Abstract
Cooper-pair density modulation (CPDM) states are superconducting phases in which the order parameter varies periodically in real space without breaking translational symmetry1,2,3. Moiré superlattices in layered materials4,5,6,7,8,9,10,11,12,13,14,15,16,17,18 have recently emerged as powerful platforms for engineering charge density with tunable lattice symmetry, offering a new route to creating and controlling CPDM states. Here we demonstrate moiré-induced CPDM states in a bilayer heterostructure formed by epitaxially stacking one quintuple layer (1QL) of topological insulator Sb2Te3 on a six-unit-cell (6UC) antiferromagnetic FeTe layer. Scanning tunnelling microscopy and spectroscopy (STM/S) measurements reveal a moiré superlattice formed between the hexagonal tellurium lattice of Sb2Te3 and the square tellurium lattice of FeTe, which spatially modulates the two superconducting gaps of the 1QL Sb2Te3/6UC FeTe bilayer. Our Josephson STM/S measurements provide direct real-space imaging of the CPDM states with a wavelength corresponding to the periodicity of the moiré superlattice. By substituting Sb2Te3 with Bi2Te3, we achieve control over both the periodicity and magnitude of the CPDM states. Our work demonstrates an epitaxial strategy for synthesizing moiré superlattices from materials with different crystal symmetries and reveals a new mechanism for engineering CPDM states in designer bilayer heterostructures.
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The data that support the findings of this article are openly available at Zenodo via https://doi.org/10.5281/zenodo.17139260.
References
Kong, L. et al. Cooper-pair density modulation state in an iron-based superconductor. Nature 640, 55–61 (2025).
Papaj, M., Kong, L., Nadj-Perge, S. & Lee, P. A. Pair density modulation from glide symmetry breaking and nematic superconductivity. Preprint at https://doi.org/10.48550/arXiv.2506.19903 (2025).
Wei, T. et al. Observation of superconducting pair density modulation within lattice unit cell. Chin. Phys. Lett. 42, 027404 (2025).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
Oh, M. et al. Evidence for unconventional superconductivity in twisted bilayer graphene. Nature 600, 240–245 (2021).
Guo, Y. et al. Superconductivity in 5.0° twisted bilayer WSe2. Nature 637, 839–845 (2025).
Xia, Y. et al. Superconductivity in twisted bilayer WSe2. Nature 637, 833–838 (2025).
Mao, J. et al. Evidence of flat bands and correlated states in buckled graphene superlattices. Nature 584, 215–220 (2020).
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).
Tsui, Y. C. et al. Direct observation of a magnetic-field-induced Wigner crystal. Nature 628, 287–292 (2024).
Li, H. et al. Wigner molecular crystals from multielectron moiré artificial atoms. Science 385, 86–91 (2024).
Thompson, E. et al. Microscopic signatures of topology in twisted MoTe2. Nat. Phys. 21, 1224–1230 (2025).
Zhang, F. et al. Experimental signature of layer skyrmions and implications for band topology in twisted WSe2 bilayers. Nat. Phys. 21, 1217–1223 (2025).
Naritsuka, M., Machida, T., Asano, S., Yanase, Y. & Hanaguri, T. Superconductivity controlled by twist angle in monolayer NbSe2 on graphene. Nat. Phys. 21, 746–753 (2025).
Fulde, P. & Ferrell, R. A. Superconductivity in a strong spin-exchange field. Phys. Rev. 135, A550 (1964).
Larkin, A. I. & Ovchinnikov, Y. N. Inhomogeneous state of superconductors. Sov. Phys. JETP 20, 762 (1965).
Vershinin, M. et al. Local ordering in the pseudogap state of the high-Tc superconductor Bi2Sr2CaCu2O8+δ. Science 303, 1995–1998 (2004).
Chen, H. D., Vafek, O., Yazdani, A. & Zhang, S. C. Pair density wave in the pseudogap state of high temperature superconductors. Phys. Rev. Lett. 93, 187002 (2004).
Hamidian, M. H. et al. Detection of a Cooper-pair density wave in Bi2Sr2CaCu2O8+x. Nature 532, 343–347 (2016).
Edkins, S. D. et al. Magnetic field–induced pair density wave state in the cuprate vortex halo. Science 364, 976–980 (2019).
Du, Z. et al. Imaging the energy gap modulations of the cuprate pair-density-wave state. Nature 580, 65–70 (2020).
Liu, Y. Z. et al. Pair density wave state in a monolayer high-Tc iron-based superconductor. Nature 618, 934–939 (2023).
Zhao, H. et al. Smectic pair-density-wave order in EuRbFe4As4. Nature 618, 940–945 (2023).
Liu, X. L., Chong, Y. X., Sharma, R. & Davis, J. C. S. Discovery of a Cooper-pair density wave state in a transition-metal dichalcogenide. Science 372, 1447–1452 (2021).
Chen, H. et al. Roton pair density wave in a strong-coupling kagome superconductor. Nature 599, 222–228 (2021).
Deng, H. et al. Chiral kagome superconductivity modulations with residual Fermi arcs. Nature 632, 775–781 (2024).
Gu, Q. et al. Detection of a pair density wave state in UTe2. Nature 618, 921–927 (2023).
Koz, C., Rößler, S., Tsirlin, A. A., Wirth, S. & Schwarz, U. Low-temperature phase diagram of Fe1+yTe studied using X-ray diffraction. Phys. Rev. B 88, 094509 (2013).
Mansour, A. N. et al. Structural characterization of Bi2Te3 and Sb2Te3 as a function of temperature using neutron powder diffraction and extended X-ray absorption fine structure techniques. J. Appl. Phys. 116, 083513 (2014).
Liang, J. et al. Studies on the origin of the interfacial superconductivity of Sb2Te3/Fe1+yTe heterostructures. Proc. Natl Acad. Sci. USA 117, 221–227 (2020).
Yi, H. et al. Dirac-fermion-assisted interfacial superconductivity in epitaxial topological-insulator/iron-chalcogenide heterostructures. Nat. Commun. 14, 7119 (2023).
He, Q. L. et al. Two-dimensional superconductivity at the interface of a Bi2Te3/FeTe heterostructure. Nat. Commun. 5, 4247 (2014).
Yi, H. et al. Interface-induced superconductivity in magnetic topological insulators. Science 383, 634–639 (2024).
Yuan, W. et al. Coexistence of superconductivity and antiferromagnetism in topological magnet MnBi2Te4 films. Nano Lett. 24, 7962–7971 (2024).
Wang, Q. Y. et al. Interface-induced high-temperature superconductivity in single unit-cell FeSe films on SrTiO3. Chin. Phys. Lett. 29, 037402 (2012).
Chen, M. et al. Discrete energy levels of Caroli-de Gennes-Matricon states in quantum limit in FeTe0.55Se0.45. Nat. Commun. 9, 970 (2018).
Chen, M. Y., Chen, X. Y., Yang, H., Du, Z. Y. & Wen, H. H. Superconductivity with twofold symmetry in Bi2Te3/FeTe0.55Se0.45 heterostructures. Sci. Adv. 4, eaat1084 (2018).
Dynes, R. C., Narayanamurti, V. & Garno, J. P. Direct measurement of quasiparticle-lifetime broadening in a strong-coupled superconductor. Phys. Rev. Lett. 41, 1509 (1978).
Du, Z. et al. Scrutinizing the double superconducting gaps and strong coupling pairing in (Li1−x Fex)OHFeSe. Nat. Commun. 7, 10565 (2016).
Fujita, K. et al. Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates. Proc. Natl Acad. Sci. USA 111, E3026–E3032 (2014).
Cho, D., Bastiaans, K. M., Chatzopoulos, D., Gu, G. D. & Allan, M. P. A strongly inhomogeneous superfluid in an iron-based superconductor. Nature 571, 541–545 (2019).
Kimura, H., Barber, R. P., Ono, S., Ando, Y. & Dynes, R. C. Scanning Josephson tunneling microscopy of single-crystal Bi2Sr2CaCu2O8+δ with a conventional superconducting tip. Phys. Rev. Lett. 101, 037002 (2008).
Joo, S. H. et al. Cooper pair density of Bi2Sr2CaCu2O8+x in atomic scale at 4.2 K. Nano Lett. 19, 1112–1117 (2019).
Liu, Y. B., Zhou, J., Wu, C. & Yang, F. Charge-4e superconductivity and chiral metal in 45-twisted bilayer cuprates and related bilayers. Nat. Commun. 14, 7926 (2023).
Chang, C.-Z., Liu, C.-X. & MacDonald, A. H. Colloquium: quantum anomalous Hall effect. Rev. Mod. Phys. 95, 011002 (2023).
Kezilebieke, S. et al. Moiré-enabled topological superconductivity. Nano Lett. 22, 328–333 (2022).
Lawler, M. J. et al. Intra-unit-cell electronic nematicity of the high-Tc copper-oxide pseudogap states. Nature 466, 347–351 (2010).
Horcas, I. et al. WSXM: a software for scanning probe microscopy and a tool for nanotechnology. Rev. Sci. Instrum. 78, 013705 (2007).
Uehara, Y., Fujita, T., Iwami, M. & Ushioda, S. Superconducting niobium tip for scanning tunneling microscope light emission spectroscopy. Rev. Sci. Instrum. 72, 2097–2099 (2001).
Ternes, M. et al. Subgap structure in asymmetric superconducting tunnel junctions. Phys. Rev. B 74, 132501 (2006).
Acknowledgements
We thank P. J. Hirschfeld, L. Kong, W. Li, C. Liu, Z. Y. Wang, P. Wu and J. Yu for helpful discussions. STM/S measurements were supported by a DOE grant (DE-SC0023113). MBE growth was supported by an ONR Award (N000142412133) and the Penn State MRSEC for Nanoscale Science (DMR-2011839). W.W. acknowledges support from a DOE grant (DE-SC0018153). Ziqiang W. acknowledges support from a DOE grant (DE-FG02-99ER45747). X.X. and C.Z.C. acknowledge support from an AFOSR grant (FA9550-21-1-0177). C.Z.C. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative (grant no. GBMF9063 to C.-Z. C).
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C.Z.C. conceived and designed the experiment. Zihao W., B.X., S.P., Z.J.Y., H.R. and C.Z.C. performed MBE growth. Zihao W., B.X., S.P., P.X., J.S., V.G. and C.Z.C. performed all STM/S measurements. W.W. and X.X. provided experimental support. D.X. and Ziqiang W. provided theoretical support. Zihao W. and C.Z.C. analysed the data and wrote the manuscript with input from all authors.
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Extended data figures and tables
Extended Data Fig. 1 6 UC FeTe and 1 QL (Bi,Sb)2Te3/6 UC FeTe bilayers.
a-c, Large STM topography (1 × 1 µm2) of 6 UC FeTe (a), 1 QL Sb2Te3/6 UC FeTe (b), and 1 QL Bi2Te3/6 UC FeTe (c). d-f, Average dI/dV spectra on 6 UC FeTe (d), 1 QL Sb2Te3/6 UC FeTe (e), and 1 QL Bi2Te3/6 UC FeTe (f). Scale bars: 100 nm (a-c). STM setpoints: Vs = 1.5 V and Is = 50 pA (a, c); Vs = 2 V and Is = 50 pA (b); Vs = 1 V, Is = 1 nA, and Ve = 20 mV (d, e); Vs = 1 V, Is = 500 pA, and Ve = 20 mV (f).
Extended Data Fig. 2 Dynes model fits with two isotropic s-wave superconducting gaps.
a, Symmetrized dI/dV spectrum (black) and two-gap Dynes model fit (red). b, Two-gap Dynes model fits of the dI/dV spectra in Fig. 2c. c, d, Waterfall plot (c) and colour plot (d) of dI/dV spectra measured along the major diagonal direction (red arrow, Fig. 2a) of the rhombic moiré pattern. e, Two-gap Dynes model fits of the dI/dV spectra in (c). f, g, Extracted Δ1 (f) and Δ2 (g) from (e). Both Δ1 and Δ2 exhibit modulations along the major diagonal direction of the rhombic moiré pattern.
Extended Data Fig. 3 Moiré pattern in 1 QL Sb2Te3/6 UC FeTe bilayers under different biases.
a-c, Atomic resolution STM images (10 × 10 nm2) measured at Vs = 50 mV (a), 10 mV (b), and 4 mV (c). d, f, Enlarged atomic resolution STM images of the area marked by the green rectangles in (a) and (b). Te+ (light purple) and Te- (dark purple) atoms are the same at Vs = 50 mV, while Te+ atoms are higher than Te- atoms at Vs = 10 mV. e, g, Vertically averaged height profile Z of (d) and (f). Z at Vs = 10 mV reveals the difference between Te+ and Te- atoms. Scale bars: 1 nm (a-c). STM setpoints: Is = 500 pA (a); Is = 500 pA (b); Is = 50 pA (c).
Extended Data Fig. 4 FT-filtered images of the moiré superlattice, Δ1, and Δ2 in 1 QL Sb2Te3/6 UC FeTe bilayers.
a, Atomic resolution STM image (14 × 14 nm2) acquired simultaneously with the spectroscopic imaging-STM measurements in Fig. 2h,i. b, FT of (a). c-e, FT-filtered images of the moiré superlattice at ±Q1 (d) and ±Q2 (e), and their sum (c). f, g, FT-filtered images of Δ1 at ±Q1 (f) and ±Q2 (g). h, i, FT-filtered images of Δ2 at ±Q1 (h) and ±Q2 (i). The gap modulations in (f-i) exhibit phase shifts relative to the moiré superlattice in (d, e), which can also be extracted using the 2D lock-in method (Figs. 2o, p, and S3). Scale bars: 2 nm (a, c-i); 1 Å−1 (b).
Extended Data Fig. 5 Deconvoluted dI/dV spectra and Josephson tunnelling signals in 1 QL Sb2Te3/6 UC FeTe bilayers.
a, Superconducting gap of the Nb tip. The red curve is the Dynes model fit. The superconducting gap size of the Nb tip Δtip = 1.37 meV. b,c, dI/dV spectra of 1 QL Sb2Te3/6 UC FeTe in Fig. 3b (b) and Fig. 3d (c) after numerically deconvolving the Nb tip contribution. The superconducting gap modulation in (c) is consistent with Fig. 2d. d,e, Waterfall plot (d) and colour plot (e) of g(r, V) spectra measured along the red arrow in Fig. 3a. f, RN(r) measured along the red arrow in Fig. 3a.
Extended Data Fig. 6 More dI/dV spectra of the 1 QL Bi2Te3/6 UC FeTe bilayer.
a, Typical dI/dV spectra measured at different T (Vs = 10 mV, Is = 500 pA, and Ve = 0.2 mV). The dI/dV spectra are vertically shifted for clarity. b, Colour plot of dI/dV spectra measured along a 19 nm line (Vs = 10 mV, Is = 2 nA, and Ve = 0.05 mV). A clear spatial variation is observed in the spectra outside the superconducting gap Δ1 ~ 1.96 meV.
Extended Data Fig. 7 Spatially averaged dI/dV spectra of the 1 QL Bi2Te3/6 UC FeTe bilayer.
a, Spatially averaged dI/dV spectrum from spectroscopic imaging-STM measurements using a PtIr tip (Vs = 8 mV, Is = 1 nA, and Ve = 0.2 mV) in Fig. S8. The average dI/dV spectra remove contributions of QPI and the moiré pattern, revealing two pairs of coherence peaks. Inset: Dynes model fit of the dI/dV spectrum. The black curve shows the symmetrized spectrum, and the red curve shows the fit, yielding Δ1 ~ 1.96 meV and Δ2 ~ 3.32 meV. b, Spatially averaged dI/dV spectrum over a 170 × 170 grid in a 30 × 30 nm2 area from spectroscopic imaging-STM measurements using a superconducting Nb tip (Vs = 10 mV, Is = 1 nA, and Ve = 0.2 mV). c, dI/dV spectrum in (b) after numerically deconvolving the Nb tip contribution. The positions of the coherence peaks match those in (a) measured by a PtIr tip. d, Differential conductance map measured at convoluted coherence peak E ~ Δ1+ Δtip using a Nb tip (Vs = 3.1 mV, Is = 100 pA, and Ve = 0.2 mV). e, FT of (d). f, Differential conductance map measured outside the convoluted superconducting gap using a Nb tip (Vs = 10 mV, Is = 500 pA, and Ve = 0.2 mV). g, FT of (f). FT of the QPI patterns in (e) and (g) exhibit a hexagonal shape, consistent with a prior study on 2 QL Bi2Te3/Fe(Se,Te) (ref. 41). Scale bars: 5 nm (d,f); 1 Å−1 (e, g).
Extended Data Fig. 8 Josephson STM/S measurements on 1 QL Bi2Te3/6 UC FeTe bilayers.
a, dI/dV spectra measured at different RN by gradually reducing the tip-to-sample distance D (Doffset from 0 pm to 60 pm). b, dI/dV spectra near Vbias = 0 mV at different RN (Doffset from 0 pm to 150 pm). c, Zero-bias dI/dV maps showing Josephson tunnelling signals. d, RN(r) map measured in the same area as (c). NJ(r) map in Fig. 4e is obtained by calculating gJ(r, V = 0 mV) × RN2(r). Scale bars: 2 nm (c, d). The STM setpoints in (a-c) are Vs = 10 mV, Is = 2 nA, and Ve = 0.05 mV. The value of Doffset in (c) is 125 pm.
Extended Data Fig. 9 dI/dV maps of the 1 QL Sb2Te3/6 UC FeTe bilayer measured with opposite bias polarities.
a, Atomic resolution STM image (10 × 10 nm2) measured at Vs = 100 mV and Is = 2 nA. b, Atomic resolution STM image (10 × 10 nm2) measured at Vs = −100 mV and Is = 2 nA. c, g(r, 100 mV) obtained simultaneously with (a). d, g(r, −100 mV) obtained simultaneously with (b). The green dots in (a-d) mark the same defect, serving as a spatial reference. e, Line profile of the black curve in (c, d), demonstrating contrast inversion in the differential conductance. The excitation voltage Ve in (a-d) is 10 mV.
Extended Data Fig. 10 Abrikosov vortex in 1 QL Sb2Te3/6 UC FeTe bilayers.
a,b, Zero-bias dI/dV maps g(r, V = 0 mV) at µ0H = 0 T (a) and 8 T (b). c, Zero-bias dI/dV maps g(r, V = 0 mV) of a single Abrikosov vortex. d, dI/dV spectra measured at µ0H = 8 T at the vortex core (red) and away from the vortex (blue). e, Azimuthally averaged zero-bias dI/dV g(r, V = 0 mV) around the vortex in (c) (black) and the exponential decay fit (red). The coherence length is estimated to be ξ = 3.8 ± 0.5 nm. f, dI/dV spectra along the red arrow in (b) (i.e., the minor diagonal direction of the rhombic moiré pattern). g, dI/dV spectra along the green arrow in (b) (i.e., the major diagonal direction of the rhombic moiré pattern). The coherence peaks are suppressed near the vortex core, and g(r, V = 0 mV) exhibits spatial modulations, indicating a moiré-modulated normal state. Scale bars: 3 nm (a,b); 2 nm (c). STM setpoints: Vs = 10 mV, Is = 500 pA, and Ve = 0.2 mV (a-c); Vs = 10 mV, Is = 1 nA, and Ve = 0.1 mV (d,f,g).
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Wang, Z., Xia, B., Paolini, S. et al. Moiré engineering of Cooper-pair density modulation states. Nature (2026). https://doi.org/10.1038/s41586-026-10325-w
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DOI: https://doi.org/10.1038/s41586-026-10325-w
