Twisted moiré heterostructures, created by stacking two layers of two-dimensional (2D) van der Waals (vdW) materials on top of each other with a relative twist angle (θ), have revealed a multitude of extraordinary physical phenomena [1][2][3][4][5]. In twisted electronics, tremendous progress has been achieved based on graphene and transition metal dichalcogenides (TMD) structures, with exotic discoveries ranging from superconductivity, correlated insulating states, ferromagnetism, and fractional quantum anomalous Hall effects [6][7][8][9]. In twisted optics and photonics, efforts have expanded across a wide range of frequencies, from the visible to IR, where moiré excitons in TMDs, nanoscale photonic crystals, and novel features in surface plasmon/phonon polaritons in twisted graphene systems and polar insulators have been realized [4,5,[10][11][12]. These achievements have also spurred the exploration of surface polaritons in twisted structures to manipulate and control long-wavelength electromagnetic fields down to the nanoscale [5][6][7][8][9][10][11][12][13][14][15][16].

A notable example is the observation of topological transitions and the canalized phonon polariton in twisted α-MoO 3 with highly directional propagation around 60°twist angles [5,[17][18][19][20][21]. In contrast to traditional polaritonic media, such as hBN or graphene-based heterostructures, the canalized flat polariton dispersion along a specific direction would enables efficient energy transfer with minimal spatial spreading. Despite these achievements, twisted-polaritonics in polar insulating systems remains in its early stage [5,19,22], particularly in identifying systems that support the propagation of canalized polaritons with enhanced tunability, broader spectral coverage, and optimized propagation efficiency. Identifying new twisted vdW heterostructures capable of supporting canalized polaritons thus offers the potential to address existing limitations while unlocking new functionalities in nano-polaritonic technologies across different frequency domains.

We report the direct observation of tunable phonon polariton transitions in twisted α-V 2 O 5 using scattering-type scanning near-field optical microscopy (s-SNOM), which enables local optical excitations of the phonon resonance states at selected long-wavelength IR frequencies [23][24][25][26]. We show that twisted α-V 2 O 5 hosts propagating polaritons that are tunable in the mid-IR wavelengths from λ IR ∼ 11.1-11.6 µm [13]. The distinct dielectric permittivity, ϵ, of α-V 2 O 5 along the three crystalline axes, as determined from previous far-field measurements, confirms the existence of three Reststrahlen bands (RB) and the corresponding phonon polaritons with them (see Supplement 1) [26]. In our studies, we focus on such hyperbolic frequency regime of RB 2 (ω ∼ 860-900 cm -1 ) where ϵ a <0, ϵ bc >0, respectively. Given the strong anisotropic in-plane ϵ in RB 2 and interlayer hybridization of twisted α-V 2 O 5 , our observation indicates a phonon polariton transitions can be detected, which, depending on the interlayer twist angle, manifests either as unidirectional canalized or closed elliptical propagations. The continuous variation in polariton wavefront geometries, along with the quantitative agreement with electromagnetic modeling, suggests that twisted α-V 2 O 5 holds promise for developing tunable IR polaritonic devices with potential applications in nanophotonic and optoelectronics.

To access the phonon polaritons in α-V 2 O 5 , we performed nano-IR imaging using s-SNOM based on a tapping-mode atomic force microscope (AFM) equipped with a metallic tip (Fig. 1(a) inset). The AFM tip with a radius of ∼20 nm, and oscillation frequency of 300 KHz with an amplitude of 80 nm, was illuminated by IR light with frequency ω = 2π/λ IR , generating a strongly enhanced local electric field underneath. This setup resolves the problem of photon-phonon momentum mismatch [27][28][29][30][31], enabling the launch of phonon polariton waves with wavelength λ p ≪ λ IR [5,17,18,[32][33][34]. The local electric field of the phonon polariton waves gets scattered into the farfield by the sample edge, enabling direct measurement of the polaritonic response with the ∼20 nm spatial resolution.

Representative nano-IR imaging data is depicted in Fig. 1, where we show the near-field image for ω = 860 cm -1 and a 100nm-thick α-V 2 O 5 flake. To excite phonon polaritons, we define gold disks as a local phonon polariton launcher on top of the α-V 2 O 5 flake to produce propagating phonon polariton waves upon IR illumination. We first focus on phonon polaritons in a thin layer of α-V 2 O 5 without twisting (Fig. 1(b)). Clearly, the detected polaritonic features around the Au disk do not propagate outward symmetrically. Instead, we observe a very clear directionality in the RB 2 frequencies. Such unidirectional polariton propagation in the RB 2 frequencies indicates a canalized wavefront in pristine α-V 2 O 5 flakes, reminiscent of previous polariton canalization observations in twisted α-MoO 3 or the dielectric engineeringinduced canalization in Li-intercalated V 2 O 5 [14].

In sharp contrast to the unidirectional polaritonic wavefront discussed above, for the same flake but adding another thin layer of α-V 2 O 5 with a relative twist angle of 71°, we see the formation of elliptic polariton wave pattern, as shown in Fig. 1(c) (see Supplement 1). The smallest wavelength is parallel to the [010] (b-axis), while the largest wavelength is along [100] (a-axis). These elliptic polaritons are reminiscent of earlier observations in other polar insulators [18,[35][36][37]. We note that such polariton wave pattern variation as a function of interlayer twist angle could not be explained by increasing the thickness of α-V 2 O 5 , which would simply increase the polariton wavelength rather than modify the wave pattern. Instead, these observations suggest that the interlayer coupling between the two branches of the polariton dispersion likely drives the transition of the wavefront from a unidirectional, canalized geometry to an elliptic one, as detailed below.

To systematically examine the twist angle dependence of the phonon polariton coupling between two adjacent α-V 2 O 5 crystals, we conducted nano-IR imaging studies on multiple devices with different interlayer twist angles (Figs. 2(a)-2(d)). At θ = 0°, the wavefront propagates along the a-axis, which we use as our reference point to compare with other twist angles. As their interlayer twist angle increases, we observe a gradual rotation and transformation of the wavefront. At θ = 30°, the wavefront largely retains its unidirectional propagation, albeit the propagating direction shows a noticeable rotation/deviation from the θ = 0°case. This deviation becomes more pronounced at θ ∼ 38°, where we observe not only the unidirectional polariton wavefront but also a further shift in propagation direction relative to the zero-twist angle. However, at θ ∼ 70°, a closed wavefront emerges around the Au launcher, signaling the completion of the polariton phase transition from an open, canalized geometry to the closed, elliptic wave structure. Clearly, a polariton phase transition is accompanied as a function of twist angles, as detailed below.

Our study of the phonon polariton dependence on interlayer twist angle is well captured by the numerical simulations. To verify the experimental observations, we performed fullwave simulations (see Supplement 1) at variable twist angles for α-V 2 O 5 , examining the real part of the z-component of the electric field (Re(E z )). The experimentally determined dielectric permittivity tensor was used as the input parameter [38] (see Supplement 1). By plotting the calculated Re(E z ) (Figs. spectrum, as shown in Figs. 2(i)-2(l). Briefly, at small twist angles (θ < 30°), the field pattern remains largely identical, although the polariton propagation direction rotates continuously as a function of the interlayer twist angle (Figs. 2(e)-2(f)). Increasing the twist angle from θ ∼ 30°to 38°not only slightly rotates the polariton propagation direction but also modifies the electrical field pattern. Beyond the critical angle, however, the polariton wavefront transforms into an elliptic geometry (see Supplement 1). These findings validate our observed polariton wavefront transformation triggered by the interlayer phonon polariton coupling initiated by the relative twist angle between the adjacent two layers.

Physically, the critical angle marks the boundary between hyperbolic and elliptical wavefronts. At this threshold, perfect canalization is expected, signifying a phase transition from open to closed polariton wave behavior. Because the permittivity values ε x and ε y vary with frequency, the open

and the critical angle, defined as ∆θ = |180 • -2 × β|, are also frequency dependent. Figure 3(a) illustrates the variation of ∆θ across frequencies, calculated numerically at ω = 860, 875, 890, and 905 cm -1 , alongside their associated polariton dispersion (Figs. 3(b)-3(e)). For instance, at ω = 860 cm -1 , perfect canalization occurs at a twist angle of 39.7°, aligning with our experimental results in Fig. 2. At higher frequencies, ∆θ increases, approaching 90°at the edge of the RB 2 frequency regime.

To gain deeper insight into the critical angle of the observed polariton transition, we further conducted analytical studies by solving the source-free Maxwell equations to derive the polariton dispersion for each α-V 2 O 5 flake, modeled as a 2D sheet. Interlayer coupling was represented by positioning the top flake directly above the bottom flake with an infinitesimal separation. For untwisted α-V 2 O 5 (Fig. 4(a)), the hyperbolic dispersion of phonon polariton propagates at the open angle β [5,39]. Upon introducing a relative twist between layers (Figs. 4(b) and 4(c)), the polariton dispersion of the fixed bottom layer diverges from that of the top layer, resulting in a rotation of the overall dispersion diagram. Consequently, the two branches of the total dispersion become increasingly parallel to one another. Around the critical angle of ∆θ ∼ 40°(Fig. 4(d)), the dispersion diagram shows two perfectly parallel lines, indicative of an idealized polariton canalization in real-space imaging. Beyond this critical twist angle, the overall dispersion transitions from hyperbolic to elliptical wavefront, as shown in Figs. 4(e)-4(h). Another way to examine the polariton phase transition is through the number of anti-crossing points in their associated hybrid dispersions 13 . For instance, there are two anti-crossing points below the critical angle and four anti-crossing points above it (see Supplement 1). In short, both our numerical and analytical studies reproduce the experimental results, highlighting the good agreement between theory and observation.

We now discuss the possible mechanisms underlying the observed canalized phonon polariton propagation at the zerotwist angle and the associated phase transition in the relevant frequency range. One plausible explanation is the large β dictated by the highly anisotropic dielectric function of α-V 2 O 5 flakes (see Supplement 1). For instance, at ω = 830 cm -1 , β approaches 90°, corresponding to hyperbolic dispersion extending further along the principal directions and effectively narrowing the pathways for group velocity. Therefore, this expanded angular range facilitates polariton propagation in more collimated or nearly "canalized" wavefronts, even in the untwisted α-V 2 O 5 flakes, characterized by highly confined energy flow. Such canalization effects can be further modulated via interlayer coupling through angle-dependent electromagnetic hybridization between anisotropic phonon polariton fields. For twisted α-V 2 O 5 flakes, the effective interaction between two hyperbolic bands leading to anti-crossing behavior (Fig. 4), which further flattens the dispersion and induces relative rotation of the overall dispersion diagram across a wide range of ∆θ. Our dispersion analysis confirms that this tunability arises from the electromagnetic nature of the twisting tunability of phonon polaritons has been confirmed by our dispersion analysis of phonon polariton dispersions. This phenomenon highlights the pivotal role of twist-induced interlayer interactions in enhancing polariton confinement and tunability.

In short, we have demonstrated a tunable polariton phase transition in twisted α-V 2 O 5 heterostructures. The observed variation in dispersion contours, transitioning from canalized to elliptic wavefront geometries in the mid-IR range, benefits from the material's highly anisotropic property and effective electromagnetic interlayer coupling. Our systematic explorations of twist angle and frequency dependencies, supported by comprehensive theoretical modeling and simulations, underscore the transformative potential of polar oxides for advancing nanophotonics and polaritonics through twisting engineering. These findings suggest that similar effects in other related vdW materials could enable the design of programmable polaritonic properties [40,41], leveraging twisting to tailor functionalities across the technologically important mid-IR to far-IR spectrum at the nanoscale.