Introduction

Element isotopes exist universally and distribute evenly in space (Fig. 1a). Various isotopes have the same number of protons (and electrons) but differ in the numbers of neutrons in the nuclei. Therefore, they possess distinct atomic masses and nuclear spins. The variation in atomic mass affects the nuclear structures1,2, rate of chemical reactions3, and lattice vibrations4,5,6 that govern thermal7,8,9,10 and elastic responses11. Electronic properties12, including superconductivity13, transport14, excitons10,15, and band structures, also vary with isotopes via electron-phonon interactions. In addition, isotopes offer an important resource for quantum technologies16,17,18,19,20 by altering the nuclear spin-related properties for quantum preservation and qubit encoding. These isotope-related merits were facilitated by isotope purifications that globally alter the overall isotope ratios in materials1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20. Notably, both naturally abundant and isotopically purified crystals are isotope-homogenous: all isotopes distribute evenly in space.

Fig. 1: The schematic of van der Waals isotope heterostructuring showcased in phonon polaritons in hBN isotopic heterostructures.
figure 1

a current materials are isotope-homogenous: isotopes always distribute evenly in space. b experiment schematic of s-SNOM imaging of engineered hyperbolic phonon polaritons in 10B−11B isotopic heterostructures.

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In this work, we explore the isotope spatial-heterogeneity by establishing a materials engineering method called van der Waals (vdW) isotope heterostructuring. vdW isotope heterostructuring configures material properties by repositioning isotopes in engineered isotopic heterostructures (Fig. 1b). The advance of this method lies in that fundamental material parameters—atomic mass and nuclear spin—of the same element can vary internally in materials and be spatially engineered. Therefore, intrinsic material responses can be reshaped from an internal perspective to offer virtues absent in current isotope-homogenous systems. We showcase vdW isotope heterostructuring in engineering confined photon-lattice waves—hyperbolic phonon polaritons (HPPs)21,22,23,24,25,26,27,28,29,30—in hexagonal boron nitride (hBN) isotopic heterostructures. By varying the composition, stacking, and thicknesses of monoisotopic 10B and 11B vdW building blocks, HPPs can be engineered into a variety of energy (ω)-momentum (k) dispersions that break the universal even-dispersion in hyperbolic materials31,32,33,34,35,36,37,38,39,40. These confined and tailored polaritons may offer on-demand nano-light for various nanophotonic and thermal functionalities. The method of vdW isotope heterostructuring showcased here can also apply to a broad range of materials and properties due to the universality and importance of isotopes.

Results

Imaging of phonon polaritons in isotopic heterostructures

Engineered HPPs in isotopic heterostructures were characterized by infrared nano-imaging using scattering-type scanning near-field optical microscopy (s-SNOM, method). The s-SNOM is an illuminated atomic force microscope (AFM) that simultaneously delivers topography and nano-optical image of the underneath sample (Fig. 1b). In the experiment, the AFM tip acts as an antenna41 to bridge the momentum mismatch and transfer energy between free-space infrared (IR) light (wavelength λ0 and frequency ω = 1/λ0) and HPPs42,43. The s-SNOM observable near-field amplitude S(ω) possesses a spatial resolution of ~10 nm. Therefore, it can map HPPs and other nano-optical phenomena in real space.

The crystalline anisotropy of hBN leads to natural hyperbolicity (εtεz < 0, εt = εx = εy and εz are in-plane and vertical permittivity, respectively) and HPPs inside the Restrahlen bands21,25. HPPs are typically imaged by s-SNOM as parallel fringes21,22,23,24,25—standing wave interference between tip-launched and edge-reflected HPPs (Fig. 1b). The fringe period is proportional to the HPP wavelength λp. In the s-SNOM images (Fig. 2), fringes show the strongest oscillation closest to crystal edges, followed by weakly damped ones away from the edges. These characteristics are revealed evidently in s-SNOM profiles (gray and green curves in Fig. 2c, d)—line cuts of the s-SNOM images (gray and blue dashed lines in Fig. 2a, b)—of the 10B and 11B hBN. HPPs in 10B and 11B hBN exhibit different energy (ω)-momentum (k = 2π/λp) dispersions: they show different λp at ω = 1440 cm−1 and 1420 cm−1 (Fig. 2a, b) and HPPs at ω = 1380 cm−1 and 1385 cm−1 can only be imaged in 11B hBN (Fig. 2c, d). This dispersion variation originates from the different atomic masses that yield Restrahlen band ω = 1394.5 cm−1 to 1650 cm−1 and 1359.8 cm−1 to 1608.7 cm−1, for 10B and 11B hBN, respectively44.

Fig. 2: The scattering-type scanning near-field optical microscopy (s-SNOM) nano-infrared images of phonon polaritons in hBN isotopic heterostructures.
figure 2

s-SNOM amplitude images of 10B−11B isotopic heterostructures at representative infrared (IR) frequency ω = 1440 cm−1 (a), 1420 cm−1 (b), 1380 cm−1 (e), and 1385 cm−1 (f). c, d s-SNOM profiles cut along dashed lines in (a) and (b) reveal short-period beats in 10B−11B isotopic heterostructures (black, red, blue, cyan, and pink) and long-period fringes in single slab 10B and 11B hBN (gray and green). L is the distance from the slab or heterostructure edge. Scale bar: 2 µm. The compositions of 10B and 11B building blocks in each region are denoted by the stacking from top to bottom.

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The dispersion variation between 10B and 11B hBN facilitates the engineering of HPPs in their stacked hybrids—isotopic heterostructures. At representative IR frequencies (Fig. 2), HPPs were imaged in 10B−11B isotopic heterostructures with distinctive characteristics. Close to the edges of isotopic heterostructures (e.g., Fig. 2a, b), HPPs exhibit short-period beats in addition to long-period fringes. As detailed in the s-SNOM profiles (Fig. 2c, d), the short-period beats in 10B−11B isotopic heterostructures (black, red, blue, cyan, and pink curves) show narrower oscillation features than the fringes in single slab 10B and 11B hBN (gray and green curves). These beats typically do not appear in s-SNOM images of hBN21,22,23,24. Moreover, HPPs in isotopic heterostructures depend strongly on the composition and stacking of the 10B and 11B building blocks. HPPs in the 2-slab heterostructure with stacking (from top to bottom) 10B | 10B, 10B | 11B, 11B | 10B, 11B | 11B, 3-slab heterostructure 10B | 11B | 11B, 11B | 10B | 11B, 11B | 11B | 10B, 10B | 10B | 11B, 10B | 11B | 10B, 11B | 10B | 10B, and 4-slab heterostructure 11B | 10B | 11B | 10B and 11B | 10B | 11B | 10B, show unique s-SNOM oscillations (Fig. 2) that all differ from each other.

Engineer polariton dispersions in isotopic heterostructures

vdW isotope heterostructuring of HPPs is unambiguously revealed in the ω-k dispersions of isotopic heterostructures that are unique at each composition and stacking (Fig. 3). The experimental data (red circles) by Fourier Transform of the s-SNOM images and profiles (Supplementary Note 1) agree excellently with the electromagnetics (EM) calculation of the complex reflectivity of the isotopic heterostructures (false color, Supplementary Note 2). HPPs can be engineered by varying the composition of the isotopic heterostructures: 1 10B slab + 1 11B slab (Fig. 3a, b), 1 10B slab + 2 11B slabs (Fig. 3c–e), 2 10B slab + 1 11B slabs (Fig. 3f–h), and 2 10B slab + 2 11B slabs (Fig. 3i, j), all reveal unique dispersions.

Fig. 3: Energy-momentum (ω-k) dispersions reveal the tailoring of phonon polaritons in isotopic heterostructures by varying the compositions and stacking of the 10B and 11B building blocks.
figure 3

Engineered phonon polaritons in 2-slab (a, b), 3-slab (c–h), and 4-slab (i, j) isotopic heterostructures with the composition and stacking denoted from top to bottom (above the dispersion plots). Various polariton branches are marked by N = 1, 0, and −1, etc. Black arrows in (d) indicate the two dispersion branches approach together. The s-SNOM experimental data and modeling results from the electromagnetics (EM) calculation of the reflectivity are plotted with red circles and false-color maps, respectively.

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Note that current hyperbolic systems have been following the universal even ω-k dispersion33 (Fig. 4): adjacent polariton branches are separated by identical momentum ∆k (red arrows). This universal response originates from the Fabry-Perot quantization condition21:

$$\Delta \varphi=2{k}_{z}d+{\varphi }_{R{{\_}}{sub}}+{\varphi }_{R{{\_}}\sup }=2\pi N.$$
(1)
Fig. 4: Universal even energy-momentum (ω-k) dispersions in isotope-homogenous hyperbolic systems.
figure 4

a–c The ω-k dispersions of naturally abundant hBN, h11BN, and h10BN, respectively. Thickness: 50 nm. Adjacent polariton branches are separated evenly by identical momentum ∆k (red arrows) in all panels. White dashed lines indicate the transverse optical (TO) phonon frequencies of naturally abundant hBN, h10BN, and h11BN, respectively. Various polariton branches are marked by N = 1, 0, and −1, etc.

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\(\Delta \varphi\) is the phase accumulation of HPPs, \({k}_{z}=\sqrt{{{\varepsilon }}_{t}{(\omega /c)}^{2}-{k}^{2}{{\varepsilon }}_{t}/{{\varepsilon }}_{z}}\) is the vertical momentum, d is the thickness of the hyperbolic slab, \({\varphi }_{{R\_sub}}\) and \({\varphi }_{{R\_sub}}\) are the phase of HPP reflection at the substrate and superstrate, and N = 1, 0, and −1, etc., is an integer and varies at different dispersion branches (e.g., Figs. 3–4). At large k, \({k}_{z}\cong {ik}\sqrt{{{\varepsilon }}_{t}/{{\varepsilon }}_{z}}\) and \(k=\frac{i}{d}\sqrt{\frac{{{\varepsilon }}_{z}}{{{\varepsilon }}_{t}}}(-\pi N+\frac{{\varphi }_{{R\_sub}}+{\varphi }_{{R\_}\sup }}{2})\). Therefore, adjacent HPP branches are evenly separated by an identical momentum \(\frac{i}{d}\sqrt{\frac{{{\varepsilon }}_{z}}{{{\varepsilon }}_{t}}}\pi\)—the universal even-dispersion. Although HPPs can be altered by state-of-the-art methods of substrate engineering45,46, coupling with graphene47 and phase change materials48,49,50, HPP branches therein were altered to the same degree: they are shifted by an identical ∆k and still follow the universal even-dispersion.

Remarkably, vdW isotope heterostructuring introduced here breaks this universal response by providing HPPs with a variety of dispersions. In ω = 1350–1400 cm−1, 10B | 10B | 11B (Fig. 3f) shows only 1 polariton branch instead of the conventional unlimited numbers of branches in hyperbolic materials. 10B | 11B | 11B (Fig. 3c) and 10B | 11B | 10B | 11B (Fig. 3j) show 2 branches with stronger N = 1 branches. 11B | 10B | 11B (Fig. 3d) exhibits approaching branches (see black arrows as a guide to the eye): the N = 1 and N = 0 branches are merging where the N = 1 branch fades at 1390 cm−1 while the N = 0 one extends to the higher ω. 10B | 11B | 10B | 11B in Fig. 5e and other compositions in Supplementary Note 3 reveal merging branches: adjacent polariton branches merges. In addition, 11B | 10B | 11B | 10B (Fig. 3i) supports unbalanced branches: the N = 0 branch is significantly weaker than the other polariton branches.

Fig. 5: Energy-momentum (ω-k) dispersions reveal the tailoring of phonon polaritons in isotopic heterostructures by varying the thicknesses of the 10B and 11B building blocks.
figure 5

a–d Phonon polaritons in 3-slab isotopic heterostructures with the identical composition and stacking 11B | 10B | 11B but with the thickness of 27 | 23 | 35 nm (a), 25 | 27 | 16 nm (b), and 6 | 11 | 9 nm (c). d, e Phonon polaritons in 4-slab isotopic heterostructures with the identical composition and stacking 11B | 10B | 11B | 10B but with the thickness of 44 | 32 | 30 | 28 nm (d) and 6 | 11 | 9 | 5 nm (e). Various polariton branches are marked by N = 1, 0, and −1, etc. The s-SNOM data and modeling results are plotted with red circles and false-color maps, respectively.

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The advanced capabilities of vdW isotope heterostructuring in engineering polariton ω-k dispersions originate from the fundamental virtue that atomic masses of the same element inside polaritonic systems can vary locally and be spatially engineered. Specifically, the atomic mass spatial-heterogeneity modifies the local permittivity, thus locally varying kz in 10B and 11B subregions and introducing additional phase jumps of HPP transmission and reflection (\({\varphi }_{{T\_}10/11}\) and \({\varphi }_{{R\_}10/11}\)) at 10B−11B interfaces inside the isotopic heterostructures (see Supplementary Note 4 for the detailed analysis). Therefore, the original Fabry-Perot quantization condition (Eq. 1) is modified. HPPs in 10B−11B isotopic heterostructures can differ from those in isotope-homogenous systems and be engineered into a variety of ω-k dispersions that break the universal even-dispersion.

In addition to the composition, HPPs can be engineered by varying the stacking of 10B and 11B building blocks. For 2-slab heterostructures with the same composition of 1 10B slab + 1 11B slab (Fig. 3a, b), 11B | 10B stacking (Fig. 3a) supports multiple HPP branches spanning from ω = 1360 to 1400 cm−1, whereas 10B | 11B stacking (Fig. 3b) supports a single branch at ω = 1360 to 1380 cm−1. In 3-slab heterostructures with the composition of 1 10B slab + 2 11B slabs, three types of stackings possess all different dispersions: 2 branches for 10B | 11B | 11B (Fig. 3c), approaching branches for 11B | 10B | 11B (Fig. 3d), and evenly distributed branches for 11B | 11B | 10B (Fig. 3e). This stacking engineering is also revealed in 3-slab heterostructures of 2 10B slabs + 1 11B slab (Fig. 3f–h) and 4-slab heterostructures of 2 10B slabs + 2 11B slabs (Fig. 3i, j): each stacking leads to unique HPP dispersion.

vdW isotope heterostructuring is not limited to varying the composition and stacking. The thickness of each building block is another degree of freedom to engineer the overall properties of the isotopic heterostructure. In Fig. 5a-c, we plot the combined experimental and theoretical dispersions in 3-slab isotopic heterostructures with identical composition and stacking 11B | 10B | 11B yet different thicknesses of the 10B and 11B building blocks. These dispersions show evident thickness dependence. The thickness of 27 | 23 | 35 nm (for 11B | 10B | 11B, Fig. 5a) exhibits approaching branches: the N = 1 branch stops at ω ~ 1385 cm−1, whereas the N = 0 branch extends into ω > 1400 cm−1. The thickness of 25 | 27 | 16 nm (Fig. 5b) exhibits unbalanced branches: the N = 1 branch extends into ω > 1400 cm−1, whereas the N = 0 branch is relatively weak and stops at ω ~ 1380 cm−1. Another thickness of 6 | 11 | 9 nm (Fig. 5c) shows balanced and approaching branches, and all HPP branches locate at larger k. The degree of freedom of building blocks’ thicknesses is further verified in 4-slab isotopic heterostructures 11B | 10B | 11B | 10B: the thickness of 44 | 32 | 30 | 28 nm (Fig. 5d) shows unbalanced branches, whereas the thickness of 6 | 11 | 9 | 5 nm (Fig. 5e) shows balanced and merging branches.

Discussion

Combined experiments and theory in Figs. 1–5 showcase the method of vdW isotope heterostructuring in engineering HPPs in 10B-11B isotopic heterostructures. A variety of energy-momentum dispersions are engineered to break the universal even-dispersion for hyperbolic systems and those engineered by state-of-the-art methods45,46,47,48,49. These unique HPP dispersions engineered in isotopic heterostructures can be attributed to the EM interactions of the 10B and 11B hBN building blocks. As a result, the standard hyperbolic modes in 10B and 11B building blocks repulse and form ω-k dispersions. Importantly, the delicate EM interactions and mode repulsion depend strongly on the composition, stacking, and thickness of the 10B and 11B building blocks, therefore offering the degrees of freedom to tailor HPPs in 10B-11B isotopic heterostructures. In Supplementary Note 5, we provide a detailed analysis of various ω-k dispersions of HPPs in 10B-11B isotopic heterostructures from the perspective of EM interactions.

The highly-confined HPPs may be delicately engineered to offer on-demand nano-light by programming the isotope building blocks in isotopic heterostructures. Therefore, the HPPs can possess unique and tailorable energy-momentum dispersions and photonic density of states. These merits offer unique approaches to control nanoscale light-matter wave propagation, light emission, quantum optics, and energy transfer, thus expanding the current nanophotonic and thermal functionalities51. Due to the universality and importance of isotopes, the method of vdW isotope heterostructuring established here can apply to a broad range of materials and engineer thermal, electronic, magnetic, quantum, and other properties where atomic mass or nuclear spin plays a role. Future works may be directed towards extending vdW isotope heterostructuring from hBN to other materials where a series of monoisotopic crystals4,7,8,9,10,15 have been produced. Yet, their isotopic heterostructures are promising but remain unexplored. It is also worth building few-atomic-layer isotopic heterostructures where isotopic moiré superlattices can be involved to configure related material properties, including moiré superconductivity52, ferroelectricity53, ferromagnetism54, excitons55,56,57,58, and many others59,60,61,62,63,64. In addition, it may be valuable to investigate the optical responses of interfaces within isotopic heterostructures, particularly at frequencies where the permittivity of the constituent slabs changes sign. Furthermore, while this work mainly exploits spatially engineered atomic masses to showcase vdW isotope heterostructuring, the other fundamental virtue of this method—spatially engineered nuclear spins—is equally promising and can be explored in spintronics18,65,66,67, chemical reactions3,68, and quantum information and technologies16,17,18,19,20.

Methods

Fabrication of isotopic heterostructures

10B-11B isotopic heterostructures were assembled using the standard vdW dry transfer method52. First, thin slabs of h10BN and h11BN were mechanically exfoliated from bulk monoisotopic crystals grown at atmospheric pressure from an iron-chromium flux69. Poly (bisphenol A carbonate) (PC)/polydimethylsiloxane (PDMS) were then used to pick up h10BN and h11BN thin slabs and stack them together into 10B-11B isotopic heterostructures.

Infrared nano-imaging

The infrared nano-imaging of polaritons in isotopic heterostructures was performed using the scattering-type scanning near-field optical microscope (s-SNOM, www.neaspec.com). The s-SNOM is a tapping-mode atomic force microscope (AFM) illuminated by monochromatic mid-IR quantum cascade lasers (QCLs) with a frequency coverage of 900–2300 cm–1. In the experiment, the AFM tip (radius ~10 nm, PtIr coating) taps at the frequency of ~280 kHz and the amplitude of ~70 nm. The s-SNOM nano-images were obtained by the pseudoheterodyne interferometric detection: the scattered signal from the AFM tip was collected and demodulated at the third harmonics of the tapping frequency to obtain the genuine near-field response.