Photoinduced Inverse Spin Hall Effect of Surface States in the

Nov 16, 2017 - Institute of Micro/Nano Devices and Solar Cells, School of Physics and Information Engineering, Fuzhou University, Fuzhou 350108, Fujia...
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Letter Cite This: Nano Lett. XXXX, XXX, XXX-XXX

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Photoinduced Inverse Spin Hall Effect of Surface States in the Topological Insulator Bi2Se3 Jinling Yu,*,† Xiaolin Zeng,† Liguo Zhang,‡ Ke He,*,‡ Shuying Cheng,†,§ Yunfeng Lai,†,§ Wei Huang,∥ Yonghai Chen,∥,⊥ Chunming Yin,#,∇ and Qikun Xue‡ †

Institute of Micro/Nano Devices and Solar Cells, School of Physics and Information Engineering, Fuzhou University, Fuzhou 350108, Fujian, China ‡ Department of Physics, State Key Laboratory of Low Dimensional Quantum Physics, Tsinghua University, Beijing 100084, China § Jiangsu Collaborative Innovation Center of Photovolatic Science and Engineering, Changzhou University, Changzhou 213164, Jiangsu China ∥ Key Laboratory of Semiconductor Materials Science, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China ⊥ College of Materials Science and Optoelectronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China # School of Physics, University of New South Wales, Sydney, New South Wales 2052, Australia ∇ CAS Key Laboratory of Microscale Magnetic Resonance, Department of Modern Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China S Supporting Information *

ABSTRACT: The three-dimensional (3D) topological insulator (TI) Bi2Se3 exhibits topologically protected, linearly dispersing Dirac surface states (SSs). To access the intriguing properties of these SSs, it is important to distinguish them from the coexisting two-dimensional electron gas (2DEG) on the surface. Here, we use circularly polarized light to induce the inverse spin Hall effect in a Bi2Se3 thin film at different temperatures (i.e., from 77 to 300 K). It is demonstrated that the photoinduced inverse spin Hall effect (PISHE) of the top SSs and the 2DEG can be separated based on their opposite signs. The temperature and power dependence of the PISHE also confirms our method. Furthermore, it is found that the PISHE in the 2DEG is dominated by the extrinsic mechanism, as revealed by the temperature dependence of the PISHE. KEYWORDS: Photoinduced inverse spin Hall effect, surface state, topological insulator, Bi2Se3, two-dimensional electron gas

T

gas (2DEG) at the surface, induced by the native crystal lattice defects19 or environmental doping.15 To suppress the contribution of the conducting bulk, several methods have been adopted, such as using very thin samples with the thickness of a few quintet layers (QLs);20,21 tuning the Fermi energy into the band gap of the bulk by doping,22,23 by changing the components,5,24 or by applying top/back gate voltage;23−25 and utilizing surface sensitive techniques16,26 or techniques disregarding conducting bulk.4 However, there is often a 2DEG existing at the surface of a 3D TI that can contribute to the electric transport or optical response,27,28 and there are very few methods that can clearly distinguish its contributions from that of SSs.29 The photoinduced inverse spin Hall effect (PISHE) is an attractive technique as it is sensitive to surface states and has been used to study the

hree-dimensional (3D) topological insulators (TIs) have attracted much attention due to the intriguing physical properties as well as the exciting application opportunities.1−12 In particular, the topologically protected Dirac states on the surface of 3D TIs provide an excellent platform for spintronic devices7,8,13 because these surface states are robust against nonmagnetic backscattering due to the helical spin-momentum locking. Bi2Se3 has proven to be 3D TI with a single pair of linear Dirac-type electronic energy bands and large bulk band gap (about 0.3 eV).14−17 The linear dispersion of the surface states of 3D TIs have been confirmed by angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling microscopy experiments.16,18 However, utilizing the topological surface states in an actual transport or optical device is still challenging because it is often difficult to separate the phenomena due to the SSs from that due to either the conductance of the bulk material or two-dimensional electron © XXXX American Chemical Society

Received: September 27, 2017 Revised: November 3, 2017 Published: November 16, 2017 A

DOI: 10.1021/acs.nanolett.7b04172 Nano Lett. XXXX, XXX, XXX−XXX

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Figure 1. (a) Schematic drawing of the measurement geometry. The blue circle with arrows on the top surface indicates the PISHE current from the top SSs of Bi2Se3 when the sample is under the illumination of circularly polarized light, while the pink circle with arrows inside the Bi2Se3 film indicates the PISHE current from the 2DEG. (b) Illustration of the experimental geometry of light spot position dependence of PISHE. Points A−D indicate the four specific positions of the light spots, which are located at the perpendicular bisector of the connection of two electrodes with coordinates of xA = −0.5, xB = −0.2, xC = 0.2, and xD = 0.5 mm, respectively. Here, the origin of the coordinates is set at the midpoint of the two electrodes, and the x and y directions are perpendicular and parallel to the connection of two electrodes, respectively. (c) The photocurrent measured at 77 K as a function of the phase angle φ under normal incidence when the light spot is at point B. The solid line (black) is the fitting curve using eq 1. The dotted lines (blue and green) and the dashed lines (red) are the ALPGE and PISHE current, respectively. The dashed-dot line indicates the background current J0. (d−g) show the dependence of the PISHE current on the phase angle φ when the light spot is focused on point A−D, respectively. The red error bar denotes the fitting uncertainty.

surface electron accumulation layer in InN films.30 It offers a method for detecting the inverse spin Hall effect (ISHE) or the inverse Rashba−Edelstein effect at room temperature.30,31 Furthermore, it is also a powerful tool to manipulate electron spins in nonmagnetic semiconductors without applying of magnetic field or introducing ferromagnetic elements.32 In this letter, we investigate the PISHE in a 3D TI Bi2Se3 using circularly polarized light of 1064 nm at a temperature range of 77−300 K. It is revealed that the top SSs and 2DEG at the surface of Bi2Se3 exhibit opposite signs in PISHE, which can be attributed to their opposite signs of the effective spin orbit coupling (SOC). We can separate the contributions of top SSs and 2DEG to the PISHE by studying the spatial distribution of the current. The temperature and power dependence of the PISHE also confirms our method. Furthermore, it is found that the PISHE in the 2DEG is dominated by the extrinsic mechanism, suggested by the temperature dependence of the PISHE. The TI sample used here is a 7QL Bi2Se3 film grown by molecular beam epitaxy on SrTiO3 (111) substrate (see the Supporting Information for more details). It is worth mentioning that the most appropriate thickness of Bi2Se3 with which to separate the PISHE current contributed by the SSs and 2DEG lies between 6 and 10 QLs. This is because for a thicker film, the contribution from the bulk increases, which is difficult to be distinguished from that of 2DEG, while for a thinner film, the top surface states will couple with the bottom

surface states.33 Besides, a Rashba-type spin splitting will be present in the surface states due to the hybridization of the two sets of gapless surface states and the broken of the structure inversion symmetry by the substrate.33 In this case, the 2DEG does not present, and the PISHE current may be a mixture of top and bottom surface, which becomes much more complex. A 2 K Hall measurement of the sample shows an n-type characteristic with a density of 2.68 × 10−13 cm−2 and a Hall mobility of 197.4 cm2 V−1 s−1. The previous ARPES of the sample, as shown in Figure 1b in ref 11, clearly demonstrates the coexistence of the SSs and 2DEG in the sample. A pair of Ti/Au electrodes with a radius of 0.2 mm and a distance of about 1.6 mm is deposited on the surface of Bi2Se3 by electron beam evaporation, as shown in Figure 1a. After bonding of the device in the air, the sample is then transferred into an optical cryostat with a 1 Pa low-pressure chamber to prevent the degradation of the sample. The cryostat also allows the variation of the temperature in the range of 77−300 K. The experimental setup is sketched in Figure 1a. A diode-pumped solid-state laser with a power of 250 mW and a wavelength of 1064 nm is used as the source. The laser beam passes through a chopper and a rotatable quarter-wave plate, which is employed to modulate the helicity of the incident light and then illuminates the sample vertically. The photocurrent is collected between the two electrodes by a preamplifier and a lock-in amplifier that is in phase with the chopper working at a frequency of 229 Hz. B

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Figure 2. (a) Schematic drawing of the measurement geometry. (b) The PISHE current, (c) background current J0, and (d) L1 and (e) L2 components of ALPGE current measured at 77 K as a function of the light spot location when the center of the light spot is moving along different dashed lines shown in panel a.

the light spot is focused on points A−D, respectively, and the dashed error bar denotes the fitting uncertainty. This phenomenon is different from that was observed in GaN/ AlGaN 2DEG and GaAs/AlGaAs 2DEG,31,38 which show only one sign flip. The three sign flips of PISHE suggest that the observed PISHE current is a composition of two sinusoid-like current with opposite directions,30 which are denoted as the first and second conducting channel (CC), respectively. The opposite PISHE current in the two CCs may be attributed to the opposite sign of effective SOC coefficient in the two CCs.30 It should be noted that circular photogalvanic effect (CPGE) does not make a contribution to the observed helicitydependent PISHE current. First, the SSs and the 2DEG of Bi2Se3 share the same point group symmetry C3v, and the bulk of Bi2Se3 belongs to point group D3d. Neither of these two point groups allows the presence of CPGE current under normal radiation.4,39 Second, CPGE current does not flip its sign when the light spot moves from the left side of the two electrodes to the right side, and it will show a maximum value at the center and symmetrically decrease at the two sides of electrodes as the light spot moves away from the electrodes.31 The circular photodrag effect should also be excluded because it is expected to be zero for these point groups under vertical illumination. The other effect that might impact the geometric distribution of the photocurrent is the thermoelectric effect, which was known to be strong in Bi2Se3.40 To investigate the influence of the thermoelectric effect on the photocurrent, we sweep the laser spot position along x axis with different y values, i.e., y = −0.05, 0, and 0.05 mm, as shown in Figure 2a. The measurements are carried out at 77 K, and the obtained PISHE, background current J0 and L1 and L2 currents are shown in Figure 2b−e. The thermoelectric effect should contribute to the background current J0, and the direction of the thermoelectric current should depend on the position of the light spot with respect to the two electrodes. It can be seen from Figure 2c that the background current J0 at x = 0 changes from negative to positive when the light spot sweeps from y = −0.05 to 0.05 mm. The contribution to J0 that switches polarity

The laser spot has a diameter of roughly 1 mm with a Gaussian profile. The circularly polarized light spot induces spin polarized carriers with Gaussian distribution in space in the unsaturated absorption area. A diffuse spin current is generated flowing along the radial direction due to the gradient of the photogenerated spin polarized carrier densities, and then owing to the spin-momentum locking effect or to the ISHE effect, the spin polarized carriers show a transverse displacement in the axial direction, which can be described by a spin transverse force, leading to a swirly current (named as PISHE current) around the light spot.30,31 The spin transverse force was first proposed by Shen34 and then was applied to explain the experiments in refs 30 and 31. The optically injected spin current in 2DEG was first reported by Cui et al.35 The PISHE current can be extracted by fitting the experimental data of light polarization dependence of photocurrent J to the following equation:4 J = JPISHE sin 2φ + L1sin 4φ + L 2cos 4φ + J0

(1)

Here, JPISHE is a helicity-dependent photocurrent, and L1 and L2 are helicity-independent photocurrents, named as anomalous linear photogalvanic effect (ALPGE), which is related to the linearly polarized light and can be attributed to the optical momentum alignment effect.36,37 J0 is the background photocurrent that is helicity-independent and originates from the photovoltaic effect, the thermoelectric effect, or the Dember effect.30 φ is the angle between the polarization direction of the incident light and the optical axis of the quarter-wave plate. Figure 1c shows a typical result of photocurrent as a function of the phase angle φ when the laser spot is at B, as shown in Figure 1b. In Figure 1b, the circles are the experimental data, and the dashed line (red), dotted lines (blue and green), and the dashed−dotted line (black) are PISHE, ALPGE, and the background photocurrent, respectively. It can be seen that the ALPGE current is much larger than the PISHE current. Surprisingly, when the light spot is moving from the left to right side along x-axis, the sign of PISHE current flips three times, which are illustrated in Figure 1d−g. Figure 1d−g shows the dependence of the PISHE current on the phase angle φ when C

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Figure 3. (a) Schematic illustration of the photoexcitation processes under a radiation of circularly polarized light of 1064 nm. The vertical arrows indicate spin-up and spin-down states. The dashed, dot and solid long arrows denote the transition of CB1 → VB2, CB1 → SS2, and SS1 → SS2, respectively. (b) A schematic of the spatial distribution of the PISHE current in the top SSs (middle panel) and in the 2DEG (bottom panel) induced by a laser spot with Gaussian distribution (top panel). The gray circle in the middle panel indicates the absorption saturation area. The dashed black arrows denote the flowing of spin current due to the gradient of spin polarized carrier density, and the red solid arrows show the spin transverse force acting on electrons or holes. The cross symbols, ⊗ (or the dot symbols, ⊙) indicate the electrons (holes) with their spin polarization direction perpendicular to the paper and pointing inward (outward). The black and blue cross symbols (or the red dot symbols) denote the electrons (holes) contributed via transitions of SS1 → SS2 and CB1 → VB2 (CB1 → SS2), respectively, as illustrated in panel a. (c) The geometry of the light spot and two electrodes. r0 is the radius of the light spot, rs represents the radius of the saturated absorption area, the black dots “a” and “b” indicate the electrodes, and the blue arrows denote the direction of the vortex electric field. (d) The PISHE current as a function of the light spot location measured at 77 K. The solid squares are the experimental data, and the blue solid lines are the fitting results. The dashed (black) and dotted (red) lines indicate the PISHE current of the top SSs and 2DEG, respectively.

CB1 → VB2 and CB1 → SS2 will contribute to the PISHE on the second CC. If the SSs has the opposite sign of effective SOC coefficient with that of the 2DEG (or bulk), the photogenerated carriers via transition SS1 → SS2 will experience spin transverse force with a opposite direction to that generated via transition CB1 → VB2 (or CB1 → SS2), resulting in PISHE current in opposite directions in the first and second CCs. Obviously, the first CC can be assigned to the top SSs of Bi2Se3. However, the second CC can possibly be the 2DEG, induced by the energy band bending of Bi2Se3 at the surface,16 or the bulk states because the PISHE is also permitted in nongyrotropic bulk system.31 According to the following reasons, the second CC can be mainly assigned to the 2DEG. First, it is reported that the top SSs indeed have opposite sign of effective SOC coefficients with that of 2DEG in Bi2Se3,16,43 which is consistent with the observation in our experiments. Second, the thicknesses of the top SSs and the 2DEG are estimated to be about 2 and 4 nm, respectively.44,45 Because the thickness of Bi2Se3 sample used here is only about 7 nm, the bulk will be very thin, and its contribution can be neglected. What is more, the 2DEG on the surface has much larger SOC than the bulk due to the large electric field induced by the huge band bending at the surface. Another possible concern is that the second CC may arise from the bottom surface states of Bi2Se3 because it also shows an opposite effective SOC with that of top surface states. However, it has been found that for Bi2Se3 thin films grown on SrTiO3 (111) substrates by MBE, there are many defects in the bottom surface due to the lattice mismatch with SrTiO3 substrate.46 Because of the layered nature of the Bi2Se3 crystal and lattice relaxation during the growth, the bottom surface is expected to be of considerably

can be attributed to a thermoelectric current. In comparison, the PISHE, the L1 and L2 component of ALPGE remain the same, which indicates that the thermoelectric effect has little influence on PISHE and ALPGE. However, to keep the background current as small as possible, all the subsequent measurements are performed at y = 0. Under the radiation of circularly polarized light (CPL) with 1064 nm, taking left-handed CPL as an example, the electrons in the first topological surface state (SS1) with angular momentum j = +1/2 will jump to the second topological surface state (SS2) with j = −1/2.41,42 Similarly, the direct optical transition from the first conduction band (CB1) with j = +1/2 in 2DEG (or bulk) to the SS2 with j = −1/2, and from the CB1 with j = −1/2 to the high-lying valence band (VB2) with j = −3/2 in 2DEG (or bulk) are also allowed, as shown in Figure 3a. Although the optical direct transitions from the first valence band (VB1) to CB1, from VB1 to SS1 and from SS1 (below Dirac point) to SS1 (above Dirac point) are also allowed, their transition probability are much smaller and, therefore, are not considered here. This is because the electrons around the Fermi level are more active and have larger transition probability. It should be noted that the PISHE current is proportional to spin relaxation time τs.31,34 Given that the spin relaxation time of surface states is much smaller than that of bulk states,41 the contribution of the PISHE current from transition CB1 → SS2 is dominated by photogenerated holes in the initial state CB1. The photogenerated holes will experience spin transverse force with a opposite direction to the electrons generated via transition CB1 → VB2,34 leading to PISHE current in the same direction with that of CB1 → VB2 (see Figure 3a). Therefore, the transition SS1 → SS2 will make contribution to the PISHE on the first CC, while the transitions D

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Figure 4. (a) Experimental and modeling results of the PISHE current as a function of the light spot location measured at different temperatures. The solid squares are the experimental data, and the blue solid lines are the fitting results. The dashed (black) and dotted (red) lines indicate the PISHE current of the top SSs and 2DEG, respectively. (b) The spin transverse force and (c) electron diffusion length as a function of temperatures obtained by the fitting shown in panel a and Figure 3d. The squares and circles denote the signals corresponding to top SSs and 2DEG in the Bi2Se3, respectively. The solid and dotted lines in panel b are the linear and a + bT−1 fitting, respectively. The dashed lines in panel c are obtained from refs 9, 10, 17, and 21.

worse quality than the top surface.46 Consequently, the bottom surface states have much lower mobility than the top surface. It has been revealed that the dephasing field, which is inversely proportional to the dephasing time, of the bottom surface states is more than two orders larger than that of the top surface states for a Bi2Se3 thin film grown on SrTiO3 (111) substrates by MBE.47 This indicates that the mobility of the bottom surface states is much smaller than that of the top surface.46 Besides, the spin relaxation time of the surface states is reported to be one order smaller than that of the bulk (or 2DEG).41 Given that the PISHE is proportional to the spin relaxation time of electrons, the PISHE current in the second CC should mainly come from 2DEG. When the light intensity irradiates on the sample is stronger than the absorption saturation of the top SSs, the light inside the absorption saturation area will be partial absorbed, and the unabsorbed part will go through the top SSs and make contribution to the PISHE of the 2DEG (see Figure 3b). The light outside the absorption saturation area will be absolutely absorbed by the top SSs, leading to the PISHE of the top SSs. The middle and bottom panel of Figure 3b show the vortex current generated on the top SSs and 2DEG, respectively. In the following, we separate the PISHE current corresponding to the top SSs and 2DEG, respectively. The details are rather tedious and thus are provided in the Supporting Information. According to the model proposed in ref 31, the electric current between the two electrodes (named a and b, respectively; see Figure 3c) can be expressed as: 1 ⎡ ⎢ Iab = Rab ⎢⎣ +

∇ × Ei⃗ = −

I0

∬

∬

3

(3)

Here, i = 1 or 2 indicate the top SSs and 2DEG, respectively, and Rab is the resistance between the electrodes a and b. f 01 (or f 02) represents the spin transverse force experienced by the electrons in the top SSs (or 2DEG), due to the spin momentum locking effect (or inverse spin Hall effect). It should be noted that the spin transverse force f 0 is proportional to the spin relaxation and spin diffusion length (see the later discussion). E⃗ stands for vortex electric field, q is the unit charge, and σ indicates the distribution variance related to the full-width at half-maximum of the light intensity. D1 (or D2) represents the overlapping area of the triangle “abo” and the light spot that contributes to the PISHE current of top SSs (or the 2DEG), l1 (or l2) is the distance between the edge of the light spot, which contributes to the PISHE current of top SSs (or the 2DEG), and the connection of two electrodes “ab” and Ls1 (or Ls2) is the electron diffusion length of the top SSs (or the 2DEG), and A1 and A2 are constants. It should be noted that the absorption saturation area of each channel should be deducted from the corresponding integral in eq 2 because there will be no spin current and, as a result, no PISHE current in that area. Assuming that the maximum light intensity is I0 and the absorption saturation ratio of the top SSs to be Q0, the radius of absorption saturation area rs can be extracted by:

⎛ l ⎞ → ⎯ ∇ × E1·exp⎜ − 1 ⎟ds D1 ⎝ A1·Ls1 ⎠

⎛ l ⎞ ⎤ ⎯→ ∇ × E2 ·exp⎜ − 2 ⎟ds ⎥ D2 ⎝ A 2 ·Ls2 ⎠ ⎥⎦

⎛ r2 ⎞ exp⎜ − 2 ⎟ ⎝ 2σ ⎠ qσ f0i r

⎛ r2 ⎞ 1 exp⎜ − s 2 ⎟ = Q 0I0 2π σ ⎝ 2σ ⎠

(4)

By fitting eqs 2−4 to the experimental data of PISHE current, we obtain the spin transverse force f 0, absorption saturation ratio Q0 and the diffusion length A × Ls of the top SSs and 2DEG at 77 K. The fitting results is shown in Figure 3d, in which the solid squares are the experimental data, and the blue

(2)

with E

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Nano Letters solid lines are the fitting results. It can be seen that, the experimental data are well-fitted by the model. In the fitting, the following experimentally measured parameters are adopted, σ = 0.2 mm, L = 0.6 mm, r0 = 0.5 mm, and Rab = 4.54 kΩ. Q0 is fitted to be 0.5. Here, 2L is the distance between the two electrodes. The spin transverse forces f 0/q of the electrons in top SSs and 2DEG are fitted to be 5.6 × 10−8 and −9.7 × 10−8 N/q at 77 K, respectively, which show opposite signs. This can be attributed to the opposite sign of the effective SOC coefficients of the top SSs and 2DEG. The PISHE of 2DEG can be induced by different mechanisms. To find the dominant mechanism of our system as well as to further confirm our method, we investigate the temperature dependence of PISHE between 77 and 300 K. At each temperature, we sweep the laser spot from the left to the right side of the electrodes along x axis, and at each spot position, we rotate the quarter-wave plate from 0° to 360° and obtain the PISHE by fitting the data to eq 1. The PISHE current as a function of the laser spot location at different temperatures are shown in Figure 4a by squares, from which one can see that the PISHE current exhibits three-time reversion at all temperatures, and the intensity of PISHE shows slight decrease when the temperature is increased from 77 to 300 K. Then, using eqs 2−4 to fit the experimental data of PISHE current, we obtain f 0, Q0, and A × Ls of the top SSs and 2DEG at different temperatures, as shown in Figure 4b,c. In the fitting, the same parameters, except for the resistance Rab, adopted in Figure 3d are used because Rab changes with temperatures (see the Supporting Information). One can see that the experimental data can be well-fitted by the model at all temperatures. One can see from Figure 4b that the magnitude of the spin transverse force of the 2DEG slightly decreases with increasing temperatures, which can be explained by the mechanism of PISHE. There are two mechanisms for PISHE (or ISHE) of 2DEG, i.e., intrinsic and extrinsic mechanisms. The former one is due to the spin-dependent scattering of the intrinsic band structure of the perfect crystal48−50 arising from Rashba50 or Dresselhaus SOC,51 and the latter one originates from the asymmetry scattering by impurities with strong spin−orbit interaction.52,53 For a 2DEG with point group symmetry of C3v, the spin transverse force based on intrinsic mechanism can be

dependence term, which indicates that the observed PISHE in the 2DEG is dominated by the extrinsic mechanism. This observation is consistent with the fact that there is a high concentration of defects and impurities in the Bi2Se3 sample. It can be seen from Figure 4b that the magnitude of the spin transverse force of the top SSs also decreases with increasing temperatures, which agrees with that was observed in ref 12. By the model fitting, we can obtain the value of A × Ls of the top SSs and the 2DEG. To further determine the value of A, we should compare the temperature dependence of A × Ls to the previous results of temperature dependence of electron diffusion length Ls. By adopting the mobility μn and electron lifetime τn of the top SSs from ref 9 and refs 10 and 21, and using the equation Ls = kBTμn τn/q ,60 we can obtain the temperature dependence of Ls for the SSs, as shown by the dashed line in Figure 4c. Here kB is the Boltzmann constant. Similarly, adopting the mobility μn and electron lifetime τn of the 2DEG from refs 21 and 17, we can get the temperature dependence of Ls for the 2DEG in Bi2Se3, also shown by dashed line in Figure 4c. Then by fitting our value of A × Ls to the value of Ls obtained by the calculation mentioned above, we can determine the constant A of the top SSs and 2DEG to be 2.325 × 104 and 2.5 × 103, respectively. The very good agreement of our results with previous data shown in Figure 4c verifies our method. It can be also seen from Figure 4c that both of the electron diffusion lengths of the top SSs and the 2DEG decrease with increasing temperatures, due to the enhancement of carrier scattering by impurities and by phonons.61 To further confirm our model, we measure the PISHE current as a function of light spot location under different excitation powers at room temperature, i.e., 100, 200, 250, and 300 mW (see the Supporting Information). When the light intensity is decreased to 100 mW, only one sign flip is observed. This is because the light is totally absorbed by the top SSs and no light reaches at the 2DEG, or most of the light is absorbed by the top SSs and the light that reaches the 2DEG is not strong enough to excite an observable PISHE current. When the power is enhanced from 100 to 200 mW, both of the PISHE current from the top SSs and 2DEG increase remarkably. As the power is increased from 200 to 300 mW, the PISHE current from the 2DEG increases almost linearly, while that of the top SSs only slightly increases. This is because in this power range, the light intensity that reaches at the 2DEG increases dramatically, while the light intensity and its spatial distribution that is absorbed by the top SSs do not change significantly. The experimental data can be well-fitted by our model (see the Supporting Information), which further confirms our model. In conclusion, the photoinduced inverse spin Hall effect has been observed in 3D TI Bi2Se3 with a thickness of 7 QLs in a temperature range from 77 to 300 K. The PISHE contributed by the top SSs and the 2DEG at the TI surface have been successfully separated based on their opposite signs. This method is further confirmed by the temperature and power dependence of the PISHE. Besides, it is also found that the PISHE of the 2DEG is dominated by extrinsic mechanism, which is suggested by its temperature dependence.

4m*2τ D

s (α 2 + β 2).31,34 In a expressed theoretically as f0 = ℏ2 2DEG τs is proportional to T−1.54 Here, T is the temperature. Due to the large band bending in the surface, the Rashba constant α is expected to be much larger than that of Dresselhaus β.16 Considering that α ∝T and that spin diffusion 1 coefficient D is proportional to T−2,55−57 we have f0 ∝ T . For extrinsic mechanism, f 0 can be theoretically expressed as

f0 ∝

−πm * λ 02εF σc 3ℏ2

+

q2λ 02 49,58 n, 4ℏ

where εF is the Fermi energy, σc

is the conductivity, n is the electron density, and λ0 is a length characterizing the strength of SO interaction. Because the Bi2Se3 sample has a high carrier density (about 1019 cm−3), its carrier density n and mobility will not change significantly with temperatures.59 As a result, the f 0 induced by the extrinsic mechanism will have a weak dependence on temperatures. f 0 of the 2DEG are well-fitted by a + b · T−1, as shown by the dotted line in Figure 4b, with a and b being −7.66 × 10−8 C/q and −1.80 × 10−6 C × K/q, respectively. It can be seen that the temperature independence term is much larger than that of T−1 F

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.7b04172. Sample and experimental details, Bi2Se3 characterization, the theoretical model of the separation of the PISHE current of the top SSs from that of 2DEG, and the power dependence of the PISHE current in Bi2Se3. (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. Phone: +86-15859008201. Fax: +860591-22865132. *E-mail: [email protected]. ORCID

Jinling Yu: 0000-0003-0108-136X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the National Natural Science Foundation of China (grant nos. 61674038, 61306120, 61474114, and 11574302) and the National Key Research and Development Program (grant no. 2016YFB0402303).

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ABBREVIATIONS PISHE, photoinduced inverse spin Hall effect; SSs, surface states; CC, conducting channels; SOC, spin−orbit coupling; 2DEG, two-dimensional electric gas; TI, topological insulator; QLs, quintet layers; ARPES, angle-resolved photoemission spectroscopy; ALPGE, abnormal linear galvanic effect; CPGE, circular photogalvanic effect; EMF, circular electromotive force; CPL, circularly polarized light

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