in loss spectroscopy, tunable resonance frequency through electrical or structural parameters, and robustness against variation in temperature and disorder (in moiré systems). Key platforms include EELS and near-field IR spectroscopy for direct detection and mapping of mode profile and spectral weight.

7. Broader Impact and Future Perspectives

The theoretical foundation established by universal VHS-driven, Berry-connected interband collective modes underpins a unifying framework for plasmonics beyond the Drude paradigm. These resonances, robust in multi-band, moiré, and disordered systems, offer new experimental knobs for electro-optic engineering and open avenues for topological, nonlinear, and quantum applications. The precision control over band structure and Berry curvature is particularly significant for stroboscopically manipulating light absorption, guiding, and emission at subwavelength scales, with implications for quantum emitters, THz photodetectors, and on-chip active devices.

Interband plasmonics thus delineates a frontier at the interface of strong correlation, nontrivial topology, and photonic device applications—an emergent domain powered by deep electronic-structure control and unprecedented collective response (Chakraborty et al., 2022, Toudert et al., 14 May 2025, Toudert et al., 2016, Toudert et al., 2017, Zhang et al., 2017).