Linear-optical access to topological insulator surface states Dmitry Panna, Raja Marjieh, Evyatar Sabag, Leonid Rybak, Amit Ribak, Amit Kanigel, and Alex Hayat

Citation: Appl. Phys. Lett. 110, 212103 (2017); doi: 10.1063/1.4984141 View online: http://dx.doi.org/10.1063/1.4984141 View Table of Contents: http://aip.scitation.org/toc/apl/110/21 Published by the American Institute of Physics

APPLIED PHYSICS LETTERS 110, 212103 (2017)

Linear-optical access to topological insulator surface states Dmitry Panna,1 Raja Marjieh,1 Evyatar Sabag,1 Leonid Rybak,1 Amit Ribak,2 Amit Kanigel,2 and Alex Hayat1 1

Department of Electrical Engineering, Technion, Haifa 3200003, Israel Departmenet of Physics, Technion, Haifa 3200003, Israel

2

(Received 9 February 2017; accepted 13 May 2017; published online 25 May 2017) We demonstrate efficient linear-optical access to surface-state spin dynamics in Bi2Se3 by probing transitions between two surface-state Dirac cones, providing a practical technique for spin-current dynamics studies in topological-insulator devices. Using broadband transient-reflectivity pumpprobe measurements, we distinguish bulk and surface state-responses, by controlling photon energy and circular polarization at oblique incidence. For pump-photon energies corresponding to bulkstate transitions, the probe polarized co-circularly with the pump shows stronger reflectivity change, compared to the anti-circularly polarized probe. However, pump photon energies corresponding to surface-state transitions result in an opposite effect, with the anti-circularly polarized probe exhibiting stronger reflectivity change. This surprising behavior stems from the surface-state in-plane spin orientation near the Dirac point, and the surface-state spin population remains at the injected energy for several ps. These results enable an efficient approach for studying spin current dynamics in topological-insulator based technologies. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4984141]

Topological insulators (TIs) are becoming a topic of great interest in both fundamental physics and in technological applications, due to their remarkable properties, with an insulating bulk and topologically protected metallic surface states.1,2 These surface states exhibit massless Dirac dispersion and locking of the spin orientation to the momentum vector,3,4 resulting in dissipationless spin currents, enabling spintronic devices. Unconventional phases of matter and quasiparticles have been predicted based on combinations of topological insulators with superconductors5 inspiring various experimental directions, including TI combinations with unconventional superconductors,6,7 paving the way for practical realizations of topological quantum computing. Electronic characterization has been able to determine much about the spin transport;8 however, it does not allow noninvasive probing of the surface states. Moreover, the investigation of the ultrafast spin dynamics is virtually impossible by electrical transport techniques. All-optical access,9–12 on the other hand, provides a very powerful method for noninvasive investigation of ultrafast processes in TIs,13–16 while separating the surface response from that of the bulk is still extremely challenging. Recently, a nonlinear-optical approach was employed to study the TI surface.17,18 However, such nonlinear-optical techniques are limited significantly by the inherently weak high-order effects. Here, we demonstrate efficient linear-optical access to TI Bi2Se3 ultrafast spin dynamics by broadband timeresolved transient reflectivity measurements. This enables a practical technique to access spin-current behavior in TI based devices. We exploit the interplay between co- and anti-circular polarizations of the pump and the probe photons at oblique incidence—to distinguish between bulk and surface state responses in optically excited transitions between two Dirac cones in Bi2Se3,19 separated by approximately 1.5 eV [Fig. 1(b)]. Optical transitions between these two 0003-6951/2017/110(21)/212103/5/$30.00

cones have been recently employed for coherent control based techniques of current injection in TIs and for the investigation of charge-carrier dynamics.20 We take advantage of the two-cone transitions under circularly polarized excitation in order to investigate spin dynamics and to distinguish the response of the surface states from those of the bulk. We study two characteristic cases of pump photon energies— 1.72 eV and 2 eV, accounting for surface-to-surface state and bulk-to-bulk state transitions between the two cones, probed by a white-light supercontinuum. In the bulk transition case, the strongest change in differential reflectivity is for the co-circularly polarized pump and probe, resulting mainly from components of the photon and electron spins oriented at small angles to the normal,

FIG. 1. (a) Schematics of the band structure for the bulk (blue) and two surface-state Dirac cones (orange) in Bi2Se3. (b) 1D section of (a) with surface-to-surface and surface-to-bulk transitions depicted by red arrows which correspond to 1.72 eV and 2 eV pump photon energies, respectively.

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whereas for surface states, the strongest change is, surprisingly, for opposite pump and probe circular polarization. We explain this behavior by the fact that in surface states, the electrons interact mainly with the parallel-to-surface components of the photon spin. We find that the effect of the polarized pump on the surface states is stronger than in the bulk case. Furthermore, carriers injected into bulk states result in significant change in differential reflectivity at a different energy from that of the pump—close to the bulk band edge. Carriers injected into surface states cause the strongest change in differential reflectivity at the injected energy, maintained for several ps. This is attributed to reduced scattering in surface states maintaining the injected carrier energy and the corresponding spin current. We studied experimentally different spin-polarized transitions in off-stoichiometric Bi2Se3 by controlling photon energy and circular polarization. In principle, there are three possible transitions: bulk-bulk, surface-bulk, and surfacesurface [Figs. 1(a) and 1(b)]. Our approach provides a technique to distinguish between surface and bulk transitions. For our experiments, we used a bulk single crystal of offstoichiometric Bi2Se3 grown in the modified Bridgman method. Based on angle-resolved photoemission spectroscopy (ARPES) and electrical transport measurements,21 we estimate its carrier concentration to be 1018 cm3, corresponding to the relatively low Fermi level position. The Fermi level position is specified relative to the bottom edge of the conduction band such that a low Fermi level corresponds to the low bulk conduction band carrier concentration. Unlike mid-infrared absorption within a Dirac cone, the near-infrared photons in our experiments can only probe transitions between the two Dirac cones with some contribution of bulk absorption. However, due to the low Fermi level in our off-stoichiometric sample, these transitions between the first and second Dirac cones (cone-to-cone) are less obscured by contributions of bulk-to-surface and bulk-tobulk transitions. The transient polarized differential reflectivity DR=R pump-probe measurement is used here to observe spin dynamics of the surface states. The equilibrium population of the sample band structure was mapped using ARPES at a temperature of 23 K with a photon energy of 20 eV. The ARPES measurement on our sample shows very low electron population in the conduction band—0.2 eV above the Dirac point [Fig. 2(a)]. This significantly reduces the contribution of several transitions involving bulk states, compared to those involving surface states— in addition to the angular momentum projection selection. In our setup [Fig. 2(b)], a 1 kHz Ti:sapphire amplifier delivering 35 fs pulses at 800 nm served to generate a whitelight supercontinuum using a sapphire plate. The generated white light was used as a probe to measure the differential reflectivity of the Bi2Se3 sample over a broad energy range using an optical spectrum analyzer. An optical parametric amplifier (OPA) provided tunable-wavelength 120 fs pulses, which served as a pump. A quarter wave plate (QWP) on the white-light probe path allows co-circular and anti-circular polarization settings between the pump and the probe, and the delay line sets the relative time delay Dt. The spot size of the pump is 100 lm in diameter with the average pump power

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FIG. 2. (a) ARPES measurement of the off-stoichiometric Bi2Se3: the Fermi energy position (horizontal dashed line) is approximately 0.2 eV above the Dirac point of the lower cone [Fig. 1(b)]. (b) The pump-probe experimental setup with an optical parametric amplifier (OPA), a neutral density (ND) filter, quarter wave plates (QWPs), lenses (L), and an optical spectrum analyzer (OSA).

of 3 mW. The probe white light spot diameter is 50 lm (smaller than that of the pump), with the probe average power of 100 lW. The reflectivity of the sample is 50%, and about 50% of the incident pump power is absorbed in the sample. The measurements were performed at room temperature at two characteristic pump-photon energies of 1.72 eV and 2 eV, accounting for surface-to-surface and surface-to-bulk transitions between lower and upper Dirac cones, respectively, as shown in Fig. 1(b). Since the pump and the probe beams are incident at small angles, in the case of pump-photon energy corresponding to surface-to-bulk transition, the spin orientation excited by the pump pulse is at an angle close to the normal. A probe pulse, co-circularly polarized with the pump, addresses the excited spin polarization along a projection onto the axis

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defined by the angular momentum orientation of the pump photons. This results in large projection of the spin and a resulting strong effect in differential reflectivity [Fig. 3(b)]. In contrast, a probe pulse, anti-circularly polarized with the pump, addresses the spin polarization with negligible projection onto the spin excited by the pump—resulting in a vanishing effect on differential reflectivity [Fig. 3(a)]. However, in the case of pump-photon energy corresponding to the surface-to-surface transition between the two Dirac cones, the response is, in fact, opposite (Fig. 4). Here, for the co-circularly polarized pump and probe [Fig. 4(b)], the change in differential reflectivity is much less pronounced with comparison to the anti-circular polarization case [Fig. 4(a)]. This behavior is caused by the fact that near the Dirac point, surface-state spins are oriented in-plane of the surface. Therefore, only the in-plane component of the photon spin is coupled to the surface-state electron spin (sx). In this case, when the pump and probe are anticircularly polarized, the spin population induced by the pump on the surface is probed [Fig. 4(a) inset]. As a consequence, significant changes in the differential reflectivity are observed. On the other hand, for the co-circularly polarized

FIG. 4. Differential reflectivity DR=R spectra for various pump-probe time delays Dt, accounting for surface-to-surface electron transition (corresponding to 1.72 eV pump) for the anti-circularly (a) and co-circularly (b) polarized pump and probe. The curves are shifted vertically for clarity. The insets show schematic drawings of pump and probe photon angular momenta and the corresponding orientation of the surface electron spin (sx).

FIG. 3. Differential reflectivity DR=R spectra for various pump-probe time delays Dt, accounting for surface-to-bulk electron transition (corresponding to 2 eV pump) for the anti-circularly (a) and co-circularly (b) polarized pump and probe. The curves are shifted vertically for clarity. The insets show schematic drawings of pump and probe photon angular momenta and the corresponding orientation of the bulk electron spin (sh).

pump and probe, the surface spin population induced by the pump is opposite to the probe polarization, and no significant reflectivity changes are observed [Fig. 4(b)]. Therefore, by changing pump-photon energy and polarization, we can distinguish between transitions from the surface-to-bulk and surface-to-surface of the lower Dirac cone to the upper Dirac cone. Another evidence for the surface-bulk distinction in our approach is manifested in the fact that in the case of the surface-to-bulk transition corresponding to 2 eV pump photon energy, the strongest response is observed around 1.82 eV, which can be explained by the relaxation of injected electrons in the bulk to the minimum of the upper conduction band. However, in the case of the surface-to-surface transition, this relaxation does not occur on such short timescales in the surface states, and the strongest response is observed near the energy, at which the carriers were injected by the pump. In the case of surface-to-bulk transition, the material response was found to be opposite to the surface-to-surface case and less pronounced. This is explained by the fact that bulk bands are spin-degenerate with no spin-momentum

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FIG. 5. Time dependence of the normalized differential reflectivity DR=R minimum for bulk (solid red line) and surface (solid blue line) responses. The dashed lines represent exponential fits with the corresponding time constants sb ¼ 1.6 ps for the bulk and ss ¼ 2 ps for the surface. The insets show schematic drawings of pump and probe photon angular momenta and the corresponding spin orientations.

correlation. This clear distinction between two opposite behaviors of the bulk and of the surface states in TIs enables us to specifically address surface-state spin dynamics. The time constants for the signal decay (Fig. 5) are sb ¼ 1.6 ps for the bulk and ss ¼ 2 ps for the surface. These values are comparable to the decay times reported in Bi2Se3 previously22,23 but slightly shorter. We attribute this shortening of decay times to the significantly higher carrier densities in our experiments due to the higher pump intensities (>100 GW/ cm2) compared to the previous reports.19,20,22,23 Under such high excitations, carrier-carrier scattering can affect the decay, which is dominated by phonon scattering at lower densities.24,25 This contribution of carrier-carrier scattering at high carrier density also results in slightly shorter decay time in the bulk compared to that of the surface states. In conclusion, we have shown linear-optical access to topological insulator ultrafast spin dynamics using broadband transient-differential reflectivity measurements. This method enables direct access to spin current dynamics in TI based spintronic devices, providing important information about the spin-current decay times in practical TIs. We have separated bulk and surface responses by changing excitation energy and incident light circular polarization in the specially prepared off-stoichiometric Bi2Se3 sample and have selectively observed spin-polarized cone-to-cone transitions. For the surface-to-bulk transition, a spin response is pronounced when pump and probe polarizations are co-circular, whereas for the surface-to-surface transition, the response is significant for anti-circular polarization. Moreover, in contrast to the faster-decaying bulk-state population, the surface-state spin population and the corresponding spin current remain near the injected energy for several ps. Our results enable a practical approach for the study of topological materials and provide an efficient method for controlling and probing spin-polarized dynamics in topological insulators for a wide application range including spintronics and quantum computation. This research was supported by the Israel science foundation (Grant No. 2220/15).

M. Z. Hasan and C. L. Kane, “Colloquium: Topological insulators,” Rev. Mod. Phys. 82, 3045 (2010). 2 Y. Xia, D. Qian, D. Hsieh, L. Wray, A. Pal, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “Observation of a large-gap topological-insulator class with a single Dirac cone on the surface,” Nat. Phys. 5, 398 (2009). 3 J. E. Moore, “The birth of topological insulators,” Nature 464, 194 (2010). 4 D. Hsieh, Y. Xia, D. Qian, L. Wray, J. H. Dil, F. Meier, J. Osterwalder, L. Patthey, J. G. Checkelsky, N. P. Ong, A. V. Fedorov, H. Lin, A. Bansil, D. Grauer, Y. S. Hor, R. J. Cava, and M. Z. Hasan, “A tunable topological insulator in the spin helical Dirac transport regime,” Nature 460, 1101 (2009). 5 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). 6 E. Wang, H. Ding, A. V. Fedorov, W. Yao, Z. Li, Y.-F. Lv, K. Zhao, L.-G. Zhang, Z. Xu, J. Schneeloch, R. Zhong, S.-H. Ji, L. Wang, K. He, X. Ma, G. Gu, H. Yao, Q.-K. Xue, X. Chen, and S. Zhou, “Fully gapped topological surface states in Bi2Se3 films induced by a d-wave high-temperature superconductor,” Nat. Phys. 9, 621 (2013). 7 P. Zareapour, A. Hayat, S. Y. F. Zhao, M. Kreshchuk, A. Jain, D. C. Kwok, N. Lee, S.-W. Cheong, Z. Xu, A. Yang, G. D. Gu, R. J. Cava, and K. S. Burch, “Proximity-induced high-temperature superconductivity in topological insulators Bi2Se3 and Bi2Te3,” Nat. Commun. 3, 1056 (2012). 8 D. Kim, P. Syers, N. P. Butch, J. Paglione, and M. S. Fuhrer, “Coherent topological transport on the surface of Bi2Se3,” Nat. Commun. 4, 2040 (2013). 9 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 (2012). 10 G. Spektor, A. David, G. Bartal, M. Orenstein, and A. Hayat, “Spin-patterned plasmonics: Towards optical access to topological-insulator surface states,” Opt. Express 23, 32759 (2015). 11 S. K. Kushwaha, I. Pletikosic´, T. Liang, A. Gyenis, S. H. Lapidus, Y. Tian, H. Zhao, K. S. Burch, J. Lin, W. Wang, H. Ji, A. V. Fedorov, A. Yazdani, N. P. Ong, T. Valla, and R. J. Cava, “Sn-doped Bi1.1Sb0.9Te2S bulk crystal topological insulator with excellent properties,” Nat. Commun. 7, 11456 (2016). 12 A. D. Dunkelberger, B. T. Spann, K. P. Fears, B. S. Simpkins, and J. C. Owrutsky, “Modified relaxation dynamics and coherent energy exchange in coupled vibration-cavity polaritons,” Nat. Commun. 7, 13504 (2016). 13 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). 14 C. W. Luo, H. J. Wang, S. A. Ku, H.-J. Chen, T. T. Yeh, J.-Y. Lin, K. H. Wu, J. Y. Juang, B. L. Young, T. Kobayashi, C.-M. Cheng, C.-H. Chen, K.-D. Tsuei, R. Sankar, F. C. Chou, K. A. Kokh, O. E. Tereshchenko, E. V. Chulkov, Yu. M. Andreev, and G. D. Gu, “Snapshots of Dirac Fermions near the Dirac Point in Topological Insulators,” Nano Lett. 13, 5797 (2013). 15 Y. D. Glinka, S. Babakiray, M. B. Holcomb, and D. Lederman, “Effect of Mn doping on ultrafast carrier dynamics in thin films of the topological insulator Bi2Se3,” J. Phys.: Condens. Matter 28, 165601 (2016). 16 D. A. Bas, R. A. Muniz, S. Babakiray, D. Lederman, J. E. Sipe, and A. D. Bristow, “Identification of photocurrents in topological insulators,” Opt. Express 24, 23583 (2016). 17 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). 18 D. Hsieh, F. Mahmood, J. W. McIver, D. R. Gardner, Y. S. Lee, and N. Gedik, “Selective probing of photoinduced charge and spin dynamics in the bulk and surface of a topological insulator,” Phys. Rev. Lett. 107, 077401 (2011). 19 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). 20 Y. D. Glinka, S. Babakiray, T. A. Johnson, A. D. Bristow, M. B. Holcomb, and D. Lederman, “Ultrafast carrier dynamics in thin-films of topological insulator Bi2Se3,” Appl. Phys. Lett. 103, 151903 (2013). 21 E. Lahoud, E. Maniv, M. Shaviv Petrushevsky, M. Naamneh, A. Ribak, S. Wiedmann, L. Petaccia, Z. Salman, K. B. Chashka, Y. Dagan, and A. Kanigel, “Evolution of the Fermi surface of a doped topological insulator with carrier concentration,” Phys. Rev. B 88, 195107 (2013).

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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 Bi 2Se3,” Phys. Rev. B 83, 235306 (2011). 23 J. Qi, X. Chen, W. Yu, P. Cadden-Zimansky, D. Smirnov, N. H. Tolk, I. Miotkowski, H. Cao, Y. P. Chen, Y. Wu, S. Qiao, and Z. Jiang, “Ultrafast carrier and phonon dynamics in Bi2Se3 crystals,” Appl. Phys. Lett. 97, 182102 (2010).

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Y. D. Glinka, S. Babakiray, T. A. Johnson, M. B. Holcomb, and D. Lederman, “Effect of carrier recombination on ultrafast carrier dynamics in thin films of the topological insulator Bi2Se3,” Appl. Phys. Lett. 105, 171905 (2014). 25 J. A. Sobota, S. Yang, J. G. Analytis, Y. L. Chen, I. R. Fisher, P. S. Kirchmann, and Z.-X. Shen, “Ultrafast optical excitation of a persistent surface-state population in the topological insulator Bi2Se3,” Phys. Rev. Lett. 108, 117403 (2012).