Helicity dependent photocurrent in electrically gated (Bi1−xSbx)2Te3 thin films

Circularly polarized photons are known to generate a directional helicity-dependent photocurrent in three-dimensional topological insulators at room temperature. Surprisingly, the phenomenon is readily observed at photon energies that excite electrons to states far above the spin-momentum locked Dirac cone and the underlying mechanism for the helicity-dependent photocurrent is still not understood. Here we show a comprehensive study of the helicity-dependent photocurrent in (Bi1−xSbx)2Te3 thin films as a function of the incidence angle of the optical excitation, its wavelength and the gate-tuned chemical potential. Our observations allow us to unambiguously identify the circular photo-galvanic effect as the dominant mechanism for the helicity-dependent photocurrent. Additionally, we use an analytical model to relate the directional nature of the photocurrent to asymmetric optical transitions between the topological surface states and bulk bands. The insights we obtain are important for engineering opto-spintronic devices that rely on optical steering of spin and charge currents.


Reviewer #2 (Remarks to the Author):
The manuscript by N. Samarth et al report a comprehensive study of the helicity-dependent photocurrent in a typical topological insulator material (Bi1−xSbx)2Te3 thin films as a function of the incidence angle of the optical excitation, the excitation wavelength and the gate-tuned chemical potential. The experimental observation confirms that the photo-galvanic effect nature of the observed helicity-dependent photocurrent response. By combining with the first-principles numerical calculation of the photocurrent, they further conclude that the helicity-dependent photocurrent originates from the asymmetric optical transitions between the topological surface states and bulk. The experimental results are quite interesting, the interpretation based on their numerical calculation is consistent with all the observed features and is thus convincing, which brings new insight for the observed helicity-dependent photocurrent in topological insulator materials. I therefore recommend publication of this work on Nature Communication. However, I would like the authors address the following two issues: 1. Since the photoexcited electron density distribution Δρ is related to the optical transition process, when authors do the first-principles numerical calculation of the photocurrent , how do they treat all the carrier relaxation processes that could be involved in between different multiple bands, when they tune the excitation photon energy? I noticed that they took the relaxation time τp as 0.1ps, does this mean that τp is always treated as a constant? 2. As illustrated in figure 4a, 4b, the autors calculated the photoexcited electron density distribution Δρ related to the optical transition processes from the bulk valence band to the surface states, and from the surface states to the bulk conduction band. From their numerical calculation, it is curious to know that if the authors find different features for the helicitydependent photocurrent resulting from the above two optical transition processes,? It seems expected that the optical transition process from bulk valence band to the surface states may exhibit different feature due to the complexicity and asymmetry of the valence band.

Reviewer #3 (Remarks to the Author):
The manuscript gives a very thorough study of photocurrents generated in topological insulator films. In this manuscript, the photocurrents are generated by transitions from/to the bulk bands to the surface states. The authors give evidence that the mechanism that dominates the generation of the photocurrent is the circular photo-galvanic effect. They also find a non-monotonic behavior of the magnitude of the photocurrent as a function of the top gate voltage (which is supposed to tune the Fermi level in the surface states), as well study the dependence of the photocurrent on the energy of the incident photons.
Regarding the suitability of the manuscript for Nature Communications. On one hand, the authors did a very comprehensive study of the photocurrent generation, and complemented the experimental work with a suitable theoretical analysis, which seems to explain most of the experimental findings. On the other hand, the results presented in this manuscript are not really surprising or demonstrate any fundamentally new effect. Moreover, many of the results, including item 2 and 3 of the main claims on page 3-4 of the manuscript, are probably not universal and very specific to the specific material studied in the current manuscript. Taking these points into account, it is my opinion that the thorough study performed in this work does merit publication in Nature Communications. However, the authors should address several technical points: 1) The evidence given in the manuscript that the Fermi level is indeed situated inside the bulk gap (and thus in the surface states) is not convincing. The peak in the resistivity presented in the manuscript can be a result of the bulk effect. Additional evidence that there is no bulk resistivity is required.
2) To unambiguously identify the effect as the circular photogalvanic effect, it is important to rule out the possibility that the effect arises due to an asymmetric heating of the sample due to incident light, which arises to the specific geometry of the sample and light spot. The authors show a linear fit to sin(phi), however changing the angle phi might also change the geometry of the experiment, i.e. the illumination spot vs. the sample shape. The authors need to rule out this effect.
3) The data for the photocurrent shows a dominant component for which is independent of the polarization. I presume that this component is also independent of the angle phi, although this is not clearly discussed. What is the origin of this component? Also, what is the origin of the nonzero components for linear polarization? 4) On page 9 and Figure 4, the authors discuss and present a calculation of the matrix element, squared, which seems to take both positive and negative signs. This is of course not possible, and the authors should explain what they mean here. 6) The authors should discuss which of the detailed features of the photocurrent response (dependence on photon energy and on the Fermi level) are universal, and which are specific to the material used in this experiment.

Response to reviewers
Reply to the first reviewer: 1) Discussing the circular photon drag effect the authors cited the book of Sturman and Fridkin "Photogalvanic effects" (Ref. 27). This book is aimed to photogalvanic effects only and does not address the photon drag effects. Therefore, I suggest replacing the reference 27 by the first theoretical paper predicting this effect and two experimental articles reporting on its observation in 2D systems with and without spin-orbit coupling.
Reply: We have followed the suggestion and replaced reference 27 by the three articles that were pointed out by the referee.
2)The theoretical model and calculations described in the manuscript suggest that the momentum relaxation time tau_p is independent of energy. Typically, tau_p is energydependent and is different for different bands. This can give rise to additional contributions to photocurrent, e.g., at the optical transitions between the first and the second surface states. Similar effect for quantum wells has been addressed by S.D. Ganichev et al., Resonant inversion of the circular photogalvanic effect in n-doped quantum wells, Phys. Rev. B 68, 035319 (2003). A corresponding comment or justification of the approximation used would be useful.
Reply: As the referee indicates, the constant value of relaxation time tau_p is indeed a simplification in our theoretical model. In realistic systems, tau_p should be energy dependent and different for different bands. To understand the influence of energy dependent relaxation time, we performed numerical calculations of the photocurrent with different relaxation times for different bands (surface, conduction and valence bands), as shown in the updated Supplementary Note 4. Supplementary Figure 5 and 6 show the photocurrents as a function of Fermi energy for different relaxation times of surface states, conduction and valence bands. We find that different relaxation times only change the results quantitatively while all the essential qualitative features, such as the peak at the Dirac point and the asymmetry between the electron and hole doping regimes, remain the same. More quantitatively, by comparing the line shape of the calculated photocurrents with that in experiments, we conclude that a shorter surface relaxation time ( " = 0.5 ( in Supplementary Figure 7) and a longer conduction band relaxation time ( ) = 2 + in Supplementary Figure 8) give rise to a better match with the experimental observations. We note that the relaxation process for photo-excited carriers in topological insulators have been studied in several time-resolved measurements [1][2][3][4][5][6] and the relaxation time reported for excited bulk carriers is slightly longer than that of surface carriers [3][4], thus providing additional support for our conclusion.
The referee also mentions the possible contribution of photocurrents from the optical transitions between the first and the second surface states. Our analytical results in Supplementary Note 4 confirm this contribution of photocurrents, which is proportional to the difference in relaxation times between two surface states. However, we note that the induced photocurrent will monotonically increase with chemical potential, contradicting our experimental observations. Therefore, the photocurrent contributed by the transitions between the two Dirac surface states is not the major origin of the HDPC we observe.
3. While being well defined I found that the used notations for the tensors and angles unnecessarily complicate the reading because they deviate from the terms typically used in literature (see e.g E.L. Ivchenko, OPTICAL SPECTROSCOPY OF SEMICONDUCTOR NANOSTRUCTURES, Alpha Science International Ltd 2005 and a number of other books on photogalvanics). In particularly, using \theta for the quarter plate rotation angle and \varphi for the angle of incidence slow down the reading, because in most of the papers and books on this topic it is just vice versa. May the authors can consider using \theta for the angle of incidence, \varphi for the quarter plane rotation angle, \gamma for the CPGE, \tilde{T} or T for the CPDE and \chi for the linear PGE.
Reply: We changed the notation for the angles, including the quarter wave plate rotation angle and the angle of incidence and the notation of the tensors for CPGE and CPDE as suggested.

Reply to the second reviewer:
1) Since the photoexcited electron density distribution Δρ is related to the optical transition process, when authors do the first-principles numerical calculation of the photocurrent , how do they treat all the carrier relaxation processes that could be involved in between different multiple bands, when they tune the excitation photon energy? I noticed that they took the relaxation time τp as 0.1ps, does this mean that τp is always treated as a constant?
Reply: This question was also raised by the first referee (Q2). Indeed, the constant relaxation time in our theoretical model is an approximation. We justify this approximation and study the effect of different relaxation times for different bands in the updated Supplementary Note 4. A detailed response is found in our reply to question 2 of the first referee.
2) As illustrated in figure 4a, 4b, the authors calculated the photoexcited electron density distribution Δρ related to the optical transition processes from the bulk valence band to the surface states, and from the surface states to the bulk conduction band. From their numerical calculation, it is curious to know that if the authors find different features for the helicity-dependent photocurrent resulting from the above two optical transition processes? It seems expected that the optical transition process from bulk valence band to the surface states may exhibit different feature due to the complexity and asymmetry of the valence band.
Reply: To address this question, we have added new calculations to the supplementary materials. The photocurrent contributions from transitions between the surface states and the bulk conduction band transitions and between bulk valence band states to the surface states are separately shown in Supplementary Figure 4 (the blue line for valence bands and black line for conduction bands). We note that the overall features for these two contributions are quite similar and only the magnitude of the contribution from valence bands is larger than that from conduction bands due to the large density of states for valence bands. We emphasize that the situation for (Bi,Sb)2Te3 is different from that for conventional III-V or II-VI semiconductors. In the conventional III-V or II-VI semiconductors, the conduction band has s-orbital nature while the valence band has p-orbital nature, leading to a more complicated band structures for valence band compared to conduction band. For (Bi,Sb)2Te3, both conduction and valence bands are from the p orbitals of Bi, Sb and Te atoms [7], and thus, they are qualitative similar for the purposes of these calculations.

Reply to the third reviewer:
1) The evidence given in the manuscript that the Fermi level is indeed situated inside the bulk gap (and thus in the surface states) is not convincing. The peak in the resistivity presented in the manuscript can be a result of the bulk effect. Additional evidence that there is no bulk resistivity is required.
Reply: In addition to the gate voltage dependent longitudinal resistance R xx , we have added the temperature dependent R xx at zero gate voltage while cooling down the sample from room temperature (RT) to 15 K in the supplementary material ( Supplementary Fig 2). We show that R xx increases monotonically as the temperature cools down, which is a signature of an insulator. This temperature dependence is consistent with the insulating samples studied in Ref [8]. Thus, the temperature dependence of R xx provides another evidence that the chemical potential at zero gate voltage is indeed in the bulk band gap.
2) To unambiguously identify the effect as the circular photogalvanic effect, it is important to rule out the possibility that the effect arises due to an asymmetric heating of the sample due to incident light, which arises to the specific geometry of the sample and light spot. The authors show a linear fit to sin(phi), however changing the angle phi might also change the geometry of the experiment, i.e. the illumination spot vs. the sample shape. The authors need to rule out this effect.
Reply: We ran a scanning photocurrent measurement on the same piece of sample, shown in the Supplementary Figure 8. The photocurrent imaging shows that the circular photo-galvanic effect (CPGE) does not vary too much when we scan the beam across the sample covered under the gate. We also note that the beam size used in the scanning measurement is more than ten times smaller than the beam size for the incidence angle dependence measurement. For a larger beam size, the photocurrent variation with position change would be even smaller. Further, there is no signature of heating induced change of CPGE in the imaging result. (If there is CPGE induced by heating, we would expect to see a larger CPGE when the beam moves away from the center of the sample, which we did not see in our scanning photocurrent measurement.) Therefore, in the incidence angle dependence study, the slight change of the beam spot position when tuning the incidence angle should not affect the CPGE. Also, additional beam size change caused by the incidence angle variation should not deliver a sine function dependence. Therefore, we are confident that the linear dependence on the sine function of the incidence angle is an effect from the physical origin of the CPGE.
3) The data for the photocurrent shows a dominant component for which is independent of the polarization. I presume that this component is also independent of the angle phi, although this is not clearly discussed. What is the origin of this component? Also, what is the origin of the nonzero components for linear polarization?
Reply: We do observe a polarization independent photocurrent and a linear polarization dependent photocurrent shown in Fig. 1(b). However, we would like to stress that the CPGE is still dominant in the total photocurrent, as shown in Fig. 1(c). We also find that the polarization independent photocurrent mainly originates in a dark current that we observe even without a laser, usually in the order of 2-10 pA. The dark current is not a real photocurrent generated by laser, and therefore, is not induced by an optical effect. Also, this polarization independent photocurrent varies little with the angle phi. The linear polarization dependent photocurrent, instead, is a real optical effect. People have already done experiments focusing on the linear polarization dependent photocurrent in topological insulators. They find that the origin of this photocurrent is possibly the photon drag effect [9][10]. We have added a few sentences in the main text to point out the origin of the other two photocurrent components. Figure 4, the authors discuss and present a calculation of the matrix element, squared, which seems to take both positive and negative signs. This is of course not possible, and the authors should explain what they mean here.

4) On page 9 and
Reply: The referee is correct that the matrix element, squared, should always be a positive number. Figure 4 does not show the full matrix element; instead, we split the matrix element into the symmetric and asymmetric parts with respect to the momentum. Figure 4 only shows the asymmetric part, which gives rise to the non-zero photocurrent and determines the direction of the photocurrent. We have changed the notation of the matrix element in the paper to make it clear. Reply: As discussed in detail in the introduction, our systematic study studies the helicity dependent photocurrent in topological insulators by tuning the incidence angle, the chemical potential and the wavelength of laser. This allows to addressed the microscopic origin of the helicity dependent photocurrent (HDPC). In addition, our demonstration of the maximal HDPC at the Dirac point suggests the important role of surface states for this phenomenon and opens a path to potential applications of topological surface states in opto-spintronics. While Ref. 15 described the elegant experimental discovery of the HDPC in topological insulators, the experiments in that manuscript did not propose a detailed explanation of the origin of the phenomenon.
6) The authors should discuss which of the detailed features of the photocurrent response (dependence on photon energy and on the Fermi level) are universal, and which are specific to the material used in this experiment.
Reply: The emergence of the peak in the HDPC as the chemical potential crosses the Dirac point is universal for materials that hold Dirac surface states and inversion symmetric bulk once a single bulk band dominates the contribution. However, the HDPC reversal at a photon energy around 1.5 eV is due to the contributions from multiple bulk states, and is thus not universal.
In materials with Dirac surface states and inversion symmetric bulk, the HDPC also originates from the asymmetric optical transitions between the Dirac surface states and the bulk states. Thus, similar matrix elements can be used to describe the optical transitions. The schematic picture of the optical transitions shown in Figure 5 also applies. Therefore, we would also expect a peak of HDPC at the Dirac point. However, the direction of the photocurrent (± ) depends on several material-dependent parameters and the spin texture of the Dirac-cone surface states. The direction of the HDPC for topological insulators with right-handed spin texture would be opposite to what we have for Bi, Sb 3 Te 6 .
The sign reversal of HDPC when we tune the photon energy is deeply connected to the bulk band structure and parity. As presented in the main text and Fig 4(c), the bulk band at the Γ point around -1.76 eV belongs to the Γ 8 9 irreducible representation while the bulk band at the Γ point around -1.92 eV belongs to the Γ 8 : irreducible representation. This leads to the sign reversal of the photocurrent at a critical photon energy around 1.5 eV. For a different material, the sign reversal might not appear in the same energy range due to the different bulk band property. However, the idea that the helicity dependent photocurrent may reverse the direction if the bulk band parity reverses holds true for other topological insulator materials. From this perspective, our photon energy dependence study of the HDPC is universal.