Abstract

Optical injection and detection of charge currents is an alternative to conventional transport and photoemission measurements, avoiding the necessity of invasive contact that may disturb the system being examined. This is a particular concern for analyzing the surface states of topological insulators. In this work one- and two-color sources of photocurrents are isolated and examined in epitaxial thin films of Bi2Se3. We demonstrate that optical excitation and terahertz detection simultaneously captures one- and two-color photocurrent contributions, which has not been required for other material systems. A method is devised to extract the two components, and in doing so each can be related to surface or bulk excitations through symmetry. The separation of such photocurrents in topological insulators opens a new avenue for studying these materials by all-optical methods.

© 2016 Optical Society of America

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    [Crossref]
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    [Crossref] [PubMed]

2015 (2)

D. A. Bas, K. Vargas-Velez, S. Babakiray, T. A. Johnson, P. Borisov, T. D. Stanescu, D. Lederman, and A. D. Bristow, “Coherent control of injection currents in high-quality films of Bi2Se3,” Appl. Phys. Lett. 106, 041109 (2015).
[Crossref]

L.-G. Zhu, B. Kubera, K. Fai Mak, and J. Shan, “Effect of Surface States on Terahertz Emission from the Bi2Se3 Surface,” Sci. Rep. 5, 10308 (2015).
[Crossref]

2014 (3)

P. Olbrich, L. Golub, T. Herrmann, S. Danilov, H. Plank, V. Bel’kov, G. Mussler, C. Weyrich, C. Schneider, J. Kampmeier, D. Grützmacher, L. Plucinski, M. Eschbach, and S. Ganichev, “Room-Temperature High-Frequency Transport of Dirac Fermions in Epitaxially Grown Sb2Te3- and Bi2Te3-Based Topological Insulators,” Phys. Rev. Lett. 113, 096601 (2014).
[Crossref]

R. A. Muniz and J. E. Sipe, “Coherent control of optical injection of spin and currents in topological insulators,” Phys. Rev. B 89, 205113 (2014).
[Crossref]

S. Sim, M. Brahlek, N. Koirala, S. Cha, S. Oh, and H. Choi, “Ultrafast terahertz dynamics of hot Dirac-electron surface scattering in the topological insulator Bi2SeS 3,” Phys. Rev. B 89, 165137 (2014).
[Crossref]

2013 (4)

J. Wang, H. Mabuchi, and X.-L. Qi, “Calculation of divergent photon absorption in ultrathin films of a topological insulator,” Phys. Rev. B 88, 195127 (2013).
[Crossref]

J. A. Sobota, S.-L. Yang, A. F. Kemper, J. J. Lee, F. T. Schmitt, W. Li, R. G. Moore, J. G. Analytis, I. R. Fisher, P. S. Kirchmann, T. P. Devereaux, and Z.-X. Shen, “Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3,” Phys. Rev. Lett. 111, 136802 (2013).
[Crossref]

Y. D. Glinka, S. Babakiray, T. A. Johnson, A. D. Bristow, M. B. Holcomb, and D. Lederman, “Ultrafast carrier dynamics in thin-films of the topological insulator Bi2Se3,” Appl. Phys. Lett. 103, 151903 (2013).
[Crossref]

S. Lu, C. Zhao, Y. Zou, S. Chen, Y. Chen, Y. Li, H. Zhang, S. Wen, and D. Tang, “Third order nonlinear optical property of Bi2Se3,” Opt. Express 21, 2072–2082 (2013).
[Crossref] [PubMed]

2012 (9)

J. D. Rowley, J. K. Pierce, A. T. Brant, L. E. Halliburton, N. C. Giles, P. G. Schunemann, and A. D. Bristow, “Broadband terahertz pulse emission from ZnGeP2,” Opt. Lett. 37, 788–790 (2012).
[Crossref] [PubMed]

C. Ruppert, J. Lohrenz, S. Thunich, and M. Betz, “Ultrafast field-resolved semiconductor spectroscopy utilizing quantum interference control of currents,” Opt. Lett. 37, 3879–3881 (2012).
[Crossref] [PubMed]

M. S. Bahramy, P. D. C. King, A. de la Torre, J. Chang, M. Shi, L. Patthey, G. Balakrishnan, P. Hofmann, R. Arita, N. Nagaosa, and F. Baumberger, “Emergent quantum confinement at topological insulator surfaces,” Nat. Commun. 3, 1159 (2012).
[Crossref] [PubMed]

F. Xiu, N. Meyer, X. Kou, L. He, M. Lang, Y. Wang, X. Yu, A. V. Federov, J. Zou, and K. L. Wang, “Quantum capacitance in topological insulators,” Sci. Rep. 2, 669 (2012).
[Crossref] [PubMed]

P. Di Pietro, F. M. Vitucci, D. Nicoletti, L. Baldassarre, P. Calvani, R. Cava, Y. S. Hor, U. Schade, and S. Lupi, “Optical conductivity of bismuth-based topological insulators,” Phys. Rev. B 86, 045439 (2012).
[Crossref]

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).
[Crossref]

J. W. McIver, D. Hsieh, S. G. Drapcho, D. H. Torchinsky, D. R. Gardner, Y. S. Lee, and N. Gedik, “Theoretical and experimental study of second harmonic generation from the surface of the topological insulator Bi2Se3,” Phys. Rev. B 86, 035327 (2012).
[Crossref]

D. Galanakis and T. D. Stanescu, “Electrostatic effects and band bending in doped topological insulators,” Phys. Rev. B 86, 195311 (2012).
[Crossref]

J. W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Control over topological insulator photocurrents with light polarization,” Nat. Nanotechnol. 7, 96–100 (2012).
[Crossref]

2011 (5)

P. Tabor, C. Keenan, S. Urazhdin, and D. Lederman, “Molecular beam epitaxy and characterization of thin Bi2Se3 films on Al2O3 (110),” Appl. Phys. Lett. 99, 013111 (2011).
[Crossref]

D. Hsieh, J. W. McIver, D. H. Torchinsky, D. R. Gardner, Y. S. Lee, and N. Gedik, “Nonlinear optical probe of tunable surface electrons on a topological insulator,” Phys. Rev. Lett. 106, 057401 (2011).
[Crossref] [PubMed]

N. Kumar, B. A. Ruzicka, N. P. Butch, P. Syers, K. Kirshenbaum, J. Paglione, and H. Zhao, “Spatially resolved femtosecond pump-probe study of topological insulator Bi2Se3,” Phys. Rev. B 83, 235306 (2011).
[Crossref]

P. Hosur, “Circular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent response,” Phys. Rev. B 83, 035309 (2011).
[Crossref]

X. F. Kou, L. He, F. X. Xiu, M. R. Lang, Z. M. Liao, Y. Wang, A. V. Fedorov, X. X. Yu, J. S. Tang, G. Huang, X. W. Jiang, J. F. Zhu, J. Zou, and K. L. Wang, “Epitaxial growth of high mobility Bi2Se3 thin films on Cds,” App. Phys. Lett. 98, 242102 (2011).
[Crossref]

2010 (6)

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

Y. Zhang, K. He, C.-Z. Chang, C.-L. Song, L.-L. Wang, X. Chen, J.-F. Jia, Z. Fang, X. Dai, W.-Y. Shan, S.-Q. Shen, Q. Niu, X.-L. Qi, S.-C. Zhang, X.-C. Ma, and Q.-K. Xue, “Crossover of the three-dimensional topological insulator Bi2Se3 to the two-dimensional limit,” Nat. Phys. 6, 584–588 (2010).
[Crossref]

S. M. Harrel, R. L. Milot, J. M. Schleicher, and C. A. Schmuttenmaer, “Influence of free-carrier absorption on terahertz generation from ZnTe(110),” Journal of Applied Physics 107, 033526 (2010).
[Crossref]

J. Seo, P. Roushan, H. Beidenkopf, Y. S. Hor, R. J. Cava, and A. Yazdani, “Transmission of topological surface states through surface barriers,” Nature 466, 343–346 (2010).
[Crossref] [PubMed]

D. Sun, C. Divin, J. Rioux, J. E. Sipe, C. Berger, W. A. de Heer, P. N. First, and T. B. Norris, “Coherent control of ballistic photocurrents in multilayer epitaxial graphene using quantum interference,” Nano Lett. 10, 1293–1296 (2010).
[Crossref] [PubMed]

F. Nastos and J. E. Sipe, “Optical rectification and current injection in unbiased semiconductors,” Phys. Rev. B 82, 235204 (2010).
[Crossref]

2009 (2)

C. Sames, J.-M. Ménard, M. Betz, A. L. Smirl, and H. M. van Driel, “All-optical coherently controlled terahertz ac charge currents from excitons in semiconductors,” Phys. Rev. B 79, 045208 (2009).
[Crossref]

Y. S. Hor, A. Richardella, P. Roushan, Y. Xia, J. G. Checkelsky, A. Yazdani, M. Z. Hasan, N. P. Ong, and R. J. Cava, “p-type Bi2Se3 for topological insulator and low-temperature thermoelectric applications,” Phys. Rev. B 79, 195208 (2009).
[Crossref]

2008 (1)

L. Fu and C. L. Kane, “Superconducting proximity effect and Majorana fermions at the surface of a topological insulator,” Phys. Rev. Lett. 100, 096407 (2008).
[Crossref] [PubMed]

2007 (1)

L. Costa, M. Betz, M. Spasenović, A. D. Bristow, and H. M. van Driel, “All-optical injection of ballistic electrical currents in unbiased silicon,” Nat. Phys. 3, 632–635 (2007).
[Crossref]

2006 (3)

M. Bieler, K. Pierz, and U. Siegner, “Simultaneous generation of shift and injection currents in (110)-grown GaAs/AlGaAs quantum wells,” J. Appl. Phys. 100, 083710 (2006).
[Crossref]

F. Nastos and J. E. Sipe, “Optical rectification and shift currents in GaAs and GaP response: Below and above the band gap,” Phys. Rev. B 74, 035201 (2006).
[Crossref]

H. Zhao, E. J. Loren, H. M. van Driel, and A. L. Smirl, “Coherence control of Hall charge and spin currents,” Phys. Rev. Lett. 96, 246601 (2006).
[Crossref] [PubMed]

2005 (1)

N. Laman, M. Bieler, and H. M. v. Driel, “Ultrafast shift and injection currents observed in wurtzite semiconductors via emitted terahertz radiation,” J. Appl. Phys. 98, 103507 (2005).
[Crossref]

2003 (2)

M. J. Stevens, A. L. Smirl, R. D. R. Bhat, A. Najmaie, J. E. Sipe, and H. M. van Driel, “Quantum interference control of ballistic pure spin currents in semiconductors,” Phys. Rev. Lett. 90, 136603 (2003).
[Crossref] [PubMed]

D. Côté, J. E. Sipe, and H. M. van Driel, “Simple method for calculating the propagation of terahertz radiation in experimental geometries,” J. Opt. Soc. Am. B 20, 1374–1385 (2003).
[Crossref]

2002 (1)

D. Côté, N. Laman, and H. M. v. Driel, “Rectification and shift currents in GaAs,” Appl. Phys. Lett. 80, 905–907 (2002).
[Crossref]

1997 (2)

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78, 306–309 (1997).
[Crossref]

S. K. Mishra, S. Satpathy, and O. Jepsen, “Electronic structure and thermoelectric properties of bismuth telluride and bismuth selenide,” J. Phys.: Condens. Matter 9, 461 (1997).

1990 (1)

Analytis, J. G.

J. A. Sobota, S.-L. Yang, A. F. Kemper, J. J. Lee, F. T. Schmitt, W. Li, R. G. Moore, J. G. Analytis, I. R. Fisher, P. S. Kirchmann, T. P. Devereaux, and Z.-X. Shen, “Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3,” Phys. Rev. Lett. 111, 136802 (2013).
[Crossref]

Arita, R.

M. S. Bahramy, P. D. C. King, A. de la Torre, J. Chang, M. Shi, L. Patthey, G. Balakrishnan, P. Hofmann, R. Arita, N. Nagaosa, and F. Baumberger, “Emergent quantum confinement at topological insulator surfaces,” Nat. Commun. 3, 1159 (2012).
[Crossref] [PubMed]

Armitage, N. P.

R. Valdés Aguilar, A. V. Stier, W. Liu, L. S. Bilbro, D. K. George, N. Bansal, L. Wu, J. Cerne, A. G. Markelz, S. Oh, and N. P. Armitage, “Terahertz response and colossal Kerr rotation from the surface states of the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 087403 (2012).
[Crossref]

Atanasov, R.

A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78, 306–309 (1997).
[Crossref]

Babakiray, S.

D. A. Bas, K. Vargas-Velez, S. Babakiray, T. A. Johnson, P. Borisov, T. D. Stanescu, D. Lederman, and A. D. Bristow, “Coherent control of injection currents in high-quality films of Bi2Se3,” Appl. Phys. Lett. 106, 041109 (2015).
[Crossref]

Y. D. Glinka, S. Babakiray, T. A. Johnson, A. D. Bristow, M. B. Holcomb, and D. Lederman, “Ultrafast carrier dynamics in thin-films of the topological insulator Bi2Se3,” Appl. Phys. Lett. 103, 151903 (2013).
[Crossref]

Bahramy, M. S.

M. S. Bahramy, P. D. C. King, A. de la Torre, J. Chang, M. Shi, L. Patthey, G. Balakrishnan, P. Hofmann, R. Arita, N. Nagaosa, and F. Baumberger, “Emergent quantum confinement at topological insulator surfaces,” Nat. Commun. 3, 1159 (2012).
[Crossref] [PubMed]

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J. W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Control over topological insulator photocurrents with light polarization,” Nat. Nanotechnol. 7, 96–100 (2012).
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D. Hsieh, J. W. McIver, D. H. Torchinsky, D. R. Gardner, Y. S. Lee, and N. Gedik, “Nonlinear optical probe of tunable surface electrons on a topological insulator,” Phys. Rev. Lett. 106, 057401 (2011).
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D. A. Bas, K. Vargas-Velez, S. Babakiray, T. A. Johnson, P. Borisov, T. D. Stanescu, D. Lederman, and A. D. Bristow, “Coherent control of injection currents in high-quality films of Bi2Se3,” Appl. Phys. Lett. 106, 041109 (2015).
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Y. D. Glinka, S. Babakiray, T. A. Johnson, A. D. Bristow, M. B. Holcomb, and D. Lederman, “Ultrafast carrier dynamics in thin-films of the topological insulator Bi2Se3,” Appl. Phys. Lett. 103, 151903 (2013).
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L. Braun, G. Mussler, A. Hruban, M. Konczykowski, M. Wolf, T. Schumann, M. Münzenberg, L. Perfetti, and T. Kampfrath, “Ultrafast photocurrents at the surface of the three-dimensional topological insulator Bi2Se3,” arXiv:1511.00482 [cond-mat] (2015). arXiv: 1511.00482.

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P. Olbrich, L. Golub, T. Herrmann, S. Danilov, H. Plank, V. Bel’kov, G. Mussler, C. Weyrich, C. Schneider, J. Kampmeier, D. Grützmacher, L. Plucinski, M. Eschbach, and S. Ganichev, “Room-Temperature High-Frequency Transport of Dirac Fermions in Epitaxially Grown Sb2Te3- and Bi2Te3-Based Topological Insulators,” Phys. Rev. Lett. 113, 096601 (2014).
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S. Sim, M. Brahlek, N. Koirala, S. Cha, S. Oh, and H. Choi, “Ultrafast terahertz dynamics of hot Dirac-electron surface scattering in the topological insulator Bi2SeS 3,” Phys. Rev. B 89, 165137 (2014).
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L. Braun, G. Mussler, A. Hruban, M. Konczykowski, M. Wolf, T. Schumann, M. Münzenberg, L. Perfetti, and T. Kampfrath, “Ultrafast photocurrents at the surface of the three-dimensional topological insulator Bi2Se3,” arXiv:1511.00482 [cond-mat] (2015). arXiv: 1511.00482.

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A. Haché, Y. Kostoulas, R. Atanasov, J. L. P. Hughes, J. E. Sipe, and H. M. van Driel, “Observation of coherently controlled photocurrent in unbiased, bulk GaAs,” Phys. Rev. Lett. 78, 306–309 (1997).
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D. A. Bas, K. Vargas-Velez, S. Babakiray, T. A. Johnson, P. Borisov, T. D. Stanescu, D. Lederman, and A. D. Bristow, “Coherent control of injection currents in high-quality films of Bi2Se3,” Appl. Phys. Lett. 106, 041109 (2015).
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J. A. Sobota, S.-L. Yang, A. F. Kemper, J. J. Lee, F. T. Schmitt, W. Li, R. G. Moore, J. G. Analytis, I. R. Fisher, P. S. Kirchmann, T. P. Devereaux, and Z.-X. Shen, “Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3,” Phys. Rev. Lett. 111, 136802 (2013).
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J. W. McIver, D. Hsieh, S. G. Drapcho, D. H. Torchinsky, D. R. Gardner, Y. S. Lee, and N. Gedik, “Theoretical and experimental study of second harmonic generation from the surface of the topological insulator Bi2Se3,” Phys. Rev. B 86, 035327 (2012).
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J. W. McIver, D. Hsieh, H. Steinberg, P. Jarillo-Herrero, and N. Gedik, “Control over topological insulator photocurrents with light polarization,” Nat. Nanotechnol. 7, 96–100 (2012).
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J. A. Sobota, S.-L. Yang, A. F. Kemper, J. J. Lee, F. T. Schmitt, W. Li, R. G. Moore, J. G. Analytis, I. R. Fisher, P. S. Kirchmann, T. P. Devereaux, and Z.-X. Shen, “Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3,” Phys. Rev. Lett. 111, 136802 (2013).
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P. Olbrich, L. Golub, T. Herrmann, S. Danilov, H. Plank, V. Bel’kov, G. Mussler, C. Weyrich, C. Schneider, J. Kampmeier, D. Grützmacher, L. Plucinski, M. Eschbach, and S. Ganichev, “Room-Temperature High-Frequency Transport of Dirac Fermions in Epitaxially Grown Sb2Te3- and Bi2Te3-Based Topological Insulators,” Phys. Rev. Lett. 113, 096601 (2014).
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L. Braun, G. Mussler, A. Hruban, M. Konczykowski, M. Wolf, T. Schumann, M. Münzenberg, L. Perfetti, and T. Kampfrath, “Ultrafast photocurrents at the surface of the three-dimensional topological insulator Bi2Se3,” arXiv:1511.00482 [cond-mat] (2015). arXiv: 1511.00482.

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M. S. Bahramy, P. D. C. King, A. de la Torre, J. Chang, M. Shi, L. Patthey, G. Balakrishnan, P. Hofmann, R. Arita, N. Nagaosa, and F. Baumberger, “Emergent quantum confinement at topological insulator surfaces,” Nat. Commun. 3, 1159 (2012).
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J. A. Sobota, S.-L. Yang, A. F. Kemper, J. J. Lee, F. T. Schmitt, W. Li, R. G. Moore, J. G. Analytis, I. R. Fisher, P. S. Kirchmann, T. P. Devereaux, and Z.-X. Shen, “Direct optical coupling to an unoccupied Dirac surface state in the topological insulator Bi2Se3,” Phys. Rev. Lett. 111, 136802 (2013).
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Y. S. Hor, A. Richardella, P. Roushan, Y. Xia, J. G. Checkelsky, A. Yazdani, M. Z. Hasan, N. P. Ong, and R. J. Cava, “p-type Bi2Se3 for topological insulator and low-temperature thermoelectric applications,” Phys. Rev. B 79, 195208 (2009).
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Zhao, H.

N. Kumar, B. A. Ruzicka, N. P. Butch, P. Syers, K. Kirshenbaum, J. Paglione, and H. Zhao, “Spatially resolved femtosecond pump-probe study of topological insulator Bi2Se3,” Phys. Rev. B 83, 235306 (2011).
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X. F. Kou, L. He, F. X. Xiu, M. R. Lang, Z. M. Liao, Y. Wang, A. V. Fedorov, X. X. Yu, J. S. Tang, G. Huang, X. W. Jiang, J. F. Zhu, J. Zou, and K. L. Wang, “Epitaxial growth of high mobility Bi2Se3 thin films on Cds,” App. Phys. Lett. 98, 242102 (2011).
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L.-G. Zhu, B. Kubera, K. Fai Mak, and J. Shan, “Effect of Surface States on Terahertz Emission from the Bi2Se3 Surface,” Sci. Rep. 5, 10308 (2015).
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Zou, J.

F. Xiu, N. Meyer, X. Kou, L. He, M. Lang, Y. Wang, X. Yu, A. V. Federov, J. Zou, and K. L. Wang, “Quantum capacitance in topological insulators,” Sci. Rep. 2, 669 (2012).
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App. Phys. Lett. (1)

X. F. Kou, L. He, F. X. Xiu, M. R. Lang, Z. M. Liao, Y. Wang, A. V. Fedorov, X. X. Yu, J. S. Tang, G. Huang, X. W. Jiang, J. F. Zhu, J. Zou, and K. L. Wang, “Epitaxial growth of high mobility Bi2Se3 thin films on Cds,” App. Phys. Lett. 98, 242102 (2011).
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Appl. Phys. Lett. (4)

Y. D. Glinka, S. Babakiray, T. A. Johnson, A. D. Bristow, M. B. Holcomb, and D. Lederman, “Ultrafast carrier dynamics in thin-films of the topological insulator Bi2Se3,” Appl. Phys. Lett. 103, 151903 (2013).
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D. Côté, N. Laman, and H. M. v. Driel, “Rectification and shift currents in GaAs,” Appl. Phys. Lett. 80, 905–907 (2002).
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D. A. Bas, K. Vargas-Velez, S. Babakiray, T. A. Johnson, P. Borisov, T. D. Stanescu, D. Lederman, and A. D. Bristow, “Coherent control of injection currents in high-quality films of Bi2Se3,” Appl. Phys. Lett. 106, 041109 (2015).
[Crossref]

P. Tabor, C. Keenan, S. Urazhdin, and D. Lederman, “Molecular beam epitaxy and characterization of thin Bi2Se3 films on Al2O3 (110),” Appl. Phys. Lett. 99, 013111 (2011).
[Crossref]

J. Appl. Phys. (2)

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Figures (5)

Fig. 1
Fig. 1 (a) Schematic diagram of experimental configuration for the Bi2Se3 film on a sapphire substrate and MgF2 capping layer. α, β and γ are the respective angles of the electric fields of the THz emission, ω pulse and 2ω pulse with respect to the (100) axis of the topological insulator. (b) Four unit cells, showing the trigonal symmetry of the Bi2Se3 lattice and the atomic layers that comprise a quintuple layer (QL). (c) Top-down view of one QL, with two examples of the pump polarization (β = γ). For the blue polarization, the lattice looks symmetric. For red polarization, the symmetry is broken and a directional shift current is expected. For α = β + π/2, the relevant symmetry plane is along the direction of the polarization vector.
Fig. 2
Fig. 2 Phase dependence of the emitted THz transients. E THz ( Δ ϕ , t det ) is the parallel component of the THz field emitted from Bi2Se3 as a function of detection delay time and relative phase. (a) β = π/6 corresponds to the blue vector in Fig. 1(c), a geometry which suppresses shift current contributions. The resulting checkerboard pattern is characteristic of injection current [23]. The inset THz transients show complete reversal of the photocurrent between Δϕ = π/2 (gray) and 3π/2 (white). (b) β = 0 corresponds to the red vector in Fig. 1(c), which allows for contributions from both shift and injection currents simultaneously. The inset transient is obtained by integrating one complete cycle of relative phase to show the remaining signal after removing the Δϕ contribution. (c) Power dependence of the maximum electric field, recorded at tdet = 0 (vertical dotted line), for ω (left, blue) or 2ω (right, red) individually to confirm the nonlinear optical scaling associated with a shift current. The dotted lines are guides to the eye, showing a linear slope.
Fig. 3
Fig. 3 Transient response of one- and two-color excitation. (a) Injection current versus τ, defined by the sinusoidal phase dependence and cross-correlation window. (b) One- and two-color THz transients versus τdet. E shift ( 2 ω ) is plotted for τ = −3.2 ps, −0.3 ps and 0.7 ps [coded by the color of vertical lines in (a)], E shift ( ω , τ ) (red dotted line) is shown for comparison, and the two-color E shift ( ω , τ ) Δ E shows the modification of the emission from ω due to the presence of 2ω. (c) Optical pump and THz probe [ Δ E / E shift ( ω ) ] versus τ at τdet = 0, due to free-carrier absorption by carriers promoted by the 2ω pulse.
Fig. 4
Fig. 4 Photocurrent separation analysis based on Eq. (6). Two-color excitation of photocurrent versus β, recording the maximum THz emission at τdet = 0 for relative phase conditions Δϕ = π/2 (green) and 3π/2 (orange). Addition and subtraction of these two signals gives the shift current Eshift (blue for positive, red for negative) and injection current Einj (olive) respectively. Solid lines are the theoretical model for Eshift and Einj, fit to experimental amplitudes.
Fig. 5
Fig. 5 One- and two-color photocurrents. Maximum THz emission (at tdet = 0) versus β are plotted for (a) parallel (α = β) and (b) perpendicular (α = β + π/2) polarization configurations, capturing the shift current due to ω excitation (blue for positive, red for negative). The solid lines are Eq. (2) with amplitudes as free parameters. Relevant angles are shown in the inset. Two-color experiments revealing the shift (blue and red) and injection (green) current, extracted using Eq. (6) are plotted for (a) parallel and (b) perpendicular polarization configurations. All data have been normalized to the magnitude of E shift ( ω ).

Equations (6)

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J a shift = ν a b c E ω b E c ω + c . c .
J shift = ν x x x cos ( 3 β ) | E ω | 2 , J shift = ν x x x sin ( 3 β ) | E ω | 2 .
d d t J a inj = η a b c d E ω b E ω c E 2 ω d e i Δ ϕ + c . c .
d d t J inj = 2 [ Re ( η x x x x ) cos ( Δ ϕ ) + Im ( η x x x x ) sin ( Δ ϕ ) ] | E ω | 2 | E 2 ω | ,
J total ( Δ ϕ = π 2 ) = J shift + J inj ( Δ ϕ = π 2 ) , J total ( Δ ϕ = 3 π 2 ) = J shift + J inj ( Δ ϕ = 3 π 2 ) ,
J inj ( π 2 ) = 1 2 [ J total ( π 2 ) J total ( 3 π 2 ) ] , J shift = 1 2 [ J total ( π 2 ) + J total ( 3 π 2 ) ] .

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