1. Main text

Since the discovery of graphene [1,2,3], hundreds of two-dimensional (2D) materials have been explored, and many more are to be discovered [4]. These materials, with unusual electronic, optical, thermal and mechanical properties, offer an ideal platform to study condensed matter physics and material science for next-generation ultrathin nanodevices. 2D material heterostructures with deterministic Lego-like atomic stacking at a precise twist angle have been recently obtained, unveiling surprising phenomena [ 5–8]. The electron correlation in these bilayers can be largely controlled by the twist angle, giving rise to superconductivity in twisted bilayer graphene [6], interlayer magnetism in stacked 2D magnetic materials [9] and other topological and quantum responses. This body of work has led to the emerging field of twistronics – manipulating the electron wavefunction via rotations [10]. Linked to this progress, new opportunities for extreme manipulation of light in stacked 2D materials have been emerging in the field of metamaterials and nanophotonics. Here, we provide a brief and focused discussion on these efforts, leading to the emergence of twistronics for photons (Fig. 1(A)).

 

Fig. 1. Photonic materials with a twist. A, Schematics of photonic materials with Lego-like twisted stacking. B, Twist-stacked metamaterials made of several layers of anisotropic nanorod arrays, enabling broadband generation of circularly polarized light [11]. C, Atom superlattice of twisted bilayer graphene (left) and its near-field map using scanning microscopy (right). Soliton domains and graphene plasmons reflected by a domain wall [17]. D, Twisted bilayer TMDCs, such as MoX₂ and WX₂, and the associated local atomic registry showcasing different symmetries. Here, X means any kind of chalcogen element [26]. E, Twisted bilayer graphene metasurfaces [30]. F, Twisted α-MoO₃ bilayer (left) and its supported phonon polariton distribution in real space as a function of rotation angle [31]. (Figures adapted and reprinted with permission from their respective sources).

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Well before twisted bilayers of 2D atomic materials were explored for their exciting electronic properties, twist-induced photonic effects have been studied in the context of artificial engineered surfaces, known as metasurfaces, stacked and twisted on top of each other to impart chiral and bianisotropic responses. For instance, Fig. 1(B) shows a planarized optical device made of a stack of twist-stacked nanorod arrays. Here, each surface is strictly achiral, but possesses a resonant anisotropic response in its plane. By twisting one with respect to the other in an array, it is possible to induce and control the magneto-electric coupling, resulting in controllable, broadband strongly bianisotropic responses over an ultrathin platform [11]. Such twist-induced effects enable high-sensitivity detection of chiral molecules down to zeptomole levels [12] and full control of light scattering in chirality-assisted metasurfaces [13]. More broadly, the twist in these optical metamaterials can control coupling and hybridization of their collective modes, dramatically enriching the available functionalities [14,15].

More recently, the attention has shifted to emerging photonic materials, specifically 2D materials. These materials do not require post-processing or nanofabrication to enable extreme light manipulation at the nanoscale: the exotic symmetries governing their lattice resonances support new emergent photonic responses in which electrons, phonons, excitons and other carriers can support extreme interactions with light. Inspired by the advent of twistronics, there has been a broad interest in exploring how the twist can be used as a new degree of freedom to control nanoscale light in these material platforms.

One possibility consists in exploiting the atomic lattice rearrangement governed by strongly coupled twisted bilayers, implying the emergence of new quantum states for light, in which the twist angle locally engineers light-matter interactions. In the case of twisted bilayer graphene (tBLG), the correlated electron behavior is modified by the moiré atomic superlattice emerging after the twist (Fig. 1(C), left), which has been raising large interest in the 2D materials community [6,7]. In the context of photonics, these superlattices form an ideal candidate to form photonic crystals to enable strong light-matter interactions at specific wavelengths, highly tunable through the twist angle. For instance, the strong interaction between photons and electron carriers in tBLG results in the generation of plasmon polaritons, half-light-half-electron quasiparticles. Graphene plasmon polaritons can be partially reflected at soliton-like domain walls formed by nonnegligible strain in moiré superlattices, where the atomic mismatch is maximized [16]. Multiple reflections and Bloch scattering emerge at these locations, and a photonic crystal of graphene plasmons can be thus established in such bilayers, as shown in Fig. 1(C) [17]. These phenomena may also emerge in twisted bilayer hexagonal boron nitride (hBN), in this case to control and govern phonon polariton (PhP) propagation. PhPs are lattice vibrations of matter hybridized with excited photons [18]. Recently, it has been found that a soliton superlattice formed in twisted hBN bilayers can broaden and harden the phonon modes supported therein, while more opportunities to manipulate the scattering features of PhPs at these reconfigurable domain boundaries remain to be explored [19].

In general, these works show how moiré soliton superlattices at the atomic scale can mold the photonic properties of materials. Beyond strain-controlled optical properties, more possibilities emerge based on other multi-physics processes. For example, electronic band hybridization can be achieved in twist-stacked graphene; such hybridized bands can greatly enhance plasmon nonreciprocity [20,21] and alter the photoresponsivity to enable high-performance photodetectors [22]. In addition, twist-induced correlated electron states can also affect the optical properties in, for example, twisted bilayer transition metal dichalcogenides (TMDCs). Monolayer TMDCs are 2D semiconductors with direct band gaps, supporting valley-locked light absorption and emission at visible frequencies [23,24]. By twisting and stacking two monolayer TMDCs, moiré fringes with spatially varying atomic symmetries are induced (Fig. 1(D)) which in turn sustain interlayer excitons, i.e., bound states of electron-hole pairs with electrons and holes belonging to different layers. The bandgap of interlayer and moiré excitons can be tuned by the twist angle; the different local atomic registry will induce different spin-orbit interactions and dramatically alter the valley-coupled interaction with light, opening various opportunities for applications [25,26]. These examples showcase a new photonic material platform established by twist-stacked 2D materials, exploiting strain solitons in moiré superlattices, modified infrared-active phonons, altered electronic band structures, and excitonic responses, for highly integrated, largely reconfigurable and novel optoelectronic applications.

Another avenue recently explored in this context has been the control of electromagnetic coupling between twisted low-dimensional photonic materials. Such scheme only deals with macroscopic systems and does not rely on effects governed by the atomic lattice, as in the previous examples. For this reason, it offers a simpler analysis and optimization, simply based on electromagnetic wave interactions while still providing highly exotic emerging optical phenomena based on twistronics concepts. As an example, deeply subwavelength graphene or hBN nanoribbon arrays can form hyperbolic metasurfaces (HMS), featuring extreme surface anisotropy [27–29]. In turn, HMS have been shown to support collimated and sub-diffractive propagation of polaritons and broadband, highly enhanced local density of states and light-matter interactions. In our recent works, we have leveraged the extreme control of plasmon and phonon polaritons in twist-stacked low-dimensional photonic materials to expand twistronics to photons and polaritons [30,31].

Figure 1(E) shows a sketch of the geometry resulting from stacking and twisting two hyperbolic metasurfaces formed by graphene nanoribbon arrays. Since each surface supports extreme anisotropy in plane and thus extremely different electromagnetic properties along orthogonal directions, the rotation between the two surfaces can efficiently control the evanescent coupling of the associated hyperbolic surface waves and significantly modify the overall dispersion of the coupled system. As a function of the rotation angle, the supported hybridized polaritons experience a transition from open hyperbolic to closed elliptic dispersion [30,32]. At this specific angle the system experiences a photonic topological transition, analogue to a Lifshitz transition in nanoelectronics [33], with isofrequency contours mimicking a Fermi surface for electrons [34]. Therefore, twisting HMS can induce a topological transition for polaritons, and, at the critical transition angle in which the band topology changes, the dispersion necessarily becomes flat, indicating that polariton propagation will experience no diffraction. In analogy to the magic-angle where flat bands and dissipation-free flow of electrons (superconductivity) arises in tBLG, the critical angle at which hyperbolic-to-elliptical transitions occur can be also referred as the “photonic magic angle” in these systems. These magic angles can be determined with simple geometric considerations, by tracing the crossing points of the hyperbolic dispersion of the two separate HMS in reciprocal space. In particular, a photonic magic angle arises at π-2$\alpha $ if α>π/4 and 2$\alpha $ if α<π/4, where $\alpha $ is the open angle of the hyperbolic bands of each HMS [30,31]. The findings have been demonstrated in experiments using twisted α-MoO₃ bilayers [31], as shown in Fig. 1(F). The α-MoO₃ crystal naturally supports extreme in-plane anisotropy for PhPs, including a broad frequency range over which surface PhPs are naturally hyperbolic [35–37]. Through real-space near-field nano-imaging techniques, a topological transition at the photonic magic angle and reconfigurable flat bands associated with diffraction-less propagation of polaritons can be observed as a function of the twist angle. Figure 1(F) shows near-field images of the PhPs excited by a localized source and the corresponding Fourier transform mapping the isofrequency contours [31]. This finding, verified in other recent papers [38,39], showcases the importance of twistronics for polaritonic systems, offering opportunities for extreme dispersion engineering of polaritons. Future efforts will aim at extending these findings and examining how twist-induced phenomena can engineer light-matter interactions for nanophotonics, thermal radiation, near-field nanoimaging, nonlinear optics, polariton networks and other applications. More complex lattice structures may support even more asymmetric phenomena, further enlarging the portfolio of photonic and polaritonic materials available in the framework of twistronic phenomena for nanoscale light.

This emerging area of research offers a straightforward path towards extreme engineering of light-matter interactions, facilitating paradigm-shift optoelectronic technologies. In this outlook, we focused on two avenues of interest in this framework: multi-physics interactions, including strain solitons, infrared-active phonon shift and band hybridization; and electromagnetic hybridization through evanescent coupling. Both these phenomena can be broadly controlled by twisting stacked layers, resulting in extreme control of the emerging photonic responses. In the future, we envision various new opportunities for these, from basic physics and material science to optical engineering and applications. New multi-physics interactions in twisted photonic materials can emerge, such as exciton excitation and transport, magneto-optical scattering and magnon polaritons (light coupled to electron spins), and quantum emission from electronic defects. In parallel, more material candidates and stacking scenarios should be carefully explored [40–42], more approaches for reconfigurability of these devices should be in parallel investigated, using, for example, phase change materials [43–44]; topological phenomena stemming from twistronics in analogy to correlated electron states, should also be pursued. Enormous applications may be readily expected to emerge such as diffraction-free infrared nanoimaging assisted by polaritons, polaritonic networks, high-sensitivity photodetection, single photon emission, and advanced metamaterials.