Abstract

VO2 is a unique phase change material with strongly anisotropic electronic properties. Recently, samples have been prepared that present a co-existence of phases and thus form metal-insulator junctions of the same chemical compound. Using first principles calculations, the optical properties of metallic and semiconducting VO2 are here discussed to design self-contained natural optical metamaterials, avoiding coupling with other dielectric media. The analysis of the optical properties complements the experiments in the description of the vast change in reflectance and metallicity for both disordered and planar compounds. The present results also predict the possibility to realize ordered VO2 junctions operating as efficient hyperbolic metamaterials in the THz-visible range, by simply adjusting the ratio between metallic and insulating VO2 content. The possibility to excite propagating volume plasmom polariton across the metamaterial is finally discussed.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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2017 (3)

J. Rensberg, Y. Zhou, S. Richter, C. Wan, S. Zhang, P. Schöppe, R. Schmidt-Grund, S. Ramanathan, F. Capasso, M. A. Kats, and C. Ronning, “Epsilon-near-zero substrate engineering for ultrathin-film perfect absorbers,” Phys. Rev. Appl. 8, 014009 (2017).
[Crossref]

R. Yahiaoui and H. H. Ouslimani, “Broadband polarization-independent wide-angle and reconfigurable phase transition hybrid metamaterial absorber,” J. Appl. Phy. 122, 093104 (2017).
[Crossref]

C. McGahan, S. Gamage, J. Liang, B. Cross, R. E. Marvel, R. F. Haglund, and Y. Abate, “Geometric constraints on phase coexistence in vanadium dioxide single crystals,” Nanotechnology 28, 085701 (2017).
[Crossref] [PubMed]

2016 (7)

M. W. Kim, S. S. Ha, O. Seo, D. Y. Noh, and B. J. Kim, “Real-Time Structural and Electrical Characterization of Metal-Insulator Transition in Strain-Modulated Single-Phase VO2 Wires with Controlled Diameters,” Nano Lett. 16, 4074–4081 (2016).
[Crossref] [PubMed]

E. Strelcov, A. Ievlev, A. Belianinov, A. Tselev, A. Kolmakov, and S. V. Kalinin, “Local coexistence of VO2 phases revealed by deep data analysis,” Sci. Rep. 6, 29216 (2016).
[Crossref]

Y. Wang, J. Zhu, W. Yang, T. Wen, M. Pravica, Z. Liu, M. Hou, Y. Fei, L. Kang, Z. Lin, C. Jin, and Y. Zhao, “Reversible switching between pressure-induced amorphization and thermal-driven recrystallization in VO2 nanosheets,” Nature Commun. 7, 12214 (2016).
[Crossref]

W. H. Brito, M. C. O. Aguiar, K. Haule, and G. Kotliar, “Metal-Insulator Transition in VO2: A DFTD-MFT Perspective,” Phys. Rev. Lett. 117, 056402 (2016).
[Crossref]

F. Menges, M. Dittberner, L. Novotny, D. Passarello, S. S. P. Parkin, M. Spieser, H. Riel, and B. Gotsmann, “Thermal radiative near field transport between vanadium dioxide and silicon oxide across the metal insulator transition,” Appl. Phys. Lett. 108, 171904 (2016).
[Crossref]

J. Rensberg, S. Zhang, Y. Zhou, A. S. McLeod, C. Schwarz, M. Goldflam, M. Liu, J. Kerbusch, R. Nawrodt, S. Ramanathan, D. N. Basov, F. Capasso, C. Ronning, and M. A. Kats, “Active optical metasurfaces based on defect-engineered phase-transition materials,” Nano Lett. 16, 1050–1055 (2016).
[Crossref]

Z. Chen, X. Wang, Y. Qi, S. Yang, J. A. N. T. Soares, B. A. Apgar, R. Gao, R. Xu, Y. Lee, X. Zhang, J. Yao, and L. W. Martin, “Self-assembled, nanostructured, tunable metamaterials via spinodal decomposition,” ACS Nano 10, 10237–10244 (2016).
[Crossref] [PubMed]

2015 (8)

Y. Abate, R. E. Marvel, J. I. Ziegler, S. Gamage, M. H. Javani, M. I. Stockman, and R. F. Haglund, “Control of plasmonic nanoantennas by reversible metal-insulator transition,” Sci. Rep. 5, 13997 (2015).
[Crossref] [PubMed]

S. Cueff, D. Li, Y. Zhou, F. J. Wong, J. A. Kurvits, S. Ramanathan, and R. Zia, “Dynamic control of light emission faster than the lifetime limit using VO2 phase-change,” Nature Commun. 6, 8636 (2015).
[Crossref]

S. Savo, Y. Zhou, G. Castaldi, M. Moccia, V. Galdi, S. Ramanathan, and Y. Sato, “Reconfigurable anisotropy and functional transformations with VO2-based metamaterial electric circuits,” Phys. Rev. B 91, 1–10 (2015).
[Crossref]

M. Gatti, F. Sottile, and L. Reining, “Electron-hole interactions in correlated electron materials: Optical properties of vanadium dioxide from first principles,” Phys. Rev. B 91, 195137 (2015).
[Crossref]

L. A. Agapito, S. Curtarolo, and M. Buongiorno Nardelli, “Reformulation of DFT + U as a pseudohybrid hubbard density functional for accelerated materials discovery,” Phys. Rev. X 5, 1–16 (2015).

P. Gopal, M. Fornari, S. Curtarolo, L. A. Agapito, L. S. I. Liyanage, and M. Buongiorno Nardelli, “Improved predictions of the physical properties of Zn- and Cd-based wide band-gap semiconductors: A validation of the ACBN0 functional,” Phys. Rev. B 91, 245202 (2015).
[Crossref]

E. E. Narimanov and A. V. Kildishev, “Metamaterials: Naturally hyperbolic,” Nature Phot. 9, 214–216 (2015).
[Crossref]

K. Korzeb, M. Gajc, and D. A. Pawlak, “Compendium of natural hyperbolic materials,” Opt. Express 23, 25406–25419 (2015).
[Crossref] [PubMed]

2014 (4)

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

A. Calzolari, A. Ruini, and A. Catellani, “Transparent Conductive Oxides as Near-IR Plasmonic Materials: The Case of Al-Doped ZnO Derivatives,” ACS Phot. 1, 703–709 (2014).
[Crossref]

B. Xiao, J. Sun, A. Ruzsinszky, and J. P. Perdew, “Testing the Jacob’s ladder of density functionals for electronic structure and magnetism of rutile VO2,” Phys. Rev. B 90, 085134 (2014).
[Crossref]

H. N. S. Krishnamoorthy, Y. Zhou, S. Ramanathan, E. Narimanov, and V. M. Menon, “Tunable hyperbolic metamaterials utilizing phase change heterostructures,” Appl. Phys. Lett. 104, 2012–2017 (2014).
[Crossref]

2013 (5)

A. Calzolari and M. Buongiorno Nardelli, “Dielectric properties and Raman spectra of ZnO from a first principles finite-differences/finite-fields approach,” Sci. Rep, 3, 2999 (2013).
[Crossref]

S. V. Zhukovsky, O. Kidwai, and J. E. Sipe, “Physical nature of volume plasmon polaritons in hyperbolic metamaterials,” Opt. Express 21, 14982–14987 (2013).
[Crossref] [PubMed]

S. Ishii, A. V. Kildishev, E. Narimanov, V. M. Shalaev, and V. P. Drachev, “Sub-wavelength interference pattern from volume plasmon polaritons in a hyperbolic medium,” Laser & Phot. Rev. 7, 265–271 (2013).
[Crossref]

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nature Phot. 7, 958 (2013).
[Crossref]

N. Engheta, “Pursuing near-zero response,” Science 340, 286–287 (2013).
[Crossref] [PubMed]

2012 (4)

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

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
[Crossref] [PubMed]

C. Weber, D. D. O’Regan, N. D. M. Hine, M. C. Payne, G. Kotliar, and P. B. Littlewood, “Vanadium dioxide: A peierls-mott insulator stable against disorder,” Phys. Rev. Lett. 108, 1–5 (2012).
[Crossref]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
[Crossref]

2011 (2)

V. Eyert, “VO2: A novel view from band theory,” Phys. Rev. Lett. 107, 016401 (2011).
[Crossref]

S. Zhang, I. S. Kim, and L. J. Lauhon, “Stoichiometry engineering of monoclinic to rutile phase transition in suspended single crystalline vanadium dioxide nanobeams,” Nano Lett. 11, 1443–1447 (2011).
[Crossref] [PubMed]

2010 (2)

A. C. Jones, S. Berweger, J. Wei, D. Cobden, and M. B. Raschke, “Nano-optical Investigations of the Metal-Insulator Phase Behavior of Individual VO2 Microcrystals,” Nano Lett. 10, 1574–1581 (2010).
[Crossref] [PubMed]

Q.-Y. Wen, H.-W. Zhang, Q.-H. Yang, Y.-S. Xie, K. Chen, and Y.-L. Liu, “Terahertz metamaterials with VO2 cut-wires for thermal tunability,” Appl. Phys. Lett. 97, 021111 (2010).
[Crossref]

2009 (3)

S. Zhang, J. Y. Chou, and L. J. Lauhon, “Direct Correlation of Structural Domain Formation with the Metal Insulator Transition in a VO2 Nanobeam,” Nano Lett. 9, 4527–4532 (2009).
[Crossref] [PubMed]

M. M. Qazilbash, M. Brehm, G. O. Andreev, A. Frenzel, P. C. Ho, B.-G. Chae, B.-J. Kim, S. J. Yun, H.-T. Kim, A. V. Balatsky, O. G. Shpyrko, M. B. Maple, F. Keilmann, and D. N. Basov, “Infrared spectroscopy and nano-imaging of the insulator-to-metal transition in vanadium dioxide,” Phys. Rev. B 79, 075107 (2009).
[Crossref]

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

2008 (1)

B.-J. Kim, Y. W. Lee, S. Choi, J.-W. Lim, S. J. Yun, H.-T. Kim, T.-J. Shin, and H.-S. Yun, “Micrometer x-ray diffraction study of VO2 films: Separation between metal-insulator transition and structural phase transition,” Phys. Rev. B 77, 235401 (2008).
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2007 (3)

V. Galitski and Y. B. Kim, “Spin-Triplet pairing instability of the spinon Fermi surface in a U(1) spin liquid,” Phys. Rev. Lett. 99, 266403 (2007).
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M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, “Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging,” Science 318, 1750 (2007).
[Crossref] [PubMed]

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,” Nature Mater. 6, 946–950 (2007).
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2006 (3)

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Expr. 14, 8247–8256 (2006).
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M. M. Qazilbash, K. S. Burch, D. Whisler, D. Shrekenhamer, B. G. Chae, H. T. Kim, and D. N. Basov, “Correlated metallic state of vanadium dioxide,” Phys. Rev. B 74, 1–5 (2006).
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T. C. Koethe, Z. Hu, M. W. Haverkort, C. Schler-Langeheine, F. Venturini, N. B. Brookes, O. Tjernberg, W. Reichelt, H. H. Hsieh, H. J. Lin, C. T. Chen, and L. H. Tjeng, “Transfer of spectral weight and symmetry across the metal-insulator transition in VO2,” Phys. Rev. Lett. 97, 1–4 (2006).
[Crossref]

2005 (2)

S. Biermann, A. Poteryaev, A. I. Lichtenstein, and A. Georges, “Dynamical singlets and correlation-assisted Peierls transition in VO2,” Phys. Rev. Lett. 94, 1–4 (2005).
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S. A. Ramakrishna, “Physics of negative refractive index materials,” Rep. Progr. Phys. 68, 449 (2005).
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2003 (1)

P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microwave and Optical Technology Letters 37, 259–263 (2003).
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1999 (1)

A. Continenza, S. Massida, and M. Posternak, “Self-energy correction of VO2 within a model GW scheme,” Phys. Rev. B 60, 15699–15704 (1999).
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1998 (1)

M. Imada, A. Fujimori, and Y. Tokura, “Metal-insulator transitions,” Rev. Mod. Phys. 70, 1039–1263 (1998).
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1995 (1)

M. Rocca, “Low-energy EELS investigation of surface electronic excitations on metals,” Surf. Sci. Rep. 22, 1–71 (1995).
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1979 (2)

D. Sawatzky and G. A. Post, “X-ray photoelectron and auger spectroscopy study of some vanadium oxides,” Phys. Rev. B 20, 1546 (1979).
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D. Kucharczyk and T. Niklewski, “Accurate Xray determination of the lattice parameters and the thermal expansion coefficients of VO22 near the transition temperature,” J. Appl. Cryst. 12, 370–373 (1979).
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1968 (1)

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172, 788 (1968).
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Abate, Y.

C. McGahan, S. Gamage, J. Liang, B. Cross, R. E. Marvel, R. F. Haglund, and Y. Abate, “Geometric constraints on phase coexistence in vanadium dioxide single crystals,” Nanotechnology 28, 085701 (2017).
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Y. Abate, R. E. Marvel, J. I. Ziegler, S. Gamage, M. H. Javani, M. I. Stockman, and R. F. Haglund, “Control of plasmonic nanoantennas by reversible metal-insulator transition,” Sci. Rep. 5, 13997 (2015).
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Agapito, L. A.

P. Gopal, M. Fornari, S. Curtarolo, L. A. Agapito, L. S. I. Liyanage, and M. Buongiorno Nardelli, “Improved predictions of the physical properties of Zn- and Cd-based wide band-gap semiconductors: A validation of the ACBN0 functional,” Phys. Rev. B 91, 245202 (2015).
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L. A. Agapito, S. Curtarolo, and M. Buongiorno Nardelli, “Reformulation of DFT + U as a pseudohybrid hubbard density functional for accelerated materials discovery,” Phys. Rev. X 5, 1–16 (2015).

Aguiar, M. C. O.

W. H. Brito, M. C. O. Aguiar, K. Haule, and G. Kotliar, “Metal-Insulator Transition in VO2: A DFTD-MFT Perspective,” Phys. Rev. Lett. 117, 056402 (2016).
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Alekseyev, L.

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,” Nature Mater. 6, 946–950 (2007).
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Alekseyev, L. V.

Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-field imaging beyond the diffraction limit,” Opt. Expr. 14, 8247–8256 (2006).
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Andreev, G. O.

M. M. Qazilbash, M. Brehm, G. O. Andreev, A. Frenzel, P. C. Ho, B.-G. Chae, B.-J. Kim, S. J. Yun, H.-T. Kim, A. V. Balatsky, O. G. Shpyrko, M. B. Maple, F. Keilmann, and D. N. Basov, “Infrared spectroscopy and nano-imaging of the insulator-to-metal transition in vanadium dioxide,” Phys. Rev. B 79, 075107 (2009).
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M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, “Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging,” Science 318, 1750 (2007).
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Apgar, B. A.

Z. Chen, X. Wang, Y. Qi, S. Yang, J. A. N. T. Soares, B. A. Apgar, R. Gao, R. Xu, Y. Lee, X. Zhang, J. Yao, and L. W. Martin, “Self-assembled, nanostructured, tunable metamaterials via spinodal decomposition,” ACS Nano 10, 10237–10244 (2016).
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Averitt, R. D.

M. Liu, H. Y. Hwang, H. Tao, A. C. Strikwerda, K. Fan, G. R. Keiser, A. J. Sternbach, K. G. West, S. Kittiwatanakul, J. Lu, S. A. Wolf, F. G. Omenetto, X. Zhang, K. A. Nelson, and R. D. Averitt, “Terahertz-field-induced insulator-to-metal transition in vanadium dioxide metamaterial,” Nature 487, 345–348 (2012).
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Balatsky, A. V.

M. M. Qazilbash, M. Brehm, G. O. Andreev, A. Frenzel, P. C. Ho, B.-G. Chae, B.-J. Kim, S. J. Yun, H.-T. Kim, A. V. Balatsky, O. G. Shpyrko, M. B. Maple, F. Keilmann, and D. N. Basov, “Infrared spectroscopy and nano-imaging of the insulator-to-metal transition in vanadium dioxide,” Phys. Rev. B 79, 075107 (2009).
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M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, “Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging,” Science 318, 1750 (2007).
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Barker, A. S.

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172, 788 (1968).
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Baroni, S.

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

Basov, D. N.

J. Rensberg, S. Zhang, Y. Zhou, A. S. McLeod, C. Schwarz, M. Goldflam, M. Liu, J. Kerbusch, R. Nawrodt, S. Ramanathan, D. N. Basov, F. Capasso, C. Ronning, and M. A. Kats, “Active optical metasurfaces based on defect-engineered phase-transition materials,” Nano Lett. 16, 1050–1055 (2016).
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M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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M. M. Qazilbash, M. Brehm, G. O. Andreev, A. Frenzel, P. C. Ho, B.-G. Chae, B.-J. Kim, S. J. Yun, H.-T. Kim, A. V. Balatsky, O. G. Shpyrko, M. B. Maple, F. Keilmann, and D. N. Basov, “Infrared spectroscopy and nano-imaging of the insulator-to-metal transition in vanadium dioxide,” Phys. Rev. B 79, 075107 (2009).
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M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, “Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging,” Science 318, 1750 (2007).
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M. M. Qazilbash, K. S. Burch, D. Whisler, D. Shrekenhamer, B. G. Chae, H. T. Kim, and D. N. Basov, “Correlated metallic state of vanadium dioxide,” Phys. Rev. B 74, 1–5 (2006).
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Belianinov, A.

E. Strelcov, A. Ievlev, A. Belianinov, A. Tselev, A. Kolmakov, and S. V. Kalinin, “Local coexistence of VO2 phases revealed by deep data analysis,” Sci. Rep. 6, 29216 (2016).
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Belov, P.

A. Poddubny, I. Iorsh, P. Belov, and Y. Kivshar, “Hyperbolic metamaterials,” Nature Phot. 7, 958 (2013).
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Belov, P. A.

P. A. Belov, “Backward waves and negative refraction in uniaxial dielectrics with negative dielectric permittivity along the anisotropy axis,” Microwave and Optical Technology Letters 37, 259–263 (2003).
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Berglund, C. N.

H. W. Verleur, A. S. Barker, and C. N. Berglund, “Optical properties of VO2 between 0.25 and 5 eV,” Phys. Rev. 172, 788 (1968).
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Berweger, S.

A. C. Jones, S. Berweger, J. Wei, D. Cobden, and M. B. Raschke, “Nano-optical Investigations of the Metal-Insulator Phase Behavior of Individual VO2 Microcrystals,” Nano Lett. 10, 1574–1581 (2010).
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Biermann, S.

S. Biermann, A. Poteryaev, A. I. Lichtenstein, and A. Georges, “Dynamical singlets and correlation-assisted Peierls transition in VO2,” Phys. Rev. Lett. 94, 1–4 (2005).
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Blanchard, R.

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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Bonini, N.

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

Brehm, M.

M. M. Qazilbash, M. Brehm, G. O. Andreev, A. Frenzel, P. C. Ho, B.-G. Chae, B.-J. Kim, S. J. Yun, H.-T. Kim, A. V. Balatsky, O. G. Shpyrko, M. B. Maple, F. Keilmann, and D. N. Basov, “Infrared spectroscopy and nano-imaging of the insulator-to-metal transition in vanadium dioxide,” Phys. Rev. B 79, 075107 (2009).
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M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, “Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging,” Science 318, 1750 (2007).
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Brito, W. H.

W. H. Brito, M. C. O. Aguiar, K. Haule, and G. Kotliar, “Metal-Insulator Transition in VO2: A DFTD-MFT Perspective,” Phys. Rev. Lett. 117, 056402 (2016).
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Brookes, N. B.

T. C. Koethe, Z. Hu, M. W. Haverkort, C. Schler-Langeheine, F. Venturini, N. B. Brookes, O. Tjernberg, W. Reichelt, H. H. Hsieh, H. J. Lin, C. T. Chen, and L. H. Tjeng, “Transfer of spectral weight and symmetry across the metal-insulator transition in VO2,” Phys. Rev. Lett. 97, 1–4 (2006).
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Buongiorno Nardelli, M.

P. Gopal, M. Fornari, S. Curtarolo, L. A. Agapito, L. S. I. Liyanage, and M. Buongiorno Nardelli, “Improved predictions of the physical properties of Zn- and Cd-based wide band-gap semiconductors: A validation of the ACBN0 functional,” Phys. Rev. B 91, 245202 (2015).
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L. A. Agapito, S. Curtarolo, and M. Buongiorno Nardelli, “Reformulation of DFT + U as a pseudohybrid hubbard density functional for accelerated materials discovery,” Phys. Rev. X 5, 1–16 (2015).

A. Calzolari and M. Buongiorno Nardelli, “Dielectric properties and Raman spectra of ZnO from a first principles finite-differences/finite-fields approach,” Sci. Rep, 3, 2999 (2013).
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Burch, K. S.

M. M. Qazilbash, K. S. Burch, D. Whisler, D. Shrekenhamer, B. G. Chae, H. T. Kim, and D. N. Basov, “Correlated metallic state of vanadium dioxide,” Phys. Rev. B 74, 1–5 (2006).
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Cai, W.

W. Cai and V. Shalaev, Optical Metamaterials: Fundamentals and Applications (Springer, 2010).
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Calandra, M.

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

Calzolari, A.

A. Calzolari, A. Ruini, and A. Catellani, “Transparent Conductive Oxides as Near-IR Plasmonic Materials: The Case of Al-Doped ZnO Derivatives,” ACS Phot. 1, 703–709 (2014).
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A. Calzolari and M. Buongiorno Nardelli, “Dielectric properties and Raman spectra of ZnO from a first principles finite-differences/finite-fields approach,” Sci. Rep, 3, 2999 (2013).
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Capasso, F.

J. Rensberg, Y. Zhou, S. Richter, C. Wan, S. Zhang, P. Schöppe, R. Schmidt-Grund, S. Ramanathan, F. Capasso, M. A. Kats, and C. Ronning, “Epsilon-near-zero substrate engineering for ultrathin-film perfect absorbers,” Phys. Rev. Appl. 8, 014009 (2017).
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J. Rensberg, S. Zhang, Y. Zhou, A. S. McLeod, C. Schwarz, M. Goldflam, M. Liu, J. Kerbusch, R. Nawrodt, S. Ramanathan, D. N. Basov, F. Capasso, C. Ronning, and M. A. Kats, “Active optical metasurfaces based on defect-engineered phase-transition materials,” Nano Lett. 16, 1050–1055 (2016).
[Crossref]

M. A. Kats, D. Sharma, J. Lin, P. Genevet, R. Blanchard, Z. Yang, M. M. Qazilbash, D. N. Basov, S. Ramanathan, and F. Capasso, “Ultra-thin perfect absorber employing a tunable phase change material,” Appl. Phys. Lett. 101, 221101 (2012).
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Car, R.

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

Castaldi, G.

S. Savo, Y. Zhou, G. Castaldi, M. Moccia, V. Galdi, S. Ramanathan, and Y. Sato, “Reconfigurable anisotropy and functional transformations with VO2-based metamaterial electric circuits,” Phys. Rev. B 91, 1–10 (2015).
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Catellani, A.

A. Calzolari, A. Ruini, and A. Catellani, “Transparent Conductive Oxides as Near-IR Plasmonic Materials: The Case of Al-Doped ZnO Derivatives,” ACS Phot. 1, 703–709 (2014).
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Cavazzoni, C.

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

Ceresoli, D.

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

Chae, B. G.

M. M. Qazilbash, K. S. Burch, D. Whisler, D. Shrekenhamer, B. G. Chae, H. T. Kim, and D. N. Basov, “Correlated metallic state of vanadium dioxide,” Phys. Rev. B 74, 1–5 (2006).
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Chae, B.-G.

M. M. Qazilbash, M. Brehm, G. O. Andreev, A. Frenzel, P. C. Ho, B.-G. Chae, B.-J. Kim, S. J. Yun, H.-T. Kim, A. V. Balatsky, O. G. Shpyrko, M. B. Maple, F. Keilmann, and D. N. Basov, “Infrared spectroscopy and nano-imaging of the insulator-to-metal transition in vanadium dioxide,” Phys. Rev. B 79, 075107 (2009).
[Crossref]

M. M. Qazilbash, M. Brehm, B.-G. Chae, P.-C. Ho, G. O. Andreev, B.-J. Kim, S. J. Yun, A. V. Balatsky, M. B. Maple, F. Keilmann, H.-T. Kim, and D. N. Basov, “Mott Transition in VO2 Revealed by Infrared Spectroscopy and Nano-Imaging,” Science 318, 1750 (2007).
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Chen, C. T.

T. C. Koethe, Z. Hu, M. W. Haverkort, C. Schler-Langeheine, F. Venturini, N. B. Brookes, O. Tjernberg, W. Reichelt, H. H. Hsieh, H. J. Lin, C. T. Chen, and L. H. Tjeng, “Transfer of spectral weight and symmetry across the metal-insulator transition in VO2,” Phys. Rev. Lett. 97, 1–4 (2006).
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Chen, K.

Q.-Y. Wen, H.-W. Zhang, Q.-H. Yang, Y.-S. Xie, K. Chen, and Y.-L. Liu, “Terahertz metamaterials with VO2 cut-wires for thermal tunability,” Appl. Phys. Lett. 97, 021111 (2010).
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Chen, Z.

Z. Chen, X. Wang, Y. Qi, S. Yang, J. A. N. T. Soares, B. A. Apgar, R. Gao, R. Xu, Y. Lee, X. Zhang, J. Yao, and L. W. Martin, “Self-assembled, nanostructured, tunable metamaterials via spinodal decomposition,” ACS Nano 10, 10237–10244 (2016).
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Chiarotti, G. L.

P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. Dal Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, “Quantum espresso: a modular and open-source software project for quantum simulations of materials,” J. Phys.: Condens. Matter. 21, 395502 (2009).

Choi, S.

B.-J. Kim, Y. W. Lee, S. Choi, J.-W. Lim, S. J. Yun, H.-T. Kim, T.-J. Shin, and H.-S. Yun, “Micrometer x-ray diffraction study of VO2 films: Separation between metal-insulator transition and structural phase transition,” Phys. Rev. B 77, 235401 (2008).
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Chou, J. Y.

S. Zhang, J. Y. Chou, and L. J. Lauhon, “Direct Correlation of Structural Domain Formation with the Metal Insulator Transition in a VO2 Nanobeam,” Nano Lett. 9, 4527–4532 (2009).
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Due to the correlated nature of VO2, at early stage after the MIT transition the optical behavior of metallic puddles might be different from the those of pure rutile ones. [27] Here we did not consider these modifications and we assumed the rutile dielectric function as the ingredient of the mixing phase, for any metal content.

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Figures (8)

Fig. 1
Fig. 1 Crystal structure of VO2 in the (a) tetragonal rutile R and (b) monoclinic M1 phase. Uniaxial c-axis is aligned along z direction. The primitive cell in panel (a) is doubled along z for clarity.
Fig. 2
Fig. 2 Electronic band structure of (a) metallic rutile and (b) semiconducting monoclinic VO2 phase. The zero energy reference is set to the Fermi energy (dashed line) of each system. Red (green) arrows mark illustrative interband (intraband) transitions.
Fig. 3
Fig. 3 Real (ϵr) and imaginary (ϵr) part of the complex dielectric function and energy loss spectrum (EELS) for VO2 in (a) rutile and (b) monoclinic phase, calculated in the direction parallel (//) and perpendicular (⊥) to c-axis, as defined in Fig. 1.
Fig. 4
Fig. 4 Scheme of the metamaterial structural models discussed in the text: (a) Bruggeman mixing model (BMM), (b) ridged heterostructure (RHS) and (c) layered heterostructures (LHS). Arrows in panels (b)–(c) identify the components of the dielectric function along the direction parallel ( ϵ ˜ ) and perpendicular ( ϵ ˜ ) to the optical axis.
Fig. 5
Fig. 5 (a) 2D plot of reflectance R ˜ ( E , f ), as a function of the incoming radiation energy E and the filling fraction f , according to the Bruggenman model [Fig. 4(a)]. The horizontal dashed line corresponds to the filling condition f = 0.4, whose real ( ϵ ˜ r ) and imaginary ( ϵ ˜ i ) part of the effective dielectric function are shown in panel (b).
Fig. 6
Fig. 6 2D plot of reflectance R ˜ ( E , f ) as a function of the incoming radiation energy E and the metallic filling fraction f, according to RHS model [Fig. 4(b)], along the direction (a) parallel and (b) perpendicular to VO2 ridges. Horizontal dashed lines correspond to the filling condition f = 0.5, whose real ( ϵ ˜ r, black line) and imaginary ( ϵ ˜ i, red line) part of the effective dielectric function are shown in panels (c) and (d), respectively.
Fig. 7
Fig. 7 (a) 2D plot of the sign function S ( E , f ) as a function of the incoming radiation energy E and the filling fraction f, resulting from the LHS model [Fig. 4(c)]. Horizontal dashed lines correspond to two selected filling fractions, whose optical properties are shown in panels (b)–(d). Parallel and perpendicular components of the (b) dielectric function ϵ ˜ and (c) quality factor Q for the two test cases 1 and 2 selected in panel (a). (d) Strength of the dielectric anisotropy Δ ϵ ˜ r.
Fig. 8
Fig. 8 (a) Vector diagram for TM propagating waves and hyperbolic dispersion isosurface corresponding to a type-II HMM. Angular dependence of (b) the real part of the effective function (φ) and (c) the θ angle between the extraordinary wave and the optical axis, at different incoming electric field for f = 0.5. For each incoming energy, the vertical (horizontal) dotted lines identify the critical angle φc (θc).

Equations (8)

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R ˜ = ( 1 n ˜ ) 2 + k ˜ 2 ( 1 + n ˜ ) 2 + k ˜ 2
n ˜ = { 1 2 [ ( ϵ ˜ r 2 + ϵ ˜ i 2 ) 1 / 2 + ϵ ˜ r ] } 1 / 2 k ˜ = { 1 2 [ ( ϵ ˜ r 2 + ϵ ˜ i 2 ) 1 / 2 + ϵ ˜ r ] } 1 / 2
f ϵ m ϵ ˜ ϵ m + ( 1 q ) q ϵ ˜ + ( 1 f ) ϵ d ϵ ˜ ϵ d + ( 1 q ) q ϵ ˜ = 0 ,
ϵ ˜ ( R H S ) = f ϵ m + ( 1 f ) ϵ d , ϵ ˜ ( R H S ) = ϵ m ϵ d f ϵ d + ( 1 f ) ϵ m ,
ϵ ˜ ( L H S ) = d m + d d d m / ϵ m + d d / ϵ d ϵ ˜ ( L H S ) = ϵ m d m + ϵ d d d d m + d d ,
S ( E , f ) = R e [ ϵ ˜ ] R e [ ϵ ˜ ] | R e [ ϵ ˜ ] R e [ ϵ ˜ ] | .
Q j = R e [ ϵ ˜ j ] I m [ ϵ ˜ j ] Δ ϵ ˜ = R e [ ϵ ˜ ϵ ˜ ] ,
1 ϵ ( φ ) = s i n 2 ( φ ) ϵ + c o s 2 ( φ ) ϵ .

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