Abstract

Bi2Se3 is a topological insulator with unique optical properties, including linearly-dispersing surface states. Many of the proposed device applications for Bi2Se3 require a lattice-matched trivially-insulating component. It is known that (Bi1-xInx)2Se3 is a trivial band insulator for moderate indium concentrations. In this paper, we grow and characterize the optical properties of (Bi1-xInx)2Se3 films with varying indium concentrations. We find that the lattice constant and optical bandgap for (Bi1-xInx)2Se3 varies linearly with concentration. We perform infrared reflection measurements as a function of polarization and angle, enabling us to model the permittivity for these materials. Again, we find that most parameters vary linearly with concentration. Our results for the pure end members are consistent with the literature values. This is the first report of optical values for the intermediate compounds, which are likely to be integral components of future topological insulator optical devices.

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

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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  4. P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
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  5. J.-Y. Ou, J.-K. So, G. Adamo, A. Sulaev, L. Wang, and N. I. Zheludev, “Ultraviolet and visible range plasmonics in the topological insulator Bi1.5Sb0.5Te1.8Se1.2.,” Nat. Commun. 5(1), 5139 (2014).
    [Crossref] [PubMed]
  6. Y.-P. Lai, I.-T. Lin, K.-H. Wu, and J.-M. Liu, “Plasmonics in topological insulators,” Nanomater. Nanotechnol. 4, 13 (2014).
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  21. C. Julien, A. Chevy, and D. Siapkas, “Optical properties of In2Se3 phases,” Phys. Status Solidi 118(2), 553–559 (1990).
    [Crossref]
  22. W. Richter, H. Köhler, and C. R. Becker, “A Raman and far-infrared investigation of phonons in the rhombohedra1 V2-VI3 Compounds,” Phys. Status Solidi 84, 619–628 (1977).
    [Crossref]
  23. T. P. Ginley and S. Law, “Growth of Bi2Se3 topological insulator films using a selenium cracker source,” J. Vac. Sci. Technol. B 34(2), 02L105 (2016).
    [Crossref]
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    [Crossref]
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    [Crossref]
  26. Y. Wang, T. P. Ginley, and S. Law, “Growth of high-quality Bi2Se3 topological insulators using (Bi1-xInx)2Se3 buffer layers,” J. Vac. Sci. Technol. B 36(2), 02D101 (2018).
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
  33. G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
    [Crossref] [PubMed]
  34. J. Hao and L. Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: generalized 4×4 transfer-matrix method,” Phys. Rev. B 77(9), 094201 (2008).
    [Crossref]
  35. M. Schubert, T. E. Tiwald, and C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61(12), 8187–8201 (2000).
    [Crossref]
  36. D. Culcer, E. H. Hwang, T. D. Stanescu, and S. Das Sarma, “Two-dimensional surface charge transport in topological insulators,” Phys. Rev. B 82(15), 155457 (2010).
    [Crossref]
  37. D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
    [Crossref]
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    [Crossref]

2018 (2)

T. P. Ginley and S. Law, “Coupled Dirac plasmons in topological insulators,” Adv. Opt. Mater. 6(13), 1800113 (2018).
[Crossref]

Y. Wang, T. P. Ginley, and S. Law, “Growth of high-quality Bi2Se3 topological insulators using (Bi1-xInx)2Se3 buffer layers,” J. Vac. Sci. Technol. B 36(2), 02D101 (2018).
[Crossref]

2017 (1)

G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
[Crossref] [PubMed]

2016 (4)

N. Balakrishnan, C. R. Staddon, E. F. Smith, J. Stec, D. Gay, G. W. Mudd, O. Makarovsky, Z. R. Kudrynskyi, Z. D. Kovalyuk, L. Eaves, A. Patanè, and P. H. Beton, “Quantum confinement and photoresponsivity of β-In2Se3 nanosheets grown by physical vapour transport,” 2D Mater. 3(2), 025030 (2016).
[Crossref]

T. P. Ginley and S. Law, “Growth of Bi2Se3 topological insulator films using a selenium cracker source,” J. Vac. Sci. Technol. B 34(2), 02L105 (2016).
[Crossref]

M. J. Brahlek, N. Koirala, J. Liu, T. I. Yusufaly, M. Salehi, M.-G. Han, Y. Zhu, D. Vanderbilt, and S. Oh, “Tunable inverse topological heterostructure utilizing (Bi1-xInx)2Se3 and multichannel weak-antilocalization effect,” Phys. Rev. B 93(12), 125416 (2016).
[Crossref]

M. Eddrief, F. Vidal, and B. Gallas, “Optical properties of Bi2Se3: from bulk to ultrathin films,” J. Phys. D Appl. Phys. 49(50), 505304 (2016).
[Crossref]

2015 (2)

D. Wu, A. J. Pak, Y. Liu, Y. Zhou, X. Wu, Y. Zhu, M. Lin, Y. Han, Y. Ren, H. Peng, Y.-H. Tsai, G. S. Hwang, and K. Lai, “Thickness-dependent dielectric constant of few-layer In2Se3 nanoflakes,” Nano Lett. 15(12), 8136–8140 (2015).
[Crossref] [PubMed]

L. Debbichi, O. Eriksson, and S. Lebègue, “Two-Dimensional Indium Selenides Compounds: An Ab Initio Study,” J. Phys. Chem. Lett. 6(15), 3098–3103 (2015).
[Crossref] [PubMed]

2014 (5)

H. D. Lee, C. Xu, S. M. Shubeita, M. Brahlek, N. Koirala, S. Oh, and T. Gustafsson, “Indium and bismuth interdiffusion and its influence on the mobility in In2Se3/Bi2Se3,” Thin Solid Films 556, 322–324 (2014).
[Crossref]

J.-Y. Ou, J.-K. So, G. Adamo, A. Sulaev, L. Wang, and N. I. Zheludev, “Ultraviolet and visible range plasmonics in the topological insulator Bi1.5Sb0.5Te1.8Se1.2.,” Nat. Commun. 5(1), 5139 (2014).
[Crossref] [PubMed]

Y.-P. Lai, I.-T. Lin, K.-H. Wu, and J.-M. Liu, “Plasmonics in topological insulators,” Nanomater. Nanotechnol. 4, 13 (2014).
[Crossref]

Y. Zhao, H. Liu, X. Guo, Y. Jiang, Y. Sun, H. Wang, Y. Wang, H.-D. Li, M.-H. Xie, X.-C. Xie, and J. Wang, “Crossover from 3D to 2D quantum transport in Bi2Se3/In2Se3 superlattices,” Nano Lett. 14(9), 5244–5249 (2014).
[Crossref] [PubMed]

R. B. Jacobs-Gedrim, M. Shanmugam, N. Jain, C. A. Durcan, M. T. Murphy, T. M. Murray, R. J. Matyi, R. L. Moore, and B. Yu, “Extraordinary photoresponse in two-dimensional In(2)Se(3) nanosheets,” ACS Nano 8(1), 514–521 (2014).
[Crossref] [PubMed]

2013 (3)

P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
[Crossref] [PubMed]

X. Tao and Y. Gu, “Crystalline-crystalline phase transformation in two-dimensional In2Se3 thin Layers,” Nano Lett. 13(8), 3501–3505 (2013).
[Crossref] [PubMed]

I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
[Crossref]

2012 (2)

D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
[Crossref]

M. Brahlek, N. Bansal, N. Koirala, S.-Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, “Topological-metal to band-insulator transition in (Bi1-xInx)2Se3 thin films,” Phys. Rev. Lett. 109(18), 186403 (2012).
[Crossref] [PubMed]

2011 (3)

Z. Y. Wang, X. Guo, H. D. Li, T. L. Wong, N. Wang, and M. H. Xie, “Superlattices of Bi2Se3/In2Se3: Growth characteristics and structural properties,” Appl. Phys. Lett. 99(2), 023112 (2011).
[Crossref]

I. Appelbaum, H. D. Drew, and M. S. Fuhrer, “Proposal for a topological plasmon spin rectifier,” Appl. Phys. Lett. 98(2), 023103 (2011).
[Crossref]

S. Kim, M. Ye, K. Kuroda, Y. Yamada, E. E. Krasovskii, E. V. Chulkov, K. Miyamoto, M. Nakatake, T. Okuda, Y. Ueda, K. Shimada, H. Namatame, M. Taniguchi, and A. Kimura, “Surface scattering via bulk continuum states in the 3D topological insulator Bi2Se3,” Phys. Rev. Lett. 107(5), 056803 (2011).
[Crossref] [PubMed]

2010 (4)

J. E. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010).
[Crossref] [PubMed]

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

Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010).
[Crossref] [PubMed]

D. Culcer, E. H. Hwang, T. D. Stanescu, and S. Das Sarma, “Two-dimensional surface charge transport in topological insulators,” Phys. Rev. B 82(15), 155457 (2010).
[Crossref]

2009 (2)

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009).
[Crossref]

2008 (1)

J. Hao and L. Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: generalized 4×4 transfer-matrix method,” Phys. Rev. B 77(9), 094201 (2008).
[Crossref]

2000 (1)

M. Schubert, T. E. Tiwald, and C. M. Herzinger, “Infrared dielectric anisotropy and phonon modes of sapphire,” Phys. Rev. B 61(12), 8187–8201 (2000).
[Crossref]

1998 (1)

J. Ye, S. Soeda, Y. Nakamura, and O. Nittono, “Crystal structures and phase transformation in In2Se3 compound semiconductor,” Jpn. J. Appl. Phys. 37(1), 4264–4271 (1998).
[Crossref]

1992 (1)

M. Stordeur, K. K. Ketavonc, A. Priemuth, H. Sobotta, and V. Riede, “Optical and Electrical Investigations of n-Type Bi2Se3 Single Crystals,” Phys. Status Solidi 169(2), 505–514 (1992).
[Crossref]

1990 (1)

C. Julien, A. Chevy, and D. Siapkas, “Optical properties of In2Se3 phases,” Phys. Status Solidi 118(2), 553–559 (1990).
[Crossref]

1979 (1)

S. Popović, A. Tonejc, B. Gržeta-Plenković, B. Čelustka, and R. Trojko, “Revised and new crystal data for indium selenides,” J. Appl. Cryst. 12(4), 416–420 (1979).
[Crossref]

1978 (1)

K. Kambas and J. Spyridelis, “Far Infrared optical study of α-In2Se3 compound,” Mater. Res. Bull. 13(7), 653–660 (1978).
[Crossref]

1977 (1)

W. Richter, H. Köhler, and C. R. Becker, “A Raman and far-infrared investigation of phonons in the rhombohedra1 V2-VI3 Compounds,” Phys. Status Solidi 84, 619–628 (1977).
[Crossref]

1968 (1)

J. Tauc, “Optical properties and electronic structure of amorphous Ge and Si,” Mater. Res. Bull. 3(1), 37–46 (1968).
[Crossref]

Adam, S.

D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
[Crossref]

Adamo, G.

J.-Y. Ou, J.-K. So, G. Adamo, A. Sulaev, L. Wang, and N. I. Zheludev, “Ultraviolet and visible range plasmonics in the topological insulator Bi1.5Sb0.5Te1.8Se1.2.,” Nat. Commun. 5(1), 5139 (2014).
[Crossref] [PubMed]

Aguilera, I.

I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
[Crossref]

Almeida, G.

G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
[Crossref] [PubMed]

Analytis, J. G.

Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010).
[Crossref] [PubMed]

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

Appelbaum, I.

I. Appelbaum, H. D. Drew, and M. S. Fuhrer, “Proposal for a topological plasmon spin rectifier,” Appl. Phys. Lett. 98(2), 023103 (2011).
[Crossref]

Balakrishnan, N.

N. Balakrishnan, C. R. Staddon, E. F. Smith, J. Stec, D. Gay, G. W. Mudd, O. Makarovsky, Z. R. Kudrynskyi, Z. D. Kovalyuk, L. Eaves, A. Patanè, and P. H. Beton, “Quantum confinement and photoresponsivity of β-In2Se3 nanosheets grown by physical vapour transport,” 2D Mater. 3(2), 025030 (2016).
[Crossref]

Bansal, N.

P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
[Crossref] [PubMed]

M. Brahlek, N. Bansal, N. Koirala, S.-Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, “Topological-metal to band-insulator transition in (Bi1-xInx)2Se3 thin films,” Phys. Rev. Lett. 109(18), 186403 (2012).
[Crossref] [PubMed]

Becker, C. R.

W. Richter, H. Köhler, and C. R. Becker, “A Raman and far-infrared investigation of phonons in the rhombohedra1 V2-VI3 Compounds,” Phys. Status Solidi 84, 619–628 (1977).
[Crossref]

Bertoni, G.

G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
[Crossref] [PubMed]

Beton, P. H.

N. Balakrishnan, C. R. Staddon, E. F. Smith, J. Stec, D. Gay, G. W. Mudd, O. Makarovsky, Z. R. Kudrynskyi, Z. D. Kovalyuk, L. Eaves, A. Patanè, and P. H. Beton, “Quantum confinement and photoresponsivity of β-In2Se3 nanosheets grown by physical vapour transport,” 2D Mater. 3(2), 025030 (2016).
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Bianchi, M.

I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
[Crossref]

Blügel, S.

I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
[Crossref]

Brahlek, M.

H. D. Lee, C. Xu, S. M. Shubeita, M. Brahlek, N. Koirala, S. Oh, and T. Gustafsson, “Indium and bismuth interdiffusion and its influence on the mobility in In2Se3/Bi2Se3,” Thin Solid Films 556, 322–324 (2014).
[Crossref]

P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
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M. Brahlek, N. Bansal, N. Koirala, S.-Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, “Topological-metal to band-insulator transition in (Bi1-xInx)2Se3 thin films,” Phys. Rev. Lett. 109(18), 186403 (2012).
[Crossref] [PubMed]

Brahlek, M. J.

M. J. Brahlek, N. Koirala, J. Liu, T. I. Yusufaly, M. Salehi, M.-G. Han, Y. Zhu, D. Vanderbilt, and S. Oh, “Tunable inverse topological heterostructure utilizing (Bi1-xInx)2Se3 and multichannel weak-antilocalization effect,” Phys. Rev. B 93(12), 125416 (2016).
[Crossref]

Butch, N. P.

D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
[Crossref]

Calvani, P.

P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
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S. Popović, A. Tonejc, B. Gržeta-Plenković, B. Čelustka, and R. Trojko, “Revised and new crystal data for indium selenides,” J. Appl. Cryst. 12(4), 416–420 (1979).
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Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010).
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Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
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Chevy, A.

C. Julien, A. Chevy, and D. Siapkas, “Optical properties of In2Se3 phases,” Phys. Status Solidi 118(2), 553–559 (1990).
[Crossref]

Cho, S.

D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
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Chu, J.-H.

Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010).
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Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
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Chulkov, E. V.

I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
[Crossref]

S. Kim, M. Ye, K. Kuroda, Y. Yamada, E. E. Krasovskii, E. V. Chulkov, K. Miyamoto, M. Nakatake, T. Okuda, Y. Ueda, K. Shimada, H. Namatame, M. Taniguchi, and A. Kimura, “Surface scattering via bulk continuum states in the 3D topological insulator Bi2Se3,” Phys. Rev. Lett. 107(5), 056803 (2011).
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D. Culcer, E. H. Hwang, T. D. Stanescu, and S. Das Sarma, “Two-dimensional surface charge transport in topological insulators,” Phys. Rev. B 82(15), 155457 (2010).
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Dai, X.

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009).
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Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
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D. Culcer, E. H. Hwang, T. D. Stanescu, and S. Das Sarma, “Two-dimensional surface charge transport in topological insulators,” Phys. Rev. B 82(15), 155457 (2010).
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L. Debbichi, O. Eriksson, and S. Lebègue, “Two-Dimensional Indium Selenides Compounds: An Ab Initio Study,” J. Phys. Chem. Lett. 6(15), 3098–3103 (2015).
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P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
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Di Pietro, P.

P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
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Dogan, S.

G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
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I. Appelbaum, H. D. Drew, and M. S. Fuhrer, “Proposal for a topological plasmon spin rectifier,” Appl. Phys. Lett. 98(2), 023103 (2011).
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Durcan, C. A.

R. B. Jacobs-Gedrim, M. Shanmugam, N. Jain, C. A. Durcan, M. T. Murphy, T. M. Murray, R. J. Matyi, R. L. Moore, and B. Yu, “Extraordinary photoresponse in two-dimensional In(2)Se(3) nanosheets,” ACS Nano 8(1), 514–521 (2014).
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N. Balakrishnan, C. R. Staddon, E. F. Smith, J. Stec, D. Gay, G. W. Mudd, O. Makarovsky, Z. R. Kudrynskyi, Z. D. Kovalyuk, L. Eaves, A. Patanè, and P. H. Beton, “Quantum confinement and photoresponsivity of β-In2Se3 nanosheets grown by physical vapour transport,” 2D Mater. 3(2), 025030 (2016).
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M. Eddrief, F. Vidal, and B. Gallas, “Optical properties of Bi2Se3: from bulk to ultrathin films,” J. Phys. D Appl. Phys. 49(50), 505304 (2016).
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L. Debbichi, O. Eriksson, and S. Lebègue, “Two-Dimensional Indium Selenides Compounds: An Ab Initio Study,” J. Phys. Chem. Lett. 6(15), 3098–3103 (2015).
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Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
[Crossref] [PubMed]

H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, “Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface,” Nat. Phys. 5(6), 438–442 (2009).
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Fisher, I. R.

Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010).
[Crossref] [PubMed]

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
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I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
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D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
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I. Appelbaum, H. D. Drew, and M. S. Fuhrer, “Proposal for a topological plasmon spin rectifier,” Appl. Phys. Lett. 98(2), 023103 (2011).
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M. Eddrief, F. Vidal, and B. Gallas, “Optical properties of Bi2Se3: from bulk to ultrathin films,” J. Phys. D Appl. Phys. 49(50), 505304 (2016).
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G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
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N. Balakrishnan, C. R. Staddon, E. F. Smith, J. Stec, D. Gay, G. W. Mudd, O. Makarovsky, Z. R. Kudrynskyi, Z. D. Kovalyuk, L. Eaves, A. Patanè, and P. H. Beton, “Quantum confinement and photoresponsivity of β-In2Se3 nanosheets grown by physical vapour transport,” 2D Mater. 3(2), 025030 (2016).
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G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
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G. Almeida, S. Dogan, G. Bertoni, C. Giannini, R. Gaspari, S. Perissinotto, R. Krahne, S. Ghosh, and L. Manna, “Colloidal monolayer β-In2Se3 nanosheets with high photoresponsivity,” J. Am. Chem. Soc. 139(8), 3005–3011 (2017).
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Giliberti, V.

P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
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T. P. Ginley and S. Law, “Coupled Dirac plasmons in topological insulators,” Adv. Opt. Mater. 6(13), 1800113 (2018).
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P. Di Pietro, M. Ortolani, O. Limaj, A. Di Gaspare, V. Giliberti, F. Giorgianni, M. Brahlek, N. Bansal, N. Koirala, S. Oh, P. Calvani, and S. Lupi, “Observation of Dirac plasmons in a topological insulator,” Nat. Nanotechnol. 8(8), 556–560 (2013).
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S. Popović, A. Tonejc, B. Gržeta-Plenković, B. Čelustka, and R. Trojko, “Revised and new crystal data for indium selenides,” J. Appl. Cryst. 12(4), 416–420 (1979).
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I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
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Y. Zhao, H. Liu, X. Guo, Y. Jiang, Y. Sun, H. Wang, Y. Wang, H.-D. Li, M.-H. Xie, X.-C. Xie, and J. Wang, “Crossover from 3D to 2D quantum transport in Bi2Se3/In2Se3 superlattices,” Nano Lett. 14(9), 5244–5249 (2014).
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H. D. Lee, C. Xu, S. M. Shubeita, M. Brahlek, N. Koirala, S. Oh, and T. Gustafsson, “Indium and bismuth interdiffusion and its influence on the mobility in In2Se3/Bi2Se3,” Thin Solid Films 556, 322–324 (2014).
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M. J. Brahlek, N. Koirala, J. Liu, T. I. Yusufaly, M. Salehi, M.-G. Han, Y. Zhu, D. Vanderbilt, and S. Oh, “Tunable inverse topological heterostructure utilizing (Bi1-xInx)2Se3 and multichannel weak-antilocalization effect,” Phys. Rev. B 93(12), 125416 (2016).
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D. Wu, A. J. Pak, Y. Liu, Y. Zhou, X. Wu, Y. Zhu, M. Lin, Y. Han, Y. Ren, H. Peng, Y.-H. Tsai, G. S. Hwang, and K. Lai, “Thickness-dependent dielectric constant of few-layer In2Se3 nanoflakes,” Nano Lett. 15(12), 8136–8140 (2015).
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M. Brahlek, N. Bansal, N. Koirala, S.-Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, “Topological-metal to band-insulator transition in (Bi1-xInx)2Se3 thin films,” Phys. Rev. Lett. 109(18), 186403 (2012).
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I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
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I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
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Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010).
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Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
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Hwang, E. H.

D. Culcer, E. H. Hwang, T. D. Stanescu, and S. Das Sarma, “Two-dimensional surface charge transport in topological insulators,” Phys. Rev. B 82(15), 155457 (2010).
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Hwang, G. S.

D. Wu, A. J. Pak, Y. Liu, Y. Zhou, X. Wu, Y. Zhu, M. Lin, Y. Han, Y. Ren, H. Peng, Y.-H. Tsai, G. S. Hwang, and K. Lai, “Thickness-dependent dielectric constant of few-layer In2Se3 nanoflakes,” Nano Lett. 15(12), 8136–8140 (2015).
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I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
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R. B. Jacobs-Gedrim, M. Shanmugam, N. Jain, C. A. Durcan, M. T. Murphy, T. M. Murray, R. J. Matyi, R. L. Moore, and B. Yu, “Extraordinary photoresponse in two-dimensional In(2)Se(3) nanosheets,” ACS Nano 8(1), 514–521 (2014).
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R. B. Jacobs-Gedrim, M. Shanmugam, N. Jain, C. A. Durcan, M. T. Murphy, T. M. Murray, R. J. Matyi, R. L. Moore, and B. Yu, “Extraordinary photoresponse in two-dimensional In(2)Se(3) nanosheets,” ACS Nano 8(1), 514–521 (2014).
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Y. Zhao, H. Liu, X. Guo, Y. Jiang, Y. Sun, H. Wang, Y. Wang, H.-D. Li, M.-H. Xie, X.-C. Xie, and J. Wang, “Crossover from 3D to 2D quantum transport in Bi2Se3/In2Se3 superlattices,” Nano Lett. 14(9), 5244–5249 (2014).
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C. Julien, A. Chevy, and D. Siapkas, “Optical properties of In2Se3 phases,” Phys. Status Solidi 118(2), 553–559 (1990).
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D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
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S. Kim, M. Ye, K. Kuroda, Y. Yamada, E. E. Krasovskii, E. V. Chulkov, K. Miyamoto, M. Nakatake, T. Okuda, Y. Ueda, K. Shimada, H. Namatame, M. Taniguchi, and A. Kimura, “Surface scattering via bulk continuum states in the 3D topological insulator Bi2Se3,” Phys. Rev. Lett. 107(5), 056803 (2011).
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D. Kim, S. Cho, N. P. Butch, P. Syers, K. Kirshenbaum, S. Adam, J. Paglione, and M. S. Fuhrer, “Surface conduction of topological Dirac electrons in bulk insulating Bi2Se3,” Nat. Phys. 8(6), 459–463 (2012).
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2D Mater. (1)

N. Balakrishnan, C. R. Staddon, E. F. Smith, J. Stec, D. Gay, G. W. Mudd, O. Makarovsky, Z. R. Kudrynskyi, Z. D. Kovalyuk, L. Eaves, A. Patanè, and P. H. Beton, “Quantum confinement and photoresponsivity of β-In2Se3 nanosheets grown by physical vapour transport,” 2D Mater. 3(2), 025030 (2016).
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ACS Nano (1)

R. B. Jacobs-Gedrim, M. Shanmugam, N. Jain, C. A. Durcan, M. T. Murphy, T. M. Murray, R. J. Matyi, R. L. Moore, and B. Yu, “Extraordinary photoresponse in two-dimensional In(2)Se(3) nanosheets,” ACS Nano 8(1), 514–521 (2014).
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M. Eddrief, F. Vidal, and B. Gallas, “Optical properties of Bi2Se3: from bulk to ultrathin films,” J. Phys. D Appl. Phys. 49(50), 505304 (2016).
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J. Vac. Sci. Technol. B (2)

Y. Wang, T. P. Ginley, and S. Law, “Growth of high-quality Bi2Se3 topological insulators using (Bi1-xInx)2Se3 buffer layers,” J. Vac. Sci. Technol. B 36(2), 02D101 (2018).
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Mater. Res. Bull. (2)

J. Tauc, “Optical properties and electronic structure of amorphous Ge and Si,” Mater. Res. Bull. 3(1), 37–46 (1968).
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X. Tao and Y. Gu, “Crystalline-crystalline phase transformation in two-dimensional In2Se3 thin Layers,” Nano Lett. 13(8), 3501–3505 (2013).
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Y. Zhao, H. Liu, X. Guo, Y. Jiang, Y. Sun, H. Wang, Y. Wang, H.-D. Li, M.-H. Xie, X.-C. Xie, and J. Wang, “Crossover from 3D to 2D quantum transport in Bi2Se3/In2Se3 superlattices,” Nano Lett. 14(9), 5244–5249 (2014).
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Nanomater. Nanotechnol. (1)

Y.-P. Lai, I.-T. Lin, K.-H. Wu, and J.-M. Liu, “Plasmonics in topological insulators,” Nanomater. Nanotechnol. 4, 13 (2014).
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J.-Y. Ou, J.-K. So, G. Adamo, A. Sulaev, L. Wang, and N. I. Zheludev, “Ultraviolet and visible range plasmonics in the topological insulator Bi1.5Sb0.5Te1.8Se1.2.,” Nat. Commun. 5(1), 5139 (2014).
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Nature (1)

J. E. Moore, “The birth of topological insulators,” Nature 464(7286), 194–198 (2010).
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Phys. Rev. B (5)

M. J. Brahlek, N. Koirala, J. Liu, T. I. Yusufaly, M. Salehi, M.-G. Han, Y. Zhu, D. Vanderbilt, and S. Oh, “Tunable inverse topological heterostructure utilizing (Bi1-xInx)2Se3 and multichannel weak-antilocalization effect,” Phys. Rev. B 93(12), 125416 (2016).
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I. A. Nechaev, R. C. Hatch, M. Bianchi, D. Guan, C. Friedrich, I. Aguilera, J. L. Mi, B. B. Iversen, S. Blügel, Ph. Hofmann, and E. V. Chulkov, “Evidence for a direct band gap in the topological insulator Bi2Se3 from theory and experiment,” Phys. Rev. B 87(12), 121111 (2013).
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J. Hao and L. Zhou, “Electromagnetic wave scatterings by anisotropic metamaterials: generalized 4×4 transfer-matrix method,” Phys. Rev. B 77(9), 094201 (2008).
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[Crossref]

Phys. Rev. Lett. (3)

S. Kim, M. Ye, K. Kuroda, Y. Yamada, E. E. Krasovskii, E. V. Chulkov, K. Miyamoto, M. Nakatake, T. Okuda, Y. Ueda, K. Shimada, H. Namatame, M. Taniguchi, and A. Kimura, “Surface scattering via bulk continuum states in the 3D topological insulator Bi2Se3,” Phys. Rev. Lett. 107(5), 056803 (2011).
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M. Brahlek, N. Bansal, N. Koirala, S.-Y. Xu, M. Neupane, C. Liu, M. Z. Hasan, and S. Oh, “Topological-metal to band-insulator transition in (Bi1-xInx)2Se3 thin films,” Phys. Rev. Lett. 109(18), 186403 (2012).
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Y. L. Chen, Z. K. Liu, J. G. Analytis, J.-H. Chu, H. J. Zhang, B. H. Yan, S. K. Mo, R. G. Moore, D. H. Lu, I. R. Fisher, S. C. Zhang, Z. Hussain, and Z. X. Shen, “Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family,” Phys. Rev. Lett. 105(26), 266401 (2010).
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Phys. Status Solidi (3)

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Science (1)

Y. L. Chen, J. G. Analytis, J.-H. Chu, Z. K. Liu, S.-K. Mo, X. L. Qi, H. J. Zhang, D. H. Lu, X. Dai, Z. Fang, S. C. Zhang, I. R. Fisher, Z. Hussain, and Z.-X. Shen, “Experimental realization of a three-dimensional topological insulator, Bi2Te3.,” Science 325(5937), 178–181 (2009).
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Thin Solid Films (1)

H. D. Lee, C. Xu, S. M. Shubeita, M. Brahlek, N. Koirala, S. Oh, and T. Gustafsson, “Indium and bismuth interdiffusion and its influence on the mobility in In2Se3/Bi2Se3,” Thin Solid Films 556, 322–324 (2014).
[Crossref]

Other (1)

Landolt-Bornstein, “Bismuth selenide (Bi2Se3) crystal structure, chemical bond, lattice parameter (including data of related compounds),” in Non-Tetrahedrally Bonded Elements and Binary Compounds I, O. Madelung, U. Rossler, and M. Shulz, eds. (1998), vol. 41C.

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Figures (4)

Fig. 1
Fig. 1 Lattice constant as a function of indium concentration determined using the [00015] x-ray diffraction peak. Dotted line is a linear fit to the data using the equation. Inset shows the [00015] peak for the five samples.
Fig. 2
Fig. 2 (a) Absorption coefficient as a function of energy for all five samples. (b) Extracted indirect (blue squares) and direct (red circles) bandgaps as a function of indium concentration. Dashed lines are a linear fit to the data.
Fig. 3
Fig. 3 (a) Reflection spectra for sample B (x = 0.32) with TE polarization and (b) TM polarization. (c) Fitted curve for sample B with TE polarization and (d) TM polarization at different incident angles. Inset in 3(a) shows a schematic of the modelling geometry.
Fig. 4
Fig. 4 The fitted high frequency permittivity as a function of indium concentration. The black and red lines are linear fittings of ε ,xy and ε ,z , respectively.

Tables (1)

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Table 1 Mean value and standard deviation of all the fitting parameters for all the samples

Equations (3)

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α= 1 d ln( T T 0 )
ε( ω )= ε i l ω LOi 2 ω 2 iω γ LOi ω TOi 2 ω 2 iω γ TOi
ε(ω)= ε ( 1 ω D 2 ω 2 +i γ D ω )

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