Mid-infrared chirality and chiral thermal emission from twisted α-MoO₃

Abstract

Chirality in the mid-infrared spectral range plays a crucial role across physical, chemical, and biological sciences, yet sources of chiral infrared light are currently difficult to obtain. Their development, using principles from the mature field of metamaterials, requires complex three-dimensional architectures that call for high-resolution lithography. Here, we leverage the natural optical anisotropy found in several van der Waals crystals, for example α-MoO₃, to demonstrate experimentally that its twisted bilayers break inversion-rotation symmetry and are thereby intrinsically chiral. Via direct thermal emission measurements of microscopic twisted bilayers, we demonstrate that these heterostructures generate chiral light through incandescence. Twisted configurations of van der Waals materials do not require any lithography and offer a platform for large-scale chiral filters and thermal sources beyond conventional meta-architectures.

Sources of chiral mid-infrared light are difficult to obtain. Here, the authors demonstrate that twisted bilayers of anisotropic α-MoO₃ van der Waals crystals can emit mid-infrared thermal chiral radiation without any lithographic processes.

Introduction

Chirality is the geometric property that makes an object not superimposable onto its mirror image through neither rotation nor translation. It plays a crucial role in the development of life as we know it^1,2 and becomes relevant across various disciplines in applied science and technology. For example, the fundamental vibrational modes of various molecules, occurring primarily in the mid-infrared (mid-IR) region of the electromagnetic spectrum, are highly sensitive to chiral configurations³. This sensitivity is often leveraged in organic chemistry and pharmaceuticals, where distinguishing between enantiomers – molecules that are mirror images of each other—is essential, since these can exhibit distinct biological activity and therapeutic effects^4,5. Nonetheless, the degree of chiral response of naturally occurring molecular systems, quantified as the differential absorption between left- and right-circularly polarized light is five orders of magnitude smaller than the absorption of unpolarized light^3,6,7. Techniques like vibrational circular dichroism spectroscopy utilize mid-IR light to differentiate enantiomers, offering vital insight into their intrinsic configurations and purity^8,9.

Since sensing and detection of biological substances operate in the mid-IR region, the role of IR light sources is critical in chiral analysis. However, mid-IR lighting technology is primarily limited to the established – but lithographically complex—quantum-cascade laser, or globars and Nernst glowers that yield incoherent light. Both approaches lack the functionality to control the polarization state of light in a compact device platform at mid-IR frequencies. At the same time, in this spectral range, naturally available chiral systems such as molecular ones do not interact strongly with circularly polarized light^3,6,7, highlighting the promise of materials engineering for mid-IR chirality and sources. Conveniently, however, at near-room temperatures, the spectrum of blackbody radiation emitted through incandescence peaks near 10 μm, thereby overlapping spectrally with the vibrational and phonon modes relevant in chiral spectroscopy. Therefore, incandescence presents a promising avenue for cost-effective mid-IR thermal sources¹⁰. Although light generated from incandescence is by nature achiral, thermal emitters with tailorable polarization characteristics have been reported in recent years, leveraging the collective response of three-dimensional metamaterials and metasurfaces¹⁰. Most recently, thermal emission with chiral characteristics has also been reported, using metamaterials composed of elementary unit cells that are geometrically asymmetric in the microscale^11,12. However, the large-scale development of such meta-architectures requires expensive high-resolution lithography and synthesis.

In Fig. 1a, we illustrate chirality across different scales, starting with the most familiar chiral object in the macro-scale, a human hand, which serves as an example of mirror asymmetry. Beyond the aforementioned principles of conventional three-dimensional metamaterials with geometrically asymmetric unit cells, even achiral objects, such as a geometric cross, can serve as a unit cell of a planarized metamaterial that demonstrates chirality through twisting adjacent unit cells^13–15, thereby inducing various effects typically observed in three-dimensional metamaterials with quasi-two-dimensional motifs^16–18. As an example, the middle of Fig. 1a shows a twisted combination of such crosses that break inversion-rotation symmetry, representing the meso-scale and the regime of metamaterials. The realization of planarized twisted metamaterials, however, is subject to similar fabrication challenges as their three-dimensional counterparts^11,12.

Fig. 1. Chirality and α-MoO₃ twisted bilayers.

a Chiral objects across different scales. (Left) A human hand. (Middle) A simplified representation of twisted metamaterials and metasurfaces for artificial chirality. (Right) A twisted α-MoO₃ bilayer that enables intrinsic chirality. b Sketch of the atomic structure of α-MoO₃ showing the spatial coordinates xyz corresponding to the crystallographic directions [100], [001] and [010], respectively⁵². c Microscope image of a twisted bilayer α-MoO₃ sample. The x- and y-axes of the crystal correspond to the bottom flake. d Atomic force microscopy (AFM) scan of the height profile of the sample shown c. e Height profile along the dashed blue line in d, where thickness d₁ refers to the top flake and d₂ to the bottom flake.

In this work, we experimentally demonstrate a fundamentally different approach to inducing chirality, leveraging the unique properties of emerging low-dimensional van der Waals crystals. Instead of relying on external lithographic patterning along the in-plane directions as in the case of metamaterials, we harness the natural, intrinsic in-plane optical anisotropy observed recently in several emerging van der Waals materials, such as α-molybdenum trioxide (α-MoO₃)^19–21 and α-vanadium pentoxide (α-V₂O₅)²², and twist adjacent layers to induce chirality. The concept of twisted anisotropic bilayers is demonstrated on the right of Fig. 1a, where twisted layers (heterostructures) of an in-plane anisotropic material are shown. This can be understood in direct analogy with the meso-scale and the case of twisted crosses; the blue and red colors in the middle- and right-side of Fig. 1a, represent, respectively, the two branches of a cross and the two dissimilar symmetry axes of an in-plane anisotropic crystalline material. In both cases, inversion-rotation symmetry is evidently broken via twisting. Importantly, however, in the platform introduced here via twisting uniform anisotropic crystals, chiral effects are enabled without the need for any patterned meta-atoms or their coupling. The reported chirality is intrinsic and thereby geometrically robust, as opposed to extrinsic chirality which is only observable for certain orientations of incident light²³. The only requirement for inducing chirality in this platform is a pronounced intrinsic in-plane anisotropic material response. While several numerical studies have recently explored twisting anisotropic materials for mid-IR and terahertz chirality^24–29, there has been no previous experimental demonstration.

We experimentally realize twisted bilayers composed of exfoliated flakes of α-MoO₃, which exhibit strong in-plane anisotropy at mid-IR frequencies²¹, and show via absorption measurements that left- and right-hand-polarized light interacts differently with twisted layers of α-MoO₃, revealing a strong chiral response. We carry out direct thermal emission measurements of van der Waals-based twisted flakes that have small lateral dimensions (tens of micrometers), and report thermally excited chiral light in a lithography-free platform. These results open up simpler ways to create photonic functionalities leveraging the unique properties of low-dimensional materials, eliminating the need for lithography in mid-IR chirality engineering.

Results

A chiral optical response can be described through circular dichroism (CD), which quantifies the difference in absorption or emission between right- and left-circularly polarized light. Based on Kirchhoff’s law of thermal radiation, a chiral response observed in an absorption experiment will manifest itself identically in light emission³⁰. This suggests that a chiral absorber also constitutes a chiral thermal emitter of light that, in contrast to conventional blackbody radiation, has a chiral degree of freedom expressed through CD. For a chiral material onto a reflective substrate with vanishing transmission, we can define CD as:

$$\text{CD}=R_{\circlearrowleft }-R_{\circlearrowright },$$ 1

where R_↺ and R_↻ denote the reflectance of left- and right-hand circularly polarized light. In this work, we confirm the chiral characteristics of twisted bilayers via both absorption and thermal emission experiments. In the following section, we identify the intrinsic material properties and underlying physical mechanisms required for engineering a chiral thermal emitter with twisted anisotropic bilayers.

Design rules for circular dichroism in twisted bilayers

Let us start with a heterostructure composed of two in-plane anisotropic materials on a reflective substrate, as shown in Fig. 2a, where the top and bottom layers are indicated, respectively, with indices 1 and 2. In principle, these two materials can be dissimilar with refractive indices n_i,1,2 = η_i,1,2 + iκ_i,1,2, where η_i,1,2 and κ_i,1,2 denote the real and imaginary parts of the refractive index, respectively, along each axis i = x, y, z. In order for this system to thermally emit chiral light, we consider the thermal emission to occur primarily on the bottom layer, for which this layer must be lossy, based on the fluctuation-dissipation theorem. By contrast, the top layer tailors the polarization of light, for which it should operate as a phase retarder that is, ideally, lossless. Without loss of generality, we assume that n_y,1 = n_y,2 = 0, and we restrict the analysis to normal incidence, hence the out-of-plane refractive index (n_z) of each layer is not relevant.

Fig. 2. Design rules for circular dichroism in twisted bilayers.

a Schematic of idealized bilayer system consisting of a lossless quarter-wave plate (thickness d₁, in-plane refractive indices n_x,1 = η_x,1, n_y,1 = 0) stacked on a lossy dichroic emitter (thickness d₂, in-plane refractive indices n_x,2 = η_x,2 + iκ_x,2, n_y,2 = 0) on a perfect electric conductor, approximated as an ideal mirror with isotropic permittivity ε_PEC = − 10000. The two layers are twisted with respect to each other by an angle α. b Circular dichroism (CD) as a function of layer thicknesses for n_x,1 = 4.6, n_x,2 = 4.6 + 0.3i, and α = 45°, where l indicates the order of the quarter-wave plate. The twist-angle dependence for the thicknesses marked by the two colored circles is shown in c. d CD as a function of the losses (imaginary parts of the refractive indices along the x-direction, κ_x,1 and κ_x,2) with η_x,1 = η_x,2 = 4.6, α = 45°, d₁ = 0.2 μm, and d₂ = 2 μm. The white dashed line marks the case where both layers are made of the same material. The black circle highlights the value of κ_x for α-MoO₃ at λ = 12.8 μm. e Dependence of CD on the real parts of the in-plane refractive indices, η_x and η_y, with κ_x = κ_y = 0.3, d₁ = 0.2 μm, d₂ = 2 μm, and α = 45°, when the bilayer is composed of the same materials n₁ = n₂. The dashed white line indicates the isotropic condition (n_x = n_y), where CD vanishes. The black circle highlights the value of η_x for α-MoO₃ at λ = 12.8 μm.

When the bottom layer exhibits in-plane dichroism (κ_x,2 ≠ κ_y,2), it emits preferentially linearly polarized light either along the x or y direction, for which it can also be viewed as an absorbing polarizer operating in emission mode. Since k_y,2 = 0, the emitted electric field emitted by the bottom layer is primarily x-polarized. Upon appropriate selection of the thickness of the top layer, d₁, it can operate as a quarter-wave plate introducing a phase shift of π/2 between the two orthogonal linear polarization components and converting the emitted light from layer 2 into circularly polarized light. For quarter-wave plate operation, the top layer must exhibit in-plane birefringence (η_x,1 ≠ η_y,1). In this configuration, henceforth, we refer to the bottom layer as the lossy dichroic emitter and the top layer as the lossless quarter-wave plate of the bilayer. In this idealized system, since κ_y,2 = n_y,1 = 0, by misaligning the in-plane crystal axes of the layers by an in-plane rotation of angle α (Fig. 2a), the thermally emitted light can become circularly polarized. The refractive index of the quarter-wave plate (layer 1) along the x-direction is taken as purely real, n_x,1 = η_x,1, while the refractive index of the dichroic emitter along the x-direction is complex, n_x,2 = η_x,2 + iκ_x,2.

Figure 2b shows transfer matrix simulations of the circular dichroism as a function of the layer thicknesses d₁ and d₂, capturing the main features of our idealized model. Tuning d₁ yields a periodic change of sign of CD, originating from the quarter-wave plate condition,

$$d_{\mathrm{QWP}}=\frac{2\left(l+\frac{1}{2}\right)\lambda }{4\mathrm{\Delta }{\eta }_1},$$ 2

where λ is the operational wavelength, Δη₁ = η_x,1 − η_y,1 = η_x,1 is the birefringence of the top layer, and l is the integer that indicates the order of the wave plate³¹. Even orders of l yield a phase difference of $\pi /2\mathrm{mod}2\pi$, for which the resulting CD is positive, (blue-colored features in Fig. 2b), whereas odd orders give a phase difference of $3\pi /2\mathrm{mod}2\pi$, for which CD is negative (orange-colored features in Fig. 2b). Thereby, light that is emitted from the dichroic emitter (layer 2) is converted into either left- or right-circularly polarized light depending on the thickness of the quarter-wave plate (layer 1).

From Fig. 2b, tuning d₂ also yields a resonant behavior of CD. In order for the bottom layer to maximally emit, it should maximally absorb. Maximizing this absorption is dictated by Fabry–Pérot resonances that arise at particular thicknesses d₂, and it is straightforward to show that the spacing of these resonances is λ/2η_x,2 (see Supplementary Note 1). By combining these two effects – quarter-wave conversion in the top layer and resonant emission in the bottom layer – the considered idealized system can produce perfectly circularly polarized emission, achieving maximal CD values of  ±1.

Figure 2c shows the circular dichroism as a function of the twist angle α for two different thickness combinations. The blue curve corresponds to d₁ = 3.1 μm, d₂ = 2.3 μm (blue dot in Fig. 2b), and the red curve to d₁ = 4.5 μm, d₂ = 2.3 μm (red dot in Fig. 2b), corresponding to the second (l = 2) and third (l = 3) order of the quarter-wave plate. In both cases, CD reaches its maximal values of  ± 1 at the twist angle α = 45°, as expected in quarter-wave plate operation. Importantly, maximal CD can also be achieved at other twist angles by adjusting the layer thicknesses.

In Fig. 2d, we demonstrate the role of the optical loss in each layer – κ_x,1 and κ_x,2. Maximal CD is achieved when the top layer is lossless (κ_x,1 = 0), as expected for ideal wave-plate operation, while the bottom layer exhibits an optimal finite value of κ_x,2. Physically, this is expected since some losses in the dichroic emitter layer are necessary to yield thermal emission, but excessive losses suppress the resonant (Fabry–Pérot) effect that enhances CD. The white curves are contour plots for which CD reaches the value of 0.4, 0.6, 0.8, while the dashed white line marks the case where both layers are made from the same material (κ_x,1 = κ_x,2 = κ_x). It is thereby demonstrated that high CD values, above 0.6, can be achieved over a broad range of κ_x. The black circle indicates the value of κ_x for α-MoO₃ at λ = 12.8 μm, demonstrating that realistic material parameters are well within the high-CD regime.

Finally, in Fig. 2e, we consider the case where the two layers consist of the same material, and evaluate how CD depends on the real part of its refractive index along each coordinate direction, η_x and η_y. In this panel, d₁ = 0.2 μm and d₂ = 2 μm, while we set κ_x = 0.3 and κ_y = 0, corresponding to realistic values for α-MoO₃^21,32. As expected, along the dashed line where η_x = η_y, CD vanishes as the bilayer does not break mirror symmetry. By contrast, CD is maximized when the refractive index along either coordinate direction vanishes, demonstrating the critical role of strong in-plane birefringence. At the wavelength of λ = 12.8 μm, the optical response of α-MoO₃ is indicated with the black circle in Fig. 2e, at which CD = 0.73.

These results demonstrate that a combination of strong in-plane anisotropy, appropriately tuned layer thicknesses to satisfy Fabry–Pérot and quarter-wave plate conditions, and moderate optical loss in the emitting layer can yield a strong chiral response in twisted bilayers. We note that, by reciprocity, the concept discussed in this section in terms of thermal emission applies to optical absorption as well, for which twisted bilayers can also serve as preferential absorbers of either left- or right-circularly polarized light. We verify this in the experiments we carried out as discussed in the following sections.

α-MoO₃ for chirality

In the previous section, we identified that creating a chiral emitter out of twisted bilayers requires a bottom layer with considerable in-plane dichroism and a top layer with in-plane birefringence. Its strong in-plane optical anisotropy makes α-MoO₃ an ideal material for realizing twisted bilayers that emit chiral light. This anisotropy arises from the orthorhombic crystal structure and interlayer interactions, enabling an intrinsic chiral response when two adjacent α-MoO₃ layers are twisted relative to each other. Exfoliated flakes of α-MoO₃ typically possess a rectangular shape, as shown in the microscope image of a twisted bilayer in Fig. 1c, where we define the crystal directions [100], [001] and [010], as the x-,y- and z-axis, respectively. In Fig. 3a, b, we present the real (η) and imaginary parts (κ), respectively, of the refractive index of α-MoO₃ along the in-plane crystal axes (x and y). The pronounced resonance along the x-direction at 12.35 μm is associated with the phonon mode of α-MoO₃ along that axis.

Fig. 3. Twisted α-MoO₃ bilayers for circular dichroism.

Real (a) and imaginary (b) parts of the refractive index of α-MoO₃ along the in-plane crystal axes x and y, extracted from exfoliated flakes using the method described in³². c Numerical simulations of CD in an α-MoO₃ bilayer with d₁ = 0.2 μm and d₂ = 2 μm. The black cross indicates the twist angle and wavelength at which 97% of the absorbed light is right-hand circularly polarized.

As shown in panel b of Fig. 3, α-MoO₃ possesses a considerable dichroic response (κ_x − κ_y), making it a suitable material for the bottom layer of the twisted chiral bilayers discussed in the previous section. At the same time, it also has a birefringence (η_x − η_y) that reaches a value of 9.4 near 12.4 μm, thereby α-MoO₃ is also a suitable material for the top component of the twisted bilayer, where polarization conversion occurs (see previous section)³³. In fact, due to the extreme value of its birefringence, the top layer can be deeply subwavelength unlike conventional quarter-wave plates³³. The suitability of α-MoO₃ for creating chiral bilayers is also confirmed with the black circles in Fig. 2d and e, marking the values of κ and η of α-MoO₃ for which CD exceeds 0.6.

Figure 3c presents transfer-matrix simulations of CD as a function of wavelength and twist angle for a α-MoO₃ bilayer with thicknesses d₁ = 0.2 μm and d₂ = 2 μm, which are selected upon optimization. The structure exhibits a high CD of 0.61 at a wavelength of 12.8 μm and a twist angle of 58°. Remarkably, at α = 67° (black cross in Fig. 2c), one circular polarization is almost completely suppressed: 97% of the absorbed light is right-hand circularly polarized, while CD remains high at 0.56 (see Supplementary Note 2).

It is important to clarify that, unlike other recently reported phenomena in α-MoO₃ that rely on its hyperbolic response in the mid-IR – such as directional and topological polaritons^34,35, negative reflection³⁶, and reversed Cherenkov radiation³⁷ – the intrinsic chirality discussed here does not require this hyperbolicity. Thereby, other materials that are strongly in-plane anisotropic but not hyperbolic could also serve as constituents of chiral bilayers, as derived in the previous section.

Absorption spectroscopy

Following the methodology outlined above, we experimentally realized twisted bilayers of α-MoO₃ through exfoliation and stacking (see Methods). Upon exfoliation, we have a variety of thicknesses of flakes to select. We use numerical predictions to select the most appropriate thicknesses of flakes that yield pronounced CD, while having control over the twist angle which we use as a degree of freedom. The lateral dimensions of the fabricated bilayers range from 10 μm to 40 μm. The two devices discussed henceforth are termed Device 1 and 2 and consist of a 0.6 μm-thick flake on top of a 1.1 μm-thick flake twisted at an angle of 33° and a 0.8 μm-thick flake on top of a 0.85 μm-thick flake, twisted at an angle of 42° (Fig. 1c–e), respectively. An atomic force microscopy (AFM) scan of the Device 2 is presented in Fig. 1d, while the corresponding height profile is shown in Fig. 1e. Both devices were transferred onto a gold-coated glass substrate to perform CD measurements in reflection. We employed a Fourier transform infrared (FTIR) microscope (36× magnification, Bruker, Hyperion II) for these measurements. The measured area of the devices was restricted to that containing twisted flakes using the knife-edge aperture of the FTIR microscope.

With respect to Eq. (1), determining the spectrum of CD requires a broadband quarter-wave plate to circularly polarize the incident beam onto the sample (red beam path in Fig. 4). Nonetheless, ideal broadband quarter-wave plates are not commercially available at mid-IR wavelengths³³. To circumvent this, we utilized a narrow-band waveplate designed for operation near the wavelength of 13 μm (CdSe from VM-TIM GmbH), and characterized the phase shift that it introduces between the x- and y-component of the electromagnetic field (δ(λ)), for the whole spectral range of interest (see diagram in Fig. 4) using the technique outlined in³⁸. The combination of this wave plate and polarizer, which initially polarizes the IR light of the FTIR spectrometer source (Bruker, Vertex 80), are shown in the beam path of Fig. 4. Consistent with Eq. (1), it can be shown that, for a reflective substrate with vanishing transmission, CD can also be expressed as (see Supplementary Note 1):

$$\text{CD}=\frac{R_{45^{\circ }}-R_{-45^{\circ }}}{\sin \left(\delta \right)},$$ 3

where $R_{45^{\circ }}$ and $R_{-45^{\circ }}$ are the intensities of the reflected electric field when the waveplate’s fast axis is rotated by 45° and  − 45°, respectively, with respect to the linearly polarized light exiting the polarizer. Within the spectral range of interest, the phase shift of the waveplate (δ) presents values near 90°, ensuring that the factor $\sin \left(\delta \right)$ remains near-unity, thereby avoiding singularities in Eq. (3) and minimizing measurement errors.

Fig. 4. Schematic of the experimental setup of the Fourier transform infrared (FTIR) microscope for absorption and emission measurements.

The microscope operates in two modes: reflection and emission. In reflection mode (red beam path), infrared light from a source within the FTIR interferometer is directed onto the sample, and the reflected light is collected by a mercury cadmium telluride (MCT) detector inside the microscope. In emission mode (blue beam path), the sample’s thermal emission is collected by the microscope objective, re-directed through the interferometer, and detected by another MCT detector. A polarizer and a waveplate are positioned between the microscope and the FTIR interferometer to analyze the polarization state of the light in both reflection and emission modes. The diagram below the waveplate illustrates the phase shift (δ) it introduces as a function of wavelength.

These FTIR measurements are shown in Fig. 5a, yielding nearly 20 % CD, confirming the predictions form the previous section as well as previous theoretical estimations^24–27. The theoretical predictions for the experimentally measured devices are shown in panel Fig. 5b, demonstrating the same spectral position where CD is maximized, but larger values of CD as compared to the experimental measurements are observed. This discrepancy arises from the small lateral dimensions of the fabricated twisted areas of α-MoO₃, which are on the scale of the measured wavelength. In particular, transfer matrix calculations assume infinitely extended surfaces, thereby they do not account for edge effects that arise in small-area exfoliated samples. The slight difference between the resonant position of CD in the two devices is expected due to thicknesses variations of the two adjacent layers differ.

Fig. 5. Experimental measurements of CD in absorption.

a FTIR microscope measurements of the CD spectrum of two twisted α-MoO₃ devices (Device 1 with d₁ = 0.6 μm, d₂ = 1.1 μm and twist angle of 33°, Device 2 with d₁ = 0.8 μm, d₂ = 0.85 μm and twist angle of 42°). b Corresponding transfer matrix simulations for the two devices shown in a.

The results of Fig. 5 confirm that twisting of anisotropic bilayers induces a strong chiral response. According to Kirchhoff’s law of thermal radiation³⁰, the preferential circular polarization observed in absorption measurements (red beam path in Fig. 4) should also manifest in thermal emission measurements (blue beam path in Fig. 4), which is confirmed in the following section.

Emission spectroscopy

We used the same experimental setup shown in Fig. 4 for the thermal emission measurements, directly measuring the radiation coming from the sample itself. The sample was placed on a heating stage and its thermal radiation was re-directed towards a mercury cadmium telluride (MCT) detector (see blue beam path). Measuring the polarization state of thermal emission from microscopic samples presents considerable experimental challenges. Most importantly, the signal of the radiation emitted by a microscopic sample is several orders of magnitude smaller than the background radiation from the surrounding and the optical components in the beam path. This makes it difficult to isolate and detect the sample’s thermal signature. To ensure reliable measurements with maximal signal, we focused on Device 2, which had a significantly larger twisted area compared to Device 1, with lateral dimensions of approximately 40 μm (Fig. 1c). Additional challenges in the measurement of thermal emission from microscopic samples include the detector drift, which is on the same order of magnitude as the signal itself, as well as heat-induced mechanical movement of the sample by tens of microns, introducing instabilities. Furthermore, the sublimation temperature of molybdenum oxide is 540 °C³⁹, thereby we operated at much lower temperatures to prevent damage of the sample, however this further limited the detectable signal. All aforementioned parameters affected measurement precision and required accurate control of the instrumentation to obtain reliable data. A detailed analysis of these factors is provided in Supplementary Note 3.

The polarization state of the emitted radiation from the twisted bilayer α-MoO₃ was characterized using Stokes polarimetry, employing a polarization state analyzer (PSA) – a combination of a linear polarizer and a waveplate – following the method outlined by Nguyen et al.¹¹ and Sabatke et al.⁴⁰. The emitted radiation from the twisted bilayers is partially polarized and can be fully described by the Stokes vector S = (S₀, S₁, S₂, S₃), where S₀ represents the total intensity of the emitted light, S₁ and S₂ quantify the difference in intensity between horizontally and vertically polarized light and diagonally and anti-diagonally polarized light, respectively. S₃ characterizes the difference in intensity between right- and left-circularly polarized light, thereby the quantity S₃/S₀ is the parameter of interest in describing chiral properties of emitted radiation^{11,12,41–43}. Due to the small lateral dimensions of the twisted area of the sample, the measured Stokes parameters contained contributions from the entire microscope field of view that includes the twisted area of the sample but also areas of the underlying single flake and that of the bare substrate. Thereby, the component S₀ accounts for the total emission from all areas of the sample, while the linear polarization components S₁ and S₂ had contributions from both the twisted region and the underlying single flake. By contrast, since neither the underlying single α-MoO₃ flake nor the substrate exhibit chiral emission, S₃, the circular polarization component, arose only from the twisted region which is the only one that breaks inversion-rotation symmetry thereby emitting chiral light.

By using the sample-independent background signal B as a reference in the FTIR emission spectroscopy, we extracted the normalized quantity $\tilde{\mathbf{S}}=\mathbf{S}/B$ from measurements with four different PSA configurations (see Supplementary Note 3). From $\tilde{\mathbf{S}}$, we calculate ${\tilde{S}}_3/{\tilde{S}}_0=S_3/S_0$, which is shown in Fig. 6. The quantity S₃/S₀ must be temperature independent, since it represents an intrinsic property of the emitted light – the difference in emissivity of the two circularly polarized components. To confirm this, we carried out measurements at four different temperatures, namely, 300 °C, 350 °C, 400 °C, and 450 °C. As confirmed from Fig. 6, the four measurements overlap, while the small oscillations observed are attributed to the background noise. To reduce the level of noise, we take the average of the four curves, as the bold black curve in Fig. 6.

Fig. 6. Experimental measurements of CD in thermal emission.

Normalized Stokes parameter S₃/S₀ of Device 2 (d₁ = 0.8 μm, d₂ = 0.85 μm and twist angle of 42°) at sample temperatures of 300 °C, 350 °C, 400 °C and 450 °C. The bold black line represents the average of these four curves.

As expected from Kirchhoff’s law, the spectrum in Fig. 6 is in qualitative agreement with the chiral features in the absorption measurements of Fig. 5a, as well as with the transfer matrix calculations (Fig. 5b). Not being able to use a knife-edge aperture to isolate the twisted region of the sample in emission measurements means that the measured S₀ includes contributions from the entire area of the sample including the un-twisted flakes and the substrate, reducing the magnitude of S₃/S₀. The inability to focus is a defining difference between thermal emission experiments as discussed in this section compared to the measurements of CD in absorption spectroscopy in the previous section (Fig. 5), where a knife-edge aperture was used. We confirmed this by repeating the absorption measurements while removing the knife-edge aperture (as in emission measurements), and thereby collecting light from the entire region of the sample, which reduced the magnitude of CD, as expected.

Despite experimental restrictions in using an aperture for focusing solely within the active, twisted area of the flakes, we retrieve a maximal value of S₃/S₀ of approximately 6% (Fig. 6). For reference, recent metasurface-based architectures^11,12,42,43 have achieved values of S₃/S₀ in thermal emission experiments ranging from 25% at wavelengths near 6 μm¹¹ to 83% at wavelengths near 5.3 μm⁴³. Nonetheless, these metasurfaces are composed of geometric shapes that break inversion symmetry, like Z-shapes^11,43 or F-shapes⁴². These approaches require lithographic patterning, whereas the chirality in thermal emission reported here arises from the intrinsic material response of α-MoO₃ and does not rely on lithography. Avenues for increasing the measured S₃/S₀ signal of our twisted bilayers include growth of larger-area flakes, for instance via chemical vapor deposition, as well as careful selection of the thickness of each flake’s thickness and twist angle.

Discussion

In this work, we showed experimentally that unpatterned flakes of van der Waals materials with an in-plane anisotropy can serve as a platform for engineering intrinsic chirality and generating chiral light. Without loss of generality, we demonstrated these properties with α-MoO₃^19–21, however the effect is general and can be observed with other low-dimensional materials as well, for example α-V₂O₅²², as well as their combinations. Both α-MoO₃ and α-V₂O₅ as well as their heterostructures have been recently reported to demonstrate various optical phemomena that originate predominantly from the directional nature of surface phonon polaritons that occur in both materials at mid-IR frequencies^{34–37,44–47}. By contrast, the intrinsic mid-IR chirality and thermally generated chiral light reported here do not rely on polaritonic waves and can be observed in any twisted configuration of in-plane anisotropic materials that have sufficient optical losses.

Despite the unoptimized nature of our flakes, we obtain considerable values of CD reaching 20% in absorption. Although these results already compare with previously reported optimized metamaterial architectures that rely on lithography^{11,12,42,48–50}, they are subject to improvement upon growth of larger-area flakes as well as thickness optimization.

Although thermal emission, in other words incandescence, is by nature unpolarized, unidirectional and incoherent, we demonstrated that twisted, unpatterned bilayers of α-MoO₃ can dramatically modify the characteristics of blackbody radiation, emitting chiral thermal radiation. We achieved this by fabricating twisted α-MoO₃ bilayers with exfoliation and stacking. Despite challenges related to conducting thermal emissivity measurements of samples with microscopic lateral dimensions and at low-temperatures, we were able to detect and confirm the circular polarization state of the emitted light. This highlights the robustness of twisted bilayer devices and their potential for applications in mid-IR polarization control, mid-IR lighting, chiral sensing and detection. The realization of twisted bilayers does not require any lithography, thereby introducing a simple, planar, and scalable roadmap for chirality engineering beyond the regime of traditional metamaterials and lithography-based meta-devices. The reported values of circular dichroism are primarily limited by the finite lateral dimensions of the flakes rather than intrinsic material constraints; therefore, larger-area fabrication approaches such as chemical vapor deposition can help to achieve even stronger chiral signatures.

Methods

We mechanically exfoliated flakes of α-MoO₃ with polydimethylsiloxane-based exfoliation and transfer (X0 retention, DGL type from Gelpak) at 90 °C⁵¹. Firstly, the bottom flake was transferred onto gold-coated (150 nm) glass and consequently the top flake was transferred onto the bottom flake at the desired twist angle, using an optical microscope which enables rotation and positioning of the flakes. The dielectric permittivity, ϵ, of the batch of α-MoO₃ (2D Semiconductors, Bridgman growth technique) used in the devices presented in this article was extracted using FTIR spectroscopy, following the method described in ref. ³². The dielectric permittivity at each frequency is determined by identifying minima in the reflectance spectra near phonon resonances. To recover ϵ(λ) over an extended spectral range, we apply this method to multiple flakes of varying thicknesses – often present on the same substrate after exfoliation – and fit a permittivity model to the extracted values at selected frequencies. These permittivity values serve as the basis for our transfer matrix simulations.

We conducted FTIR micro-spectroscopy measurements using a Bruker Hyperion II microscope coupled with a Bruker Vertex 80 FTIR spectrometer equipped with a MCT detector. A × 36 Cassegrain objective was employed for collection. We utilized a linear ZnSe holographic wire grid polarizer from Thorlabs and a CdSe waveplate from VM-TIM GmbH. The size of the measured area was controlled using the knife-edge aperture of the microscope.

Author contributions

Following the CRediT taxonomy, Conceptualization: G.T.P. Investigation: M.T.E., E.K., M.S., R.B., A.D.; Formal Analysis: M.T.E., E.K., M.S., M.F.P.; Methodology: M.T.E., M.S., E.K. Resources: G.T.P.; Software: M.T.E.; Visualization: M.T.E.; Writing – original draft: M.T.E.; Writing – review & editing: M.T.E., E.K., M.S., M.F.P., R.B., A.D., G.T.P.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewers for their contribution to the peer review of this work. A peer review file is available.

Data availability

The Source Data underlying the figures of this study are available with the paper. All raw data generated during the current study are available from the corresponding authors upon request. Source data are provided with this paper.

Code availability

The code used for the TMM simulations is available at: https://github.com/mtenders/GeneralizedTransferMatrixMethod.jl.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-025-66036-9.