Abstract
Threedimensional topological insulators are a class of Dirac materials, wherein strong spinorbit coupling leads to twodimensional surface states. The latter feature spinmomentum locking, i.e., each momentum vector is associated with a spin locked perpendicularly to it in the surface plane. While the principal spin generation capability of topological insulators is well established, comparatively little is known about the interaction of the spins with external stimuli like polarized light. We observe a helical, biasdependent photoconductance at the lateral edges of topological Bi_{2}Te_{2}Se platelets for perpendicular incidence of light. The same edges exhibit also a finite biasdependent Kerr angle, indicative of spin accumulation induced by a transversal spin Hall effect in the bulk states of the Bi_{2}Te_{2}Se platelets. A symmetry analysis shows that the helical photoconductance is distinct to common longitudinal photoconductance and photocurrent phenomena, but consistent with optically injected spins being transported in the side facets of the platelets.
Introduction
Selectively addressing the twodimensional surface states (SSs) of threedimensional (3D) topological insulators (TIs)^{1,2,3,4} in electrical transport experiments is challenging due to the intrinsic doping of TIs, resulting in sizable contribution of the bulk states (BSs) to the conductivity. Nevertheless, electrically induced spinpolarized currents due to spinmomentum locking^{5} have been demonstrated in lateral spin valve devices with a ferromagnetic spin detector based on a number of bismuth and antimony chalcogenides^{6,7,8,9}. Alternatively, the SSs and their dynamics can be probed via optical excitation of photocurrents, whose decay enables access to the spinrelaxation time of both SSs and BSs in 3D Tis^{10,11,12,13,14,15,16}. Timeresolved ARPES experiments have demonstrated dynamics control of spinpolarized currents in Sb_{2}Te_{3}^{17,18} and Bi_{2}Se_{3}^{11,19}, as well as emergent FloquetBloch states due to hybridization of the SSs and pulsed circularly polarized light (CPL)^{20}. According to theory^{21,22}, CPL can couple to the electron spin in a material and the helicity of the incident photons determines the spinpolarization of the resultant inplane photocurrents due to asymmetric excitation of spinup and spindown carriers. This circular photogalvanic effect has been experimentally demonstrated in Bi_{2}Se_{3}^{23,24,25}, Sb_{2}Te_{3}^{26}, and (Bi_{1−x}Sb_{ x })_{2}Te_{3}^{27} and can be tuned via electrostatic gating^{24}, Fermi energy tuning^{27}, and proximity interactions^{28}. In addition, a helicitydependent photovoltaic effect has been reported for normally incident light in vicinity of the metal contacts on a Bi_{2}Se_{3} nanosheet^{29}.
Importantly, along with the SSgenerated inplane spin polarization, the strong spinorbit coupling (SOC) of the bulk bands can give rise to outofplane spin polarization diffusing perpendicularly to the applied current direction via the intrinsic spin Hall effect^{30,31,32,33,34}. Theory further predicts that a bulkmediated diffusion of spin density can take place between the top and bottom TI surfaces^{30}. So far, only little experimental data are available on bulk spin currents in 3D TIs. Spincharge conversion via the inverse spin Hall effect has been demonstrated for a TI/metallic ferromagnet heterostructure^{35}. In general, however, SOCenhanced scattering suggests strongly reduced spin diffusion lengths in 3D TIs, which makes spin detection and manipulation challenging.
In the present work, we explore the spin texture of Bi_{2}Te_{2}Se (BTS) platelets under electrical current flow using two complementary experimental methods, namely helical photoconductance measurements and magnetooptical Kerr microscopy. Our data is fully consistent with a bulkspin Hall effect generating a spin accumulation in the sidefacets of the BTS platelets, and an optical spininjection, which can be readout as a helical photoconductance with a lifetime characteristic of the SSs in the platelets’ sidefacets.
Results
Helicity dependent photoconductance spectroscopy
We contact individual BTS platelets on a transparent sapphire substrate by two Ti/Au contacts, and focus a circularly polarized laser with a photon energy of 1.54 eV normally incident onto the platelets (Fig. 1a and Methods). We apply a bias voltage V_{sd} between the contacts, such that a local electron current density j flows in the sample (black arrow in Fig. 1a). Figure 1b presents an optical microscope image of an exemplary device, comprising a BTS platelet with a width of ~9 µm and a height of 90 nm, while the Aucontacts have a distance of 10 µm. We define three positions, specifically the left edge (blue circle), the center (gray circle), and the right edge (red circle). We record the photoconductance signal upon scanning the laser with a spot size of ~1.5 µm across the platelet (Fig. 1c, d), while the light polarization is modulated at a frequency much slower than any carriercarrier or carrierphonon interaction rates (see Methods section). The corresponding photoconductance maps acquired under an applied bias voltage V_{sd} of + 1.2 V (Figs. 1c) and −1.2 V (Fig. 1d) display a helicity dependent photoconductance with opposite sign at both edges. In particular, these signals reflect the difference ΔG_{helical} = G_{helical}(σ^{+})–G_{helical}(σ^{−}) of the photoconductance G_{helical}, where σ^{+} (σ^{−}) corresponds to right (left) circular polarization of the incoming light. The absence of a photoconductance signal away from the edges is consistent with the inplane spin polarization associated to the SSs at the top/bottom surface of the platelet and the normal incidence of the circularly polarized light^{18}. In order to gain further insight into the origin of the edge signals, we use a quarter wave plate to resolve the sign change of G_{helical} as a function of helicity. Figure 1e–g show the corresponding photoconductance G_{total}, which equals the conductance under illumination and the dark conductance subtracted via a lockin detection (cf. Methods). The obtained helicitydependent photoconductance difference ΔG_{helical}, as well as the polarizationindependent photoconductance G_{photo} are highlighted in Fig. 1e to g. We note that the main oscillation in G_{total} follows the linear polarization of the excitation, and it stems most likely from an anisotropy of the absorption at a finite bias under a linearly polarized excitation^{36,37,38} (cf. Supplementary Fig. 1 and Supplementary Fig. 2). Importantly, this linear contribution of the photoconductance does not show any significant features at the platelets’ edges (cf. Supplementary Fig. 3). In the following, we interpret G_{helical} to occur in the topological side surfaces of the BTS platelets as a consequence of a spincurrent caused by the bulk spinHall effect^{30,31,32,33,34}. In this scenario, the spin accumulation induced by the biasdriven current density j (black arrow in Fig. 1a, c, d) is characterized by an outofplane spin polarization pointing in opposite directions at the left and right edge of the BTS platelet (blue and red arrows).
Helicitydependent vs. longitudinal photoconductance
Figure 2a reveals that ΔG_{helical} depends linearly on the laser power P_{laser} (up to 12 mW), without reaching saturation. By contrast, the polarizationindependent photoconductance G_{photo} displays a polarity change vs. laser power, as discussed in detail in [12] (Fig. 2b). Correspondingly, we attribute the polarity change to a saturation of the lifetimelimited photoconductance in the bulk states and the one in the SSs at the top and bottom surface for P_{laser} ≥ 5 mW, while a bolometric photoconductance with a negative sign dominates the high power regime. We note that a bolometric photoconductance is driven by a heated phonon bath of the BTS platelets^{12}. Figure 2a highlights that ΔG_{helical} captures an effect that is clearly distinguished from the conventional longitudinal photoconductance effects in the bulk and surface states of BTS. This difference becomes particularly evident at a laser power of ~6 mW, where the polarizationindependent G_{photo} is zero, while ΔG_{helical} can be fully controlled with the laser polarization. The latter observation indicates that ΔG_{helical} is not a modulation of G_{photo}. In other words, for an absorption effect, ΔG_{helical} would follow G_{photo} in amplitude and direction. To a first approximation, ΔG_{helical} is decoupled from the helicity independent longitudinal photoconductance, which justifies our approach of subtracting the helicity independent conductance contributions as an offset and only evaluating the helicity dependent photoconductance (cf. Fig. 3 and Supplementary Fig. 1).
Symmetry considerations for the helicity dependent photoconductance
The schematic sketches of the excitation configuration of our photoconductance experiment in Fig. 3a, b define the electron and photon wave vectors k_{electron} and k_{photon}, as well as the spin polarization S at the left and right edges of the BTS platelet. As apparent from Fig. 3c to h, a finite G_{helical} is observed only at a finite bias voltage, thereby excluding G_{helical} as a photocurrent effect which would have a finite magnitude at zero bias. We note that for V_{sd} = 0 (Figs. 3d and 3g), the originally detected signal I_{helical} ~ 0 nA is plotted instead of G_{helical}, as an experimental conductance is not defined at zero bias. As another relevant observation, G_{helical} flips by π when either the bias V_{sd} is reversed (cf. Fig. 3c vs. 3e and Fig. 3f vs. 3 h), or when the laser spot position is exchanged between the left and right platelet edge.
Table 1 summarizes the experimentally observed symmetry characteristics of G_{helical} as concluded from Figs. 1–3, and contrasts them with those of the polarizationindependent G_{photo} and of helical photocurrents in materials with a broken symmetry^{39,40}. The latter type of current is denoted as I_{edge} in the table, in order to associate it with the circular photogalvanic effect which is well documented for topological insulators^{21,22,23,24,25,40}. From the observed bias dependence, any photocurrent effect can be excluded as origin of G_{helical}. However, it should be emphasized that such currents indeed emerge at the sidefacets of the BTS platelets, although their amplitude is very small (cf. Supplementary Fig. 4). The small amplitude is explainable by the fact that the optical cross section of the side facets is about 100 times smaller compared to that of the bulk volume in the BTS platelets. It is furthermore noteworthy that the helical photoconductance G_{helical} does not depend on the direction of the photon wavevector k_{photon} (cf. Fig. 3 vs. Supplementary Fig. 5 and Supplementary Fig. 6). Moreover, from the polarity change of G_{helical} with V_{sd}, one can exclude a longitudinal photoconductance response based upon the following argument. In case of a longitudinal response, the sign of G_{helical} would reflect the preferred current direction in xdirection upon laser illumination. From a symmetry perspective, a current reversal is equivalent to a simultaneous operation going from left edge to right edge and a rotation of the sample by a spatial angle of π. The latter combined operations have to be an even operation due to rotational symmetry, while a bias reversal of G_{helical} is odd (cf. Table 1), which contradicts the experimental findings. Nonetheless, there remains a process which is fully consistent with the observed symmetries, specifically a transverse photoconductance. In fact, the latter can effectively modulate the conductivity along the edges of the BTS platelets, and thus supports the assumption of a bulk spin current in 3D TIs, which has been analytically predicted based upon topological arguments^{30}. Recently, bulk spin currents have been identified as a possible spin generation mechanism in 3D topological insulators via the spin Hall effect^{30,31,32,33,34}. Indeed, this mechanism would yield an accumulated spin polarization parallel to the SSbased spin polarization in the side facets of BTS platelets (cf. red and blue arrows in Fig. 1a), as recently verified and discussed^{30,31,32,33,34,35}. Furthermore, it should result in an opposite spin accumulation at the opposite edges of the BTS platelets, and also reverse sign upon reversing the longitudinal charge current direction.
In order to verify the presence of vertically aligned spins accumulated at the edges of the BTS platelets, we investigate the device by magnetooptical Kerrmicroscopy. The detected Kerr angles θ_{k} (Figs. 4a–4c) are biasdependent and their sign is opposite at the opposite edges of the platelet. Likewise, the sign of θ_{k} at the edges switches with the sign of the applied bias (Figs. 4a and 4c), whereas θ_{k} vanishes at the center of the platelet (Fig. 4b). In close correspondence, also G_{helical} follows such a bias and position dependence (Figs. 4d to 4f).
Discussion
The above outlined mechanism of helicity dependent photoconductance in BTS can be rationalized by a microscopic model as follows. The spin relaxation of photogenerated charge and spin carriers in 3D TIs, including BTS, occurs on ultrafast timescales on the order of 100 fs^{11}. This fast relaxation suggests that the underlying spin dynamics of G_{helical} are governed by spin diffusion rather than a spin precession process^{31}. The spin diffusion length in Bi_{2}Se_{3} was experimentally determined to be below 10 nm at room temperature^{41}. This length is significantly smaller than both, the diffusion length of hot carriers that ranges between 200 and 300 nm in bismuthchalcogenides^{42}, and the laser spot size of ~1.5 µm in our experiment. Moreover, we observe that G_{helical} is located at the edges of the BTS platelets (Fig. 1d). Interestingly, we can observe the edgelocalized G_{helical} also in a BTS platelet with a spatial width as small as d_{platelet} ~300 nm (cf. Supplementary Fig. 7). The latter observation is consistent with a dominating spin diffusion length smaller than ½ ˑd_{platelet} ~ 150 nm at the edges. It has been reported that the inverse spin Hall effect in the bulk states of ndoped Bi_{2}Se_{3} is comparable to or even dominating over the surface Edelstein effects^{35,41}. Hence, a bulk spin Hall effect should be favorable over an outofplan spin component due to warping effects in the top and bottom surface of the BTS platelets^{21}. Moreover, the side facets are expected to exhibit a spinmomentum locking^{43} even in the presence of disorder. Under sufficiently high surface disorder, the spin relaxation time has been predicted to be increased similar as the D’yakonov–Perel mechanism in a motional narrowing regime^{30}. Analogously, the spin generation efficiency and surface conductivity are suggested to be strongly enhanced at the disordered facets of the BTS platelets^{30}, as previously demonstrated for surfaces of BiSbTeSe_{2}^{44}. Along these lines, we interpret G_{helical} as a measure of optically excited spins which are driven by the spin Hall mechanism to (or away from) the edges (blue and red arrows in Fig. 1a), where they experience an increased (or decreased) conductivity. This scenario is able to account for all our experimental findings. In particular, it explains not only the polarization dependence in Figs. 1e to 1g, but also all other experimental observations summarized in Table 1. This interpretation suggests that G_{helical} is a readout of a bulk spin current by scattering optically injected spins into the surface states of the sidefacets in the BTS platetes^{30}. Regarding the carriers involved in the optical excitation, it is important that we do not claim that the spinpolarization is generated in the topological surface states. Instead, we interpret the spinpolarization to predominantly originate from topologically trivial bands. In this context, it is relevant that, in particular for high doping levels, also the topologically trivial conduction band in BTS exhibits a strongly anisotropic spinorbit splitting close to the surface^{45}. The same holds for the valence bands which are energetically buried 0.81.6 eV below the Fermilevel^{46}. Importantly, we determine the decay time of G_{helical} to be τ_{decay} = (463 ± 13) ps (cf. Supplementary Fig. 8). This value, while exceeding the spin relaxation time by far, agrees very well with the surface lifetime of the BTS platelets^{12,47}; thereby strongly supporting the above mechanism. In other words, after a pulsed laser excitation, G_{helical} prevails as long as τ_{decay} within the surface states of the side facets.
Overall, the possibility to optically detect the spin Hall effectdriven spins at structurally disordered 3D TI surfaces relaxes the technical demands on device fabrications, thus underscoring the theoretical prediction that surface disorder in 3D TIs might even be beneficial for spintronic applications^{30}. Furthermore, the demonstrated readout principle might prove useful also for probing the spatial accumulation of spins in related materials such as Weyl semimetals.
Methods
Bi_{2}Te_{2}Se platelet growth and charge carrier density
BTS platelets are grown by a catalystfree vaporsolid method on Si substrates covered by a 300 nm thick SiO_{2} layer. Bi_{2}Se_{3} and Bi_{2}Te_{3} crystal sources (99.999% purity) are heated up to ~580 °C in a tube furnace. Ultrapure argon gas transports the evaporated material to the growth substrates, which are heated to 450°−480 °C during a growth time of 30 min. The pressure in the furnace is maintained at 75–85 mbar at Argon flow rate of 150 sccm. Thus obtained platelets have a length in the range of 560 µm, a lateral width of 0.0510 µm, and a thickness of 15–200 nm. The platelets are mechanically transferred onto Al_{2}O_{3} substrates and lithographically contacted by metal strips made of thermally evaporated Ti/Au (10 nm/250 nm). Fourterminal Hallmeasurements on single BTS platelets with a width of a few hundreds of nm revealed ndoping character, with an electron concentration of 10^{19} cm^{−3} at room temperature.
Timeintegrated photoconductance spectroscopy
For the excitation of the BTS platelets, we use a Tisapphire laser that emits light at laser pulses with 150 fs pulse duration and a repetition rate of 76 MHz. In all cases, the photon energy is set to be 1.54 eV. The position of the laser spot with size ~1.5 µm is set with a spatial resolution of ~100 nm. The helical photoconductance is measured with a standard lockin measurement technique, where the laser is modulated by an optical chopper at a frequency of f_{chop} = 2.7 kHz or a piezoelastic modulator (PEM) at a frequency of 50 kHz. The PEM is set to switch the polarization of the exciting laser between σ^{−} and σ^{+} polarized light. Alternatively, we utilize a quarter wave plate to control the circular polarization of the laser. The pulsed excitation scheme allows us to compare our timeintegrated photoconductance results with our lifetime measurements from autocorrelation spectroscopy (cf. Supplementary Fig. 8) and with earlier results (see ref. [12]). We do consider our timeintegrated measurements as steady state results and we can reproduce them with a CW excitation (cf. Supplementary Fig. 9). We performed the helicity resolved photoconductance experiments on three different devices. In all cases, we observed the described signals of opposite sign at the edges. All presented experiments are performed at room temperature and in a vacuum chamber at ~5 × 10^{−6} mbar.
Autocorrelation photoconductance spectroscopy
For characterizing the decay dynamics of G_{helical}, we split the pulsed laser beam into a pump and a probe pulse with comparable intensity, and focus the pump (probe) from the front (back) onto the BTS platelets (cf. Supplementary Fig. 8). The probebeam, which is modulated by an optical chopper at a frequency of ~1930 Hz, hits the sample at a time delay Δt. The timeresolved autocorrelation signal is then detected with a lockin amplifier on the sumfequency of the pump and the probepulse as a function of the time delay Δt. The probepulse is delayed via a mechanical delay stage.
Magnetooptical Kerr microscopy
For the Kerreffect spectroscopy we utilize the same measurement setup as for the photoconductance spectroscopy. The laser is polarized purely linearly. The polarization of the reflected light is rotated by 45° via a halfwaveplate. Afterwards, a Wollaston prism splits the reflected light into two crosspolarized beams with an angle of 20° which are detected by two balanced photodetectors. The differencesignal and sumsignal of the detectors are detected by two lockin amplifiers at a chopperfrequency of 2.7 kHz. To calibrate the reflected signal, the laserspot is positioned onto a normally reflecting surface (e.g., gold) and the halfwaveplate is adjusted, such that the difference signal of the detectors is perfectly zero. Any rotation of the reflected light’s polarization shifts the balance between the detectors, which is then detected in the difference but not in the sumsignal. Hence the sumsignal is used to calibrate the differencesignal in order to get rid of laserintensity based noise and fluctuations.
Data availability
All relevant data that supports our experimental findings is available from the corresponding author upon reasonable request.
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Acknowledgements
We acknowledge S. Tarasenko, H. Hübl, and M. Münzenberg for very helpful discussions, and the DFG (Projects HO 3324/82, SFB 1277A04, and the excellence cluster "Nanosystems Initiative Munich" (NIM)), as well as the ERCgrant NanoREAL for financial support.
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P.S. and A.W.H. designed the experiments, K.V., M.B., K.K. provided the materials, P.S. performed all experiments, and P.S., A.W.H., S.G., K.V., K.K., M.B. analyzed the data and wrote the manuscript.
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Seifert, P., Vaklinova, K., Ganichev, S. et al. Spin Hall photoconductance in a threedimensional topological insulator at room temperature. Nat Commun 9, 331 (2018). https://doi.org/10.1038/s41467017026711
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