Graphene Photonic Superlattice

• Graphene-based photonic superlattices are artificially engineered periodic structures that modulate graphene’s gate-tunability and optical response at the nanoscale.
• They enable dynamic electrical and nonlinear optical control, transitioning between topological and trivial phases via precise modulation of averaged permittivity.
• Robust topological interface modes and strong disorder tolerance make these superlattices ideal for reconfigurable photonic circuits and quantum optoelectronic devices.

Graphene-based photonic superlattices are artificial periodic structures in which graphene’s unique electronic and optical properties are modulated at the nanoscale, resulting in tailored photonic band structures and emergent light–matter phenomena. These structures leverage graphene’s gate-tunability, atomic thickness, and strong interactions with electromagnetic fields, often in concert with periodic potentials or patterned heterostructures, to enable robust and dynamically reconfigurable photonic functionalities at infrared, terahertz, and optically relevant frequencies.

1. Tunable Optical Properties via Superlattice Geometry

A central principle of graphene-based photonic superlattices is the periodic modulation of parameters that govern the electromagnetic response—such as dielectric permittivity, conductivity, Fermi velocity, or band gap—across the superlattice unit cell. Representative architectures include periodically stacked graphene/dielectric/metals, lateral patterned potentials using gates, self-assembled nanostructures, and moiré superlattices stemming from twisted bilayers. The resulting periodicity, with a period $\Lambda$ typically on the order of tens to hundreds of nanometers, folds both the electronic and photonic band structures, producing unique minibands, Dirac points (DPs), flatbands, and bandgaps (Berman et al., 2010, Deng et al., 2015, Sunku et al., 2019).

For metallo-dielectric superlattices with intercalated graphene layers, the spatially averaged permittivity $\bar{\varepsilon}$ becomes the control parameter for photonic band topology. Specifically, photonic DPs arise when $\text{Re}(\bar{\varepsilon}) = 0$, realizing a condition akin to zero-average refractive index in other photonic crystals (Deng et al., 2015, Deng et al., 19 Sep 2025). In moiré superlattices, atomic reconstruction at small twist angles creates a solitonic network of domain walls that acts as a natural plasmonic crystal, offering subwavelength modulation of plasmon polariton propagation (Sunku et al., 2019).

2. Electrical and Optical Control Mechanisms

Graphene’s tunability by electrostatic gating is exploited to dynamically adjust both its electronic and photonic properties. The optical permittivity of graphene, governed by the Kubo formula, can be efficiently modulated through its chemical potential $\mu_c$, set by gate voltage or chemical doping. The averaged permittivity for a superlattice structure

$$\bar{\varepsilon} = \frac{\varepsilon_d t_d + \varepsilon_m t_m + 2 \varepsilon_g t_g}{t_d + t_m + 2 t_g}$$

changes sign as $\mu_c$ is swept, enabling electrically induced transitions between topological and trivial photonic phases. This mechanism directly controls the appearance or disappearance of topological interface modes (Deng et al., 19 Sep 2025).

In addition to electrical gating, nonlinear optical effects such as the Kerr effect can also tune the photonic dispersion by modifying $\bar{\varepsilon}$ through high optical power. Devices utilizing this principle have demonstrated spectral shifts of photonic DPs exceeding 30 nm at mid-infrared and THz frequencies (Deng et al., 2015).

3. Topological Interface Modes and Zak Phase Control

A key feature of these superlattices is the emergence of topologically protected interface modes at their boundary with a uniform dielectric. The presence or absence of these modes is governed by the sign of $\bar{\varepsilon}$:

• For $\bar{\varepsilon} < 0$, the superlattice exhibits a nontrivial Zak phase ($\pi$), and topological interface modes appear, localized at the superlattice–dielectric interface.
• For $\bar{\varepsilon} > 0$, the Zak phase reverts to zero, and these modes vanish.

The transition point ($\bar{\varepsilon} = 0$) is marked by a Dirac point in the photonic band structure at the Brillouin zone center ($k_x = 0$), where the two transmission bands touch and the Zak phase jumps. This is a genuine topological phase transition, accompanied by observable changes in interface mode presence and their robustness (Deng et al., 19 Sep 2025, Deng et al., 2015).

The propagation constant $\beta$ of these interface modes decreases monotonically as $\mu_c$ increases, effectively tuning the phase velocity of the mode and offering dynamic electrical control over signal processing functionalities.

4. Robustness and Disorder Tolerance

Topological interface modes in graphene-based photonic superlattices inherit their robustness from the quantized Zak phase of the underlying bulk minibands. Simulations and experimental evidence confirm that these modes are insensitive to substantial fabrication and structural disorders—for example, random thickness variation in the dielectric layers up to 50% does not substantially affect the eigenvalue or mode profile (Deng et al., 19 Sep 2025). This robustness is critical for real-world photonic applications, where tolerance to imperfections is often essential.

5. Device Applications and Implications

The dynamic tunability and topological protection inherent to graphene-based photonic superlattices position them as strong candidates for a broad class of advanced optoelectronic devices, including:

• Electrically reconfigurable all-optical switches and on-chip modulators.
• Robust photonic communication channels exploiting topological interface modes that are immune to backscattering.
• Directional beam-steering elements for dynamic signal routing.
• Platforms for topological photonic quantum information due to the inherent protection against disorder and losses.
• Studies of relativistic quantum effects in optics, such as photonic Zitterbewegung, enabled by the presence of Dirac points and conical band intersections (Deng et al., 2015).

The capability to shift between topologically distinct phases and modulate both the existence and phase velocity of photonic interface modes by electrical gating is particularly attractive for next-generation, programmable photonic circuits and integrated quantum devices.

6. Summary Table of Key Control Parameters

Control Parameter	Physical Effect	Photonic Consequence
Chemical potential ($\mu_c$)	Graphene’s permittivity $\varepsilon_g$ tunable	Switches $\bar{\varepsilon}$ sign; toggles interface modes
Averaged permittivity ($\bar{\varepsilon}$)	Sets photonic band topology	Zero-crossing yields DP; negative yields Zak phase $\pi$
Optical power	Kerr-induced nonlinear response	Allows ultrafast all-optical DP control
Layer thicknesses ($t_d$, $t_m$, $t_g$)	Determines relative weight of material phases	Refines band structure and interface mode field profiles

A highly controlled unit cell geometry, precise electronic and optical doping, and robust fabrication are each essential in realizing the desired superlattice properties required for photonic device realization.

7. Outlook and Future Directions

Exciting future directions include integrating these superlattice platforms with other two-dimensional materials, further miniaturizing and multiplexing device architectures, and exploring non-Hermitian or nonlinear topological photonics regimes. Deepening the theoretical understanding of Zak phase transitions and device-level implications for energy transport, loss mitigation, and new operational paradigms may catalyze the development of quantum photonic circuits and optoelectronic applications that exploit the unique topological and dynamic control features enabled by graphene-based photonic superlattices (Deng et al., 19 Sep 2025, Deng et al., 2015).