Ultralow-Dispersion Radio-Frequency Epsilon-Near-Zero Metacomposite via 3D-Printed FeCoNi-N-CNTs Architecture

Abstract

Epsilon-near-zero (ENZ) materials exhibit unique electromagnetic responses when approaching plasma frequency, attracting considerable attention for advanced wave manipulation. However, achieving ENZ characteristics in the radio frequency (RF) range is often hindered by pronounced dielectric dispersion and limited material design approaches. Herein, we demonstrate a rationally engineered metacomposite that simultaneously delivers RF ENZ response and record-low dispersion. The material is fabricated by 3D printing a polydimethylsiloxane (PDMS) matrix embedded with in situ self-assembled FeCoNi nanoparticles and nitrogen-doped carbon nanotubes, which is denoted as FeCoNi-N-CNTs. This gives rise to a metacomposite showing a smooth transition of the real permittivity (ε′) from –27.5 at 1 MHz to 1.5 at 110 MHz, with a zero-crossing point at 53 MHz. Remarkably, the variation in ε′ (Δε′) is only 29 across this 110-fold frequency span, representing the lowest dispersion reported to date among RF ENZ systems. Hall-effect measurements indicate preserved high carrier mobility, a key factor in dispersion suppression. Mechanistic analyses reveal that FeCoNi and N doping induce band flattening, increasing the electron effective mass and reducing carrier density. This study not only establishes a new design strategy for low-dispersion ENZ metacomposites but also paves the way for innovative RF applications such as compact antennas, sensitive sensors, and reconfigurable metamaterial equipment.

Keywords

Radio frequency / Epsilon-near-zero / Low dielectric dispersion / Additive manufacturing / Metacomposite

References

[1] Runge M, Woerner M, Bondar DI, Elsaesser T. Solvated electrons in polar liquids as ϵ-near-zero materials tunable in the terahertz frequency range. Phys Rev Lett, 2025, 134 056901

[2] McDonnell C, Carletti L, Vincenti MA, Della Valle G, De Angelis C, Celebrano M, Ellenbogen T. THz field induced second harmonic generation in epsilon near zero indium tin oxide thin films. Nano Lett, 2025, 25 12201

[3] Baù E, Aigner A, Biechteler J, Heimig C, Weber T, Gölz T, Maier SA, Tittl A. Spatially Encoded Polaritonic Ultra-Strong Coupling in Gradient Metasurfaces with Epsilon-Near-Zero Modes. Adv Mater. 2025; n/a: e10402.

[4] Mathew A, Aschwanden R, Tripathi A, Jangid P, Sain B, Zentgraf T, Kruk S. Nonreciprocal metasurfaces with epsilon-near-zero materials. Nano Lett, 2025, 25 3259

[5] Ferrante C, Principi E, Assogna L, Sahoo A, Batignani G, Fumero G, Foglia L, Mincigrucci R, Giannessi L, Scopigno T, Masciovecchio C, Marini A. Epsilon-near-zero nonlinearity enhancement in the extreme ultraviolet. Light Sci Appl, 2025, 14 374

[6] Gurung S, Bej S, Dang Q, Sahoo A, Anopchenko A, Yi Z, Sokolov AV, Marini A, Lee HWH. Control of ultrafast hot electron dynamics in epsilon-near-zero conductive oxide thin films. Sci Adv. 11: eadu8850.

[7] Shi W, Wang Z, Liu J, Xu W, Zhang C, Zhang C, Li W, Gao K, Liu H. Enhanced the tunable nonlinearity of epsilon-near-zero nonlocal metasurface by quasi-guided mode. Laser Photonics Rev, 2025, 19 2402312

[8] Dal Negro L, Franchi R, Ornigotti M. Nonlinear quantum electrodynamics of epsilon-near-zero nanostructures. Phys Rev B Condens Matter, 2025, 112 165433

[9] Mambra A, Pant R, Mitra J. Leveraging epsilon-near-zero phenomena for on-chip photonic modulation. Phys Rev B Condens Matter, 2025, 112 085308

[10] Whittier C, Casagrande T, Chalifour M, Kelley KP, Tolchin MJ, He M, Nolen JR, Maria J-P, Caldwell JD, Masiello DJ, Bassim ND, Lagos MJ. Spatial distribution and sensitivity of localized plasmon modes in individual infrared SPP/ENZ resonators probed via EELS. ACS Photonics, 2025, 12 7020

[11] Li P, Yan W, Wang S, Fu P, Zhang Y, Li Y. Engineering epsilon-near-zero media with waveguides. Adv Phys Res, 2024, 3 2400070

[12] Nie Z, Murzyn K, Guery L, van den Hooven TJ, Kraus PM. Ultrafast permittivity engineering enables broadband enhancement and spatial emission control of harmonic generation in ZnO. ACS Photonics, 2024, 11 5084

[13] Hemayat S, Darbari S. Far-field position-tunable trapping of dielectric particles using a graphene-based plasmonic lens. Opt Express, 2022, 30 5512

[14] Iyer PP, Pendharkar M, Agarwal A, Foronda H, Iza M, Mishra UK, Nakamura S, DenBaars S, Keller S, Palmstrøm C, Schuller JA. High-Q, size-independent, and reconfigurable optical antennas embedded in zero-index cavities. ACS Nano, 2025, 19 36148

[15] Wang D, Lu Z, Warkander S, Gupta N, Wang Q, Ci P, Guo R, Li J, Javey A, Yao J, Wang F, Wu J. Long-range optical coupling with epsilon-near-zero materials. Nat Commun, 2025, 16 9172

[16] Bu H, Fu P, Li Y. Engineering integral and differential dispersion with subwavelength-scaled planar metastructures for image encryption. Laser Photonics Rev. 2025; n/a: e02463.

[17] Wang C, Wei X, Yun L, Hu E, Liu C, Zheng J, Zhang Z, Yu K, Wei W. Numerical study of a tapered fiber magnetic field sensor based on the ENZ mode. Appl Opt, 2024, 63 8648

[18] Sui J-Y, Du R, Liao S-Y, Zhang H-F. A multitasking renal function assessment Janus biosensor based on photonic spin Hall effect at epsilon-near-zero threshold frequency of YaBa₂Cu₃O₇ ceramic material. Ceram Int, 2025, 51 2526

[19] Yan W, Zhou Z, Li H, Li Y. Transmission-type photonic doping for high-efficiency epsilon-near-zero supercoupling. Nat Commun, 2023, 14 6154

[20] Wu J, Clementi M, Huang C, Ye F, Fu H, Lu L, Zhang S, Li Q, Brès C-S. Thermo-optic epsilon-near-zero effects. Nat Commun, 2024, 15 794

[21] Kim H, Kim G, Jeon Y-U, Lee W, Lee B-H, Kim IS, Lee K, Kim SJ, Kim J. Perovskite Lanthanum-Doped Barium Stannate: a refractory near-zero-index material for high-temperature energy harvesting systems. Adv Sci, 2024, 11 2302410

[22] Hwang JS, Xu J, Raman AP. Simultaneous control of spectral and directional emissivity with gradient epsilon-near-zero InAs photonic structures. Adv Mater, 2023, 35 2302956

[23] Liu M, Xia S, Wan W, Qin J, Li H, Zhao C, Bi L, Qiu C-W. Broadband mid-infrared non-reciprocal absorption using magnetized gradient epsilon-near-zero thin films. Nat Mater, 2023, 22 1196

[24] Yu P, Besteiro LV, Huang Y, Wu J, Fu L, Tan HH, Jagadish C, Wiederrecht GP, Govorov AO, Wang Z. Broadband metamaterial absorbers. Adv Opt Mater, 2019, 7: 1800995

[25] Ma X, Teng X, Xu L, Bao A, Qu H, Li Q, Zhang S, Zhu J. Visible light and infrared camouflage based on epsilon near zero materials. Adv Opt Mater, 2025, 13: 2403438

[26] Xu R, Crassee I, Bechtel HA, Zhou Y, Bercher A, Korosec L, Rischau CW, Teyssier J, Crust KJ, Lee Y, Gilbert Corder SN, Li J, Dionne JA, Hwang HY, Kuzmenko AB, Liu Y. Highly confined epsilon-near-zero and surface phonon polaritons in SrTiO₃ membranes. Nat Commun, 2024, 15: 4743

[27] Wu H, Zhang Z, Wang C, Abualnaja KM, Abo-Dief HM, Hou Q, Algadi H, Yin R, Liu X, Xie P, Liu Y. Radio-frequency broadband epsilon-near-zero response in biocompatible silver nanoparticles/polystyrene films with three-dimensional honeycomb-like superstructures. Adv Compos Hybrid Mater, 2023, 6: 206

[28] Ansari B, Kalhoro AN, Shah S, Memon F, Ali A, Afridi S. Ability and limitations of the effective medium theory in terms of the filling fraction and number of layers for hyperbolic metamaterials. Appl Opt, 2025, 64: 2497

[29] Estevez D, Qin F. High-performance carbonaceous absorbers: from heterogeneous absorbents to data-driven metamaterials. Carbon, 2025, 233 119850

[30] Dong E, Zhang T, Zhang J, Su X, Qu S, Ye X, Gao Z, Gao C, Hui J, Wang Z, Fang NX, Zhang Y. Soft Metalens For Broadband Ultrasonic Focusing Through Aberration Layers. Nat Commun, 2025, 16: 308

[31] Li X, Ma D, Xu X, Wang H, Jin F, Cheng J, Guo B, Liu C, Wang H. Graded dielectric metamaterial with designable permittivity fabricated by 3D printing. Adv Funct Mater. 2025; n/a: e14533.

[32] Zhu S, Zhao X, Han L, Zi J, Hu X, Chen H. Controlling water waves with artificial structures. Nat Rev Phys, 2024, 6: 231

[33] Wang Z, Nasir S, Bharadwaj S, Liu Y, Mambakkam SV, Yu M, Law S. Terahertz Dirac hyperbolic metamaterial. ACS Photonics, 2024, 11: 4134

[34] Wang Z, Sun K, Wu H, Qu Y, Tian J, Ju L, Fan R. Epsilon-near-zero response derived from collective oscillation in the metacomposites with ultralow plasma frequency. Compos Sci Technol, 2022, 227 109600

[35] Shi Z-c, Fan R-h, Zhang Z-d, Qian L, Gao M, Zhang M, Zheng L-t, Zhang X-h, Yin L-w. Random composites of nickel networks supported by porous alumina toward double negative materials. Adv Mater. 2012; 24: 2349.

[36] Dai J, Jiang H, Guo Z, Qiu J. Tunable Epsilon-and-Mu-Near-Zero metacomposites. Adv Funct Mater, 2024, 34 2308338

[37] Wei Z, Zhao L, Wang Z, Xu C, Zhang Y, Liu Y, Gao W, Fan R. Experimental observation of purely resistive effect in epsilon-near-zero transition metal perovskite. Acta Mater, 2024, 266 119704

[38] Zhang X, Yan X, He Q, Wei H, Long J, Guo J, Gu H, Yu J, Liu J, Ding D, Sun L, Wei S, Guo Z. Electrically conductive Polypropylene nanocomposites with negative permittivity at low Carbon Nanotube loading levels. ACS Appl Mater Interfaces, 2015, 7 6125

[39] Fu X, Han Y, Wang J, Yang J, Sun Y, Ding C, Jia Y, Wang J, Qu S, Cui T. 2nd-Order Debye relaxation in electromagnetic metasurfaces for wideband dispersion engineering. Light Sci Appl, 2025, 14 143

[40] Wang J-S. Beyond the Drude model: surface and nonlocal effects in near-field radiative heat transfer and the Casimir puzzle. Phys Rev B Condens Matter, 2025, 111 245404

[41] Luo S, Misra RP, Sam A, Frömbgen T, Kirchner B, Blankschtein D. Explicit modeling of electronic polarization reveals water-mediated screening of ion adsorption at Hexagonal Boron Nitride interfaces. ACS Nano, 2025, 19 27500

[42] Willby C, Kiffner M, Tindall J, Crain J, Jaksch D. Quantum information perspective on many-body dispersive forces. Phys Rev Lett, 2025, 135 110403

[43] Reshef O, De Leon I, Alam MZ, Boyd RW. Nonlinear optical effects in epsilon-near-zero media. Nat Rev Mater, 2019, 4 535

[44] Ma L, Yang Y, Wang L. Frequency-selective characteristics of Plasma-Energy Selective Surface Structure in high-power microwave protection. IEEE Trans Plasma Sci, 2025, 53 2241

[45] Alilou S, Shahrassai L, Sobhanian S. Study of the skin depth and electromagnetic field evolution in laser-generated plasma with different density profiles. Chaos Solitons Fractals, 2025, 199 116891

[46] Cen Y, Tan Y, Wang L, Cai J, Wang H, Ma J, Su T. Regulation mechanism of negative dielectric properties of single-phase SnO₂ based ceramics via (Sb, Mn) co-doped strategy. J Eur Ceram Soc, 2025, 45 117700

[47] Baranwal R, Upadhyay S. Room-temperature negative dielectric constant behavior in La1-xSrxFeO3 (0 ≤ x≤ 0.5) within the radio frequency range by plasmonic oscillations. Ceram Int. 2025; 51: 57654.

[48] Goh GL, Lee SZH, Goh DJS, Goh GD, Cheah E, Yeong WY. Printing 3D metallic structures through reduction processes: principle, approaches, and applications. Prog Mater Sci, 2026, 157 101610

[49] Liu G, Zhang X, Lu X, Zhao Y, Zhou Z, Xu J, Yin J, Tang T, Wang P, Yi S, Fan J, Zhuo X, Chan YH, Wong WL, Bian H, Zuo J, Dai Y, Wu J, Lu J. 4D additive–subtractive manufacturing of shape memory ceramics. Adv Mater, 2023, 35 2302108

[50] Luo J, Luo Q, Li Q, Sun G. Mesoscale insights into fiber reorientation driven pseudo-ductility in 3D printed CFRP composites. Compos A, 2026, 200 109327

[51] Sohrabi-Kashani A, Yazdani Sarvestani H, Lacelle T, Martinez-Rubi Y, Zou S, Robitaille A, Lavoie H, Jakubinek MB, Ashrafi B. 3D-printed boron nitride nanotube-reinforced polymer-derived ceramics with reduced porosity and enhanced strength. Compos B, 2026, 308 112991

[52] Didilis K, Selicani GV, Tinti VB, Mobin M, Brouczek D, Staal L, Marani D, Insinga AR, Haugen AB, Esposito V. Topology-driven electromechanical actuation in 3D-printed TPMS piezoelectric ceramics. Acta Mater, 2026, 303 121724

[53] Sun K, Wang C, Tian J, Zhang Z, Zeng N, Yin R, Duan W, Hou Q, Zhao Y, Wu H, Fan R. Magnetic-driven broadband epsilon-near-zero materials at radio frequency. Adv Funct Mater, 2024, 34 2306747

[54] Hu L, Zhang Y, Wu H, Li J, Li Y, McKenna M, He J, Liu F, Pennycook SJ, Zeng X. Entropy engineering of SnTe: multi-principal-element alloying leading to ultralow lattice thermal conductivity and state-of-the-art thermoelectric performance. Adv Energy Mater, 2018, 8 1802116

[55] Liu Y, Jiang H, Zhu Y, Yang X, Li C. Transition metals (Fe, Co, and Ni) encapsulated in nitrogen-doped carbon nanotubes as bi-functional catalysts for oxygen electrode reactions. J Mater Chem A, 2016, 4 1694

[56] Cao X, Ren S, Yu Z, Fan Q, Lv Q, Yu R, Li A, Yang J, Mao J. Synergistic integration of atomic-scale Ni-N sites and Ni nanoparticles for enhanced protonation in pH-universal electrochemical CO₂ reduction. Chem Catal. 2025; 5.

[57] Wei J, Gao P, Wang S, Ma Y, Cao D, Cheng D. Lowering the kinetic barrier via the synergistic catalysis of N-CNTs supported RhP subnanoclusters and confined Co nanoparticles for olefins hydroformylation. ACS Catal, 2025, 15 1399

[58] Li P, Wang C, Zhang G, Fan K, Liu Y, Li B, Liu P, Zong L, Wang L. Pre-coordination synthesis of active Fe single-atom catalyst enabling efficient and ultralong-life oxygen depolarized cathode applications. Chem Eng J, 2025, 522 167199

[59] Zhang Z, Qiu Y, Wang Y, Yu M, Ma Z, Wang R, Liu S. Entropy-Engineered HEO/Fe, N-CNT Bioanode via Flash Joule Heating: Accelerated Electron Harvesting and Directed Geobacter Enrichment for High-Power Microbial Fuel Cells. Small. 2025; n/a: e11164.

[60] Sun K, Duan W, Lei Y, Wang Z, Tian J, Yang P, He Q, Chen M, Wu H, Zhang Z, Fan R. Flexible multi-walled carbon nanotubes/polyvinylidene fluoride membranous composites with weakly negative permittivity and low frequency dispersion. Compos Part A Appl Sci Manuf, 2022, 156 106854

[61] Zou X, Huang X, Goswami A, Silva R, Sathe BR, Mikmeková E, Asefa T. Cobalt-embedded nitrogen-rich carbon nanotubes efficiently catalyze hydrogen evolution reaction at all pH values. Angew Chem Int Ed Engl, 2014, 53 4372

[62] Zhao R, Liang Z, Gao S, Yang C, Zhu B, Zhao J, Qu C, Zou R, Xu Q. Puffing up energetic metal–organic frameworks to large carbon networks with hierarchical porosity and atomically dispersed metal sites. Angew Chem Int Ed Engl, 2019, 58 1975

[63] Hao J, Zhuang Z, Cao K, Gao G, Wang C, Lai F, Lu S, Ma P, Dong W, Liu T, Du M, Zhu H. Unraveling the electronegativity-dominated intermediate adsorption on high-entropy alloy electrocatalysts. Nat Commun, 2022, 13 2662

[64] Huang K, Peng D, Yao Z, Xia J, Zhang B, Liu H, Chen Z, Wu F, Wu J, Huang Y. Cathodic plasma driven self-assembly of HEAs dendrites by pure single FCC FeCoNiMnCu nanoparticles as high efficient electrocatalysts for OER. Chem Eng J, 2021, 425 131533

[65] Zhu H, Sun S, Hao J, Zhuang Z, Zhang S, Wang T, Kang Q, Lu S, Wang X, Lai F, Liu T, Gao G, Du M, Wang D. A high-entropy atomic environment converts inactive to active sites for electrocatalysis. Energy Environ Sci, 2023, 16 619

[66] Han X, Zhang T, Wang X, Zhang Z, Li Y, Qin Y, Wang B, Han A, Liu J. Hollow mesoporous atomically dispersed metal-nitrogen-carbon catalysts with enhanced diffusion for catalysis involving larger molecules. Nat Commun, 2022, 13 2900

[67] Shi Q, He Y, Bai X, Wang M, Cullen DA, Lucero M, Zhao X, More KL, Zhou H, Feng Z, Liu Y, Wu G. Methanol tolerance of atomically dispersed single metal site catalysts: mechanistic understanding and high-performance direct methanol fuel cells. Energy Environ Sci, 2020, 13 3544

[68] Rong C, Shen X, Wang Y, Thomsen L, Zhao T, Li Y, Lu X, Amal R, Zhao C. Electronic structure engineering of single-atom Ru sites via Co–N4 sites for bifunctional pH-universal water splitting. Adv Mater, 2022, 34 2110103

[69] Wu H, Yin R, Qian L, Zhang Z. Three-dimensional graphene network/phenolic resin composites towards tunable and weakly negative permittivity. Mater Des, 2017, 117 18

[70] Li B, Sui G, Zhong W-H. Single negative metamaterials in unstructured polymer nanocomposites toward selectable and controllable negative permittivity. Adv Mater, 2009, 21 4176

[71] Qin F, Peng M, Estevez D, Brosseau C. Electromagnetic composites: from effective medium theories to metamaterials. J Appl Phys, 2022, 132 101101

[72] Sun K, Fan R, Yin Y, Guo J, Li X, Lei Y, An L, Cheng C, Guo Z. Tunable negative permittivity with Fano-like resonance and magnetic property in percolative silver/yittrium iron garnet nanocomposites. J Phys Chem C, 2017, 121 7564

[73] Kasagi T, Goda K, Yamamoto S. Complex permittivity spectra of granular polymer composites with dispersed Ag-coated Cu flakes. J Electron Mater, 2024, 53 7865

[74] Fan G, Zhang X, Wang Q, Su R, Tang Y, Hao C, Liu Y. Dielectric evolution of permittivity transition from positive to negative induced by percolation in ceramic composites. Ceram Int, 2023, 49 35518

[75] Shetty HD, Prasad V. Existence of negative permittivity in carbon coated iron nanoparticle - PDMS composites. Mater Chem Phys, 2017, 196 153

[76] Lei X, Tang Q, Zheng Y, Kidkhunthod P, Zhou X, Ji B, Tang Y. High-entropy single-atom activated carbon catalysts for sustainable oxygen electrocatalysis. Nat Sustain, 2023, 6 816

[77] Xu L, Tian B, Wang T, Yu Y, Wu Y, Cui J, Cao Z, Wu J, Zhang W, Zhang Q, Liu J, Li Z, Tian Y. Direct Z-scheme polymeric heterojunction boosts photocatalytic hydrogen production via a rebuilt extended π-delocalized network. Energy Environ Sci, 2022, 15 5059

[78] Guo P, Schaller RD, Ketterson JB, Chang RPH. Ultrafast switching of tunable infrared plasmons in indium tin oxide nanorod arrays with large absolute amplitude. Nat Photonics, 2016, 10 267

[79] Iyer PP, Pendharkar M, Palmstrøm CJ, Schuller JA. Ultrawide thermal free-carrier tuning of dielectric antennas coupled to epsilon-near-zero substrates. Nat Commun, 2017, 8: 472

[80] Van Welzenis RG, Ridley BK. On the properties of InSb quantum wells. Solid-State Electron, 1984, 27: 113

[81] Chen Z, Guo X, Zhang F, Shi Q, Tang M, Ang R. Routes for advancing SnTe thermoelectrics. J Mater Chem A, 2020, 8: 16790

[82] Lv H, Guo Y, Wu G, Ji G, Zhao Y, Xu ZJ. Interface Polarization strategy to solve electromagnetic wave interference issue. ACS Appl Mater Interfaces, 2017, 9: 5660

[83] He N, Liu M, Qi J, Tong J, Sao W, Yang X, Shi L, Tong G. Plasmon resonance strategy to enhance permittivity and microwave absorbing performance of Cu/C core-shell nanowires. Chem Eng J, 2019, 378 122160

[84] Eggert B, Delczeg-Czirjak EK, Hauback B, Frommen C. Magnetic transitions in V-Fe-Co-Ni-Cu-based high entropy alloys. Mater Today Phys, 2023, 35 101116

Funding

Weifang Science and Technology Development Plan Project(2023GX028)

Shandong Medical and Health Science and Technology Development Program(202413020625)

the Fundamental Research Funds for the Central Universities(3132025180)

Dalian Maritime University Teacher Development Project Funding(JF2025Y03)

RIGHTS & PERMISSIONS

Donghua University, Shanghai, China