Abstract

Hyperbolic isofrequency of materials (referred to as hyperbolic materials) renders an unusual electromagnetic response and has potential applications, such as all-angle negative refraction, sub-diffraction imaging and nano-sensing. Compared with artificially structured hyperbolic metamaterials, natural hyperbolic materials have many obvious advantages. However, present natural hyperbolic materials are facing the limitations of narrow operating frequency intervals and high loss stemming from electron-hole excitations. Using first-principles calculations, we demonstrated that the recently-discovered nodal-line semimetallic yttrium nitride (YN) can be tuned to a type-I natural hyperbolic material with a broad frequency window from near-IR (∼1.4 μm) to the visible regime (∼769 nm) along with ultra-low energy loss, owning to the unique electronic band structure near the Fermi level. The unusual optical properties of YN, such as all-angle negative refraction and anisotropic light propagation were verified. The tunable hyperbolic dispersion can be interpreted in terms of the linear relation between critical frequency and plasma frequency. A branch of plasmon dispersion with strong anisotropy in the low-energy region was also revealed in the electron-doped YN. This work is expected to offer a promising strategy for exploring high-performance hyperbolic materials and regulating plasmon properties.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2020 (1)

Z. Guo, H. Jiang, and H. Chen, “Hyperbolic metamaterials: From dispersion manipulation to applications,” J. Appl. Phys. 127(7), 071101 (2020).
[Crossref]

2019 (4)

O. Takayama and A. V. Lavrinenko, “Optics with hyperbolic materials [Invited],” J. Opt. Soc. Am. B 36(8), F38–F48 (2019).
[Crossref]

H. Gao, Z. Wang, X. Ma, X. Zhang, W. Li, and M. Zhao, “Hyperbolic dispersion and negative refraction in a metal-organic framework Cu-BHT,” Phys. Rev. Mater. 3(6), 065206 (2019).
[Crossref]

H. Gao, X. Zhang, W. Li, and M. Zhao, “Tunable broadband hyperbolic light dispersion in metal diborides,” Opt. Express 27(25), 36911–36922 (2019).
[Crossref]

R. M. Córdova-Castro, M. Casavola, M. van Schilfgaarde, A. V. Krasavin, M. A. Green, D. Richards, and A. V. Zayats, “Anisotropic plasmonic CuS nanocrystals as a natural electronic material with hyperbolic optical dispersion,” ACS Nano 13(6), 6550–6560 (2019).
[Crossref]

2018 (4)

C. Cheng, G. Jiang, G. P. Simon, J. Z. Liu, and D. Li, “Low-voltage electrostatic modulation of ion diffusion through layered graphene-based nanoporous membranes,” Nat. Nanotechnol. 13(8), 685–690 (2018).
[Crossref]

W. Ma, P. Alonso-Gonzalez, S. Li, A. Y. Nikitin, J. Yuan, J. Martin-Sanchez, J. Taboada-Gutierrez, I. Amenabar, P. Li, S. Velez, C. Tollan, Z. Dai, Y. Zhang, S. Sriram, K. Kalantar-Zadeh, S.-T. Lee, R. Hillenbrand, and Q. Bao, “In-plane anisotropic and ultra-low-loss polaritons in a natural van der Waals crystal,” Nature 562(7728), 557–562 (2018).
[Crossref]

H. Huang, W. Jiang, K. Jin, and F. Liu, “Tunable topological semimetal states with ultraflat nodal rings in strained YN,” Phys. Rev. B 98(4), 045131 (2018).
[Crossref]

E. Shkondin, T. Repän, M. E. Aryaee Panah, A. V. Lavrinenko, and O. Takayama, “High aspect ratio plasmonic nanotrench structures with large active surface area for label-free mid-infrared molecular absorption sensing,” ACS Appl. Nano Mater. 1(3), 1212–1218 (2018).
[Crossref]

2017 (5)

M. N. Gjerding, R. Petersen, T. G. Pedersen, N. A. Mortensen, and K. S. Thygesen, “Layered van der Waals crystals with hyperbolic light dispersion,” Nat. Commun. 8(1), 320 (2017).
[Crossref]

S. Guan, S. Y. Huang, Y. Yao, and S. A. Yang, “Tunable hyperbolic dispersion and negative refraction in natural electride materials,” Phys. Rev. B 95(16), 165436 (2017).
[Crossref]

P. Cudazzo and M. Gatti, “Collective charge excitations of the two-dimensional electride Ca2N,” Phys. Rev. B 96(12), 125131 (2017).
[Crossref]

B. Mortazavi, M. Shahrokhi, M. Makaremi, and T. Rabczuk, “Anisotropic mechanical and optical response and negative Poisson’s ratio in Mo2C nanomembranes revealed by first-principles simulations,” Nanotechnology 28(11), 115705 (2017).
[Crossref]

B. Yan and C. Felser, “Topological materials: Weyl semimetals,” Annu. Rev. Condens. Matter Phys. 8(1), 337–354 (2017).
[Crossref]

2016 (2)

H. Weng, X. Dai, and Z. Fang, “Topological semimetals predicted from first-principles calculations,” J. Phys.: Condens. Matter 28(30), 303001 (2016).
[Crossref]

K. V. Sreekanth, Y. Alapan, M. ElKabbash, E. Ilker, M. Hinczewski, U. A. Gurkan, A. De Luca, and G. Strangi, “Extreme sensitivity biosensing platform based on hyperbolic metamaterials,” Nat. Mater. 15(6), 621–627 (2016).
[Crossref]

2015 (3)

L. Ferrari, C. Wu, D. Lepage, X. Zhang, and Z. Liu, “Hyperbolic metamaterials and their applications,” Prog. Quantum Electron. 40, 1–40 (2015).
[Crossref]

K. Korzeb, M. Gajc, and D. A. Pawlak, “Compendium of natural hyperbolic materials,” Opt. Express 23(20), 25406–25424 (2015).
[Crossref]

Z. F. Wang and F. Liu, “Self-Assembled Si(111) surface states: 2D Dirac material for THz plasmonics,” Phys. Rev. Lett. 115(2), 026803 (2015).
[Crossref]

2014 (4)

P. Shekhar, J. Atkinson, and Z. Jacob, “Hyperbolic metamaterials: Fundamentals and applications,” Nano Convergence 1(1), 14 (2014).
[Crossref]

E. J. F. Dickinson, H. Ekström, and E. Fontes, “COMSOL Multiphysics®: Finite element software for electrochemical analysis. A mini-review,” Electrochem. Commun. 40, 71–74 (2014).
[Crossref]

T. Low, R. Roldán, H. Wang, F. Xia, P. Avouris, L. M. Moreno, and F. Guinea, “Plasmons and screening in monolayer and multilayer black phosphorus,” Phys. Rev. Lett. 113(10), 106802 (2014).
[Crossref]

J. Sun, N. M. Litchinitser, and J. Zhou, “Indefinite by nature: From ultraviolet to terahertz,” ACS Photonics 1(4), 293–303 (2014).
[Crossref]

2013 (7)

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nat. Photonics 7(12), 948–957 (2013).
[Crossref]

T. Xu, A. Agrawal, M. Abashin, K. J. Chau, and H. J. Lezec, “All-angle negative refraction and active flat lensing of ultraviolet light,” Nature 497(7450), 470–474 (2013).
[Crossref]

K. Andersen and K. S. Thygesen, “Plasmons in metallic monolayer and bilayer transition metal dichalcogenides,” Phys. Rev. B 88(15), 155128 (2013).
[Crossref]

V. P. Drachev, V. A. Podolskiy, and A. V. Kildishev, “Hyperbolic metamaterials: New physics behind a classical problem,” Opt. Express 21(12), 15048–15064 (2013).
[Crossref]

L. Sang, M. Liao, and M. Sumiya, “A comprehensive review of semiconductor ultraviolet photodetectors: from thin film to one-dimensional nanostructures,” Sensors 13(8), 10482–10518 (2013).
[Crossref]

A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, and G. Ceder, “Commentary: The Materials Project: A materials genome approach to accelerating materials innovation,” APL Mater. 1(1), 011002 (2013).
[Crossref]

X. Yang, C. Cheng, Y. Wang, L. Qiu, and D. Li, “Liquid-mediated dense integration of graphene materials for compact capacitive energy storage,” Science 341(6145), 534–537 (2013).
[Crossref]

2012 (3)

D. Lu and Z. Liu, “Hyperlenses and metalenses for far-field super-resolution imaging,” Nat. Commun. 3(1), 1205 (2012).
[Crossref]

C. L. Cortes, W. Newman, S. Molesky, and Z. Jacob, “Quantum nanophotonics using hyperbolic metamaterials,” J. Opt. (Bristol, U. K.) 14(6), 063001 (2012).
[Crossref]

J. B. Khurgin and A. Boltasseva, “Reflecting upon the losses in plasmonics and metamaterials,” MRS Bull. 37(8), 768–779 (2012).
[Crossref]

2011 (3)

J. Sun, J. Zhou, B. Li, and F. Kang, “Indefinite permittivity and negative refraction in natural material: graphite,” Appl. Phys. Lett. 98(10), 101901 (2011).
[Crossref]

X. Qi and S. Zhang, “Topological insulators and superconductors,” Rev. Mod. Phys. 83(4), 1057–1110 (2011).
[Crossref]

J. Yan, J. J. Mortensen, K. W. Jacobsen, and K. S. Thygesen, “Linear density response function in the projector augmented wave method: Applications to solids, surfaces, and interfaces,” Phys. Rev. B 83(24), 245122 (2011).
[Crossref]

2010 (5)

C. Tserkezis, N. Stefanou, and N. Papanikolaou, “Extraordinary refractive properties of photonic crystals of metallic nanorods,” J. Opt. Soc. Am. B 27(12), 2620–2627 (2010).
[Crossref]

D. K. Efetov and P. Kim, “Controlling electron-phonon interactions in graphene at ultrahigh carrier densities,” Phys. Rev. Lett. 105(25), 256805 (2010).
[Crossref]

M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys. 82(4), 3045–3067 (2010).
[Crossref]

J. Enkovaara, C. Rostgaard, J. J. Mortensen, J. Chen, M. Dułak, L. Ferrighi, J. Gavnholt, C. Glinsvad, V. Haikola, and H. A. Hansen, “Electronic structure calculations with GPAW: a real-space implementation of the projector augmented-wave method,” J. Phys.: Condens. Matter 22(25), 253202 (2010).
[Crossref]

P. R. West, S. Ishii, G. V. Naik, N. K. Emani, V. M. Shalaev, and A. Boltasseva, “Searching for better plasmonic materials,” Laser Photonics Rev. 4(6), 795–808 (2010).
[Crossref]

2009 (2)

A. V. Kabashin, P. Evans, S. Pastkovsky, W. Hendren, G. A. Wurtz, R. Atkinson, R. Pollard, V. A. Podolskiy, and A. V. Zayats, “Plasmonic nanorod metamaterials for biosensing,” Nat. Mater. 8(11), 867–871 (2009).
[Crossref]

M. A. Noginov, Y. A. Barnakov, G. Zhu, T. Tumkur, H. Li, and E. E. Narimanov, “Bulk photonic metamaterial with hyperbolic dispersion,” Appl. Phys. Lett. 94(15), 151105 (2009).
[Crossref]

2008 (2)

Y. Liu, G. Bartal, and X. Zhang, “All-angle negative refraction and imaging in a bulk medium made of metallic nanowires in the visible region,” Opt. Express 16(20), 15439–15448 (2008).
[Crossref]

J. Yao, Z. Liu, Y. Liu, Y. Wang, C. Sun, G. Bartal, A. M. Stacy, and X. Zhang, “Optical negative refraction in bulk metamaterials of nanowires,” Science 321(5891), 930 (2008).
[Crossref]

2007 (4)

A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A. Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refraction in semiconductor metamaterials,” Nat. Mater. 6(12), 946–950 (2007).
[Crossref]

H. Lee, Z. Liu, Y. Xiong, C. Sun, and X. Zhang, “Development of optical hyperlens for imaging below the diffraction limit,” Opt. Express 15(24), 15886–15891 (2007).
[Crossref]

Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyperlens magnifying sub-diffraction-limited objects,” Science 315(5819), 1686 (2007).
[Crossref]

Y. Xiong, Z. Liu, C. Sun, and X. Zhang, “Two-dimensional imaging by far-field superlens at visible wavelengths,” Nano Lett. 7(11), 3360–3365 (2007).
[Crossref]

2003 (3)

D. R. Smith and D. Schurig, “Electromagnetic Wave Propagation in Media with Indefinite Permittivity and Permeability Tensors,” Phys. Rev. Lett. 90(7), 077405 (2003).
[Crossref]

P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microw. Opt. Technol. Lett. 37(4), 259–263 (2003).
[Crossref]

C. Luo, S. G. Johnson, J. D. Joannopoulos, and J. B. Pendry, “Negative refraction without negative index in metallic photonic crystals,” Opt. Express 11(7), 746–754 (2003).
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2002 (1)

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Figures (6)

Fig. 1.
Fig. 1. Lattice structure, electronic and optical properties of pristine YN (a) The unit cell of hexagonal YN crystal. Y and N atoms are represented respectively by the large and small balls. (b) The orbital-resolved electronic band structure of YN. The energy at the Fermi level was set to zero. The inset gives the zoom-in band structure of the nodal ring around the Г point. (c) Real and imaginary parts of the permittivity of YN. The shaded region shows the hyperbolic frequency window. The solid lines and dotted lines represent the data obtained by using γ = 0.002 and 0.04 eV, respectively.
Fig. 2.
Fig. 2. Electronic and optical properties of electron-doped YN (a) The electronic band structure of YN with the Fermi level being modulated by different electron-doping concentrations (ne). The red dotted lines indicate the Fermi levels at ne = 0, 1.0× 1022, 2.0× 1022, and 3.33× 1022 cm-3. (b) Real and imaginary parts of the permittivities of electron-doped YN at ne = 1.0× 1022 cm-3. The solid lines and dotted lines represent the data obtained by using γ = 0.002 and 0.04 eV, respectively. (c) The isofrequency contour for air (blue), doped YN (red) and intrinsic YN (green) in the photon energy of 1.49 eV. (d) Isofrequency curves for real (blue) and imaginary (red) parts of wavevector of the electron-doped YN at ne = 1.0× 1022 cm-3 in the photon energy of 1.49 eV, with ${\varepsilon _ \bot } = 5.\textrm{60} + 0.32i$ , ${\varepsilon _{\textrm{||}}} = \textrm{ - }1.67 + 0.39i$ . The unit of the wavevector (k) is Å-1.
Fig. 3.
Fig. 3. Hyperbolic dispersion and negative refraction phenomena of electron-doped YN. (a) The equifrequency contour (EFC) projected onto the kx-kz plane. The negative refraction happens at the interface between the air (blue circle) and doped YN (red hyperbola). The refracted wave vectors and Poynting vectors are indicated by the solid blue and the yellow arrows, respectively. The solutions represented by the dashed arrows are physically incorrect. (b) Simulated electric field distribution in the x-z plane for the TM light with λ=832 nm and an incident of 45°. The color map shows the distribution of the electric field, and the Poynting vectors are marked by dark gray arrows.
Fig. 4.
Fig. 4. Frequency parameters of electron-doped YN (a) The critical frequency (ωc) where $\textrm{Re}\varepsilon ({{\omega_c}} )= 0$ of YN at different electron-doping concentration (ne). The shadow region indicates the hyperbolic area. (b) The frequency window of hyperbolic dispersion of electron-doped YN at different doping concentration. (c) Variation of plasma frequency (ωp) of electron-doped YN as a functional of electron doping concentration. (d) The relation between critical frequency and plasma frequency. The line indicates the linear fitting expression ωc = 0.3 × ωp + 0.07.
Fig. 5.
Fig. 5. In-plane and out-of-plane electron energy loss spectra L( q ,Ω) of (a),(b) pristine YN and (c),(d) electron-doped YN at ne = 1.0 × 1022 cm-3 as a function of the photon energy Ω and momentum q.
Fig. 6.
Fig. 6. The plasmon dispersions of (a) high-energy-excited and (b) low-energy-excited branches extracted from traces of peaks of electron-doped YN at ne = 1.0× 1022 cm-3.

Equations (8)

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k x 2 + k y 2 R e ε | | + k z 2 R e ε = ( ω c ) 2
ε G G R P A ( q , ω ) = δ G G 4 π | q + G | 2 χ G G 0 ( q , ω )
L ( q , ω ) =  -  I m ε M 1 ( q , ω )
ε ( ω ) α β intra = 1 ω p , α β 2 ω 2 + i γ ω
S = 1 2 R e { E × H } = ε k 2 ω ε 0 ε ε | | H 0 2
θ r = t a n 1 ( S x S z ) = t a n 1 ( ε s i n θ i ε | | 2 ε | | s i n 2 θ i )
ω p , α β 2 = 4 π e 2 V n , k 2 f n k ( e α E n , k k ) ( e β E n , k k )
Ω ( q ) = Ω 0 + A q 2

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