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Spin photocurrent spectra induced by Rashba- and Dresselhaus-type circular photogalvanic effect (CPGE) at inter-band excitation have been experimentally investigated in InGaAs/AlGaAs quantum wells at a temperature range of 80 to 290 K. It is found that, the sign of Rashba-type current reverses at low temperatures, while that of Dresselhaus-type remains unchanged. The temperature dependence of ratio of Rashba and Dresselhaus spin-orbit coupling parameters, increasing from −6.7 to 17.9, is obtained, and the possible reasons are discussed. We also develop a model to extract the Rashba-type effective electric field at different temperatures. It is demonstrated that excitonic effect will significantly influence the Rashba-type CPGE, while it has little effect on Dresselhaus-type CPGE.
© 2015 Optical Society of America
1. Introduction
Spintronics has raised enormous interest in the recent decades, both from a fundamental aspect and for possible applications [1–12 ]. The spin-orbit coupling (SOC) and the resulting spin splitting are the central mechanisms for spin-related effects in semiconductors, which allow for the manipulation of spin-polarized carriers [2, 11–13 ]. The SOC can be divided into two types, one is Dresselhaus term induced by the bulk inversion asymmetry (BIA) [14], and the other is Rashba term induced by the structure inversion asymmetry (SIA) [15]. These two terms can interfere with each other, which leads to an anisotropy of spin splitting. Besides, for (001)-grown zinc-blende QWs with a equal strength of k-linear Rashba and Dresselhaus terms, the spin splitting will vanish in certain k-space direction, and as a consequence, the dominant mechanism of spin dephasing (Dyakonov-Perel relaxation) will be suppressed [16, 17]. Since Rashba/Dresselhaus zero magnetic field spin splittings give rise to a large number of diverse physical phenomena, their characterization and control are of fundamental importance for spin physics in semiconductors [17]. Recently, studying of the SIA/BIA-interplay has been carried out in a number of theoretical [18,19] and experimental works [17]. However, there are few reports concerning the evolutions of Rashba and Dresselhaus SOC with temperatures or their relative ratios under different temperatures [20]. In the recent years, circular photogalvanic effect (CPGE), which is induced by unbalanced occupation of carriers in momentum space excited by circularly polarized light due to the SOC and optical selection rules [4, 21], is emerging as an effective experimental tool to measure spin splitting and SOC in low-dimensional semiconductor systems [2, 10]. Besides, it is also possible to develop some new spin photoelectric devices based on CPGE. Ganichev et al. separated Rashba- and Dresselhaus-type SOC in (001)-grown GaAs and InAs based two dimensional electron systems by using the angular distribution of the CPGE or spin-galvanic effect induced by terahertz radiations [4, 7]. Belkov et al. investigated CPGE spectra in (113)A-oriented p-doped GaAs QWs at inter-band excitation [22]. In our previous works [23, 24], we studied the CPGE spectra induced by Rashba and Dresselhaus SOC in undoped (001) GaAs/AlGaAs and InGaAs/AlGaAs QWs, in which we suspected that the excitonic effect may play a dominant role. Now we carry out temperature-dependent CPGE spectra measurements to investigate the contribution of the excitonic effect to CPGE current as well as the ratios of Rashba and Dresselhaus SOC at different temperatures.
In this paper, we investigate the spin photocurrent spectra induced by Rashba- and Dresselhaus-type CPGE at inter-band excitation in InGaAs/AlGaAs QWs at a temperature range of 80 to 290 K. It is found that, for the transition of 1H1E (i.e., transition of the electrons from first valence subband to the first conduction subband), the sign of Rashba-type CPGE reverses at low temperatures, while that of Dresselhaus-type remains unchanged. Besides, the temperature dependence of the ratio of Rashba and Dresselhaus spin-orbit coupling parameters (RD ratio) is also obtained. What is more, we also develop a model to determine the Rashba-type effective electric field at different temperatures.
2. Sample and experiments
The sample studied here is the same with that used in [25], which is an In0.15Ga0.85As/Al0.3Ga0.7As QWs grown on a (001) SI-GaAs substrate by molecular beam epitaxy (MBE). The sample is cleaved along [110] and [11̄0] directions into a square of 4 × 4 mm2. Then a pair of ohmic contacts with 3 mm apart along [100] direction are made by indium deposition and annealed at about 420 °C in nitrogen atmosphere, as shown in Fig. 1.
Fig. 1 Geometries used to measure the CPGE current induced by (a) Rashba- and (b) Dresselhaus-type SOC. (c) Microscopic picture of the origin of the CPGE current induced by inter-band excitation in C 2v point group samples taking into account the splitting of conduction and valence bands in k-space. The left-hand circularly polarized light σ + irradiating obliquely on the sample induces the transition from s=−3/2 heavy holes to s=−1/2 electrons, while the right-hand circularly polarized light σ − with oblique incidence triggers the transition from s=3/2 heavy holes to s=1/2 electrons. Due to spin splitting and optical selection rules, the transitions mentioned above will lead to unbalanced occupation of carriers in momentum space resulting in a spin-polarized electric current.
A supercontinuum laser source with a repetition rate of 40 MHz and an average power of 4 W is used as a radiation source. Then the light goes through a monochromator, a polarizer and a photoelastic modulator (PEM) to become a periodically oscillating polarization between right- (σ −) and left- (σ +) hand circularly polarized light. To obtain the temperature dependent photocurrent spectra, the sample is mounted in an optical cryostat which allows the variation of the temperature in the range of 77–300 K. A gaussian profile light spot with a diameter of about 2 mm irradiates at the central line between two electrodes with a power of about 285 μW at 950 nm (see Fig. 1). In order to extract the common photocurrent I PC under DC bias, a chopper with a frequency of 220 Hz and a lock-in amplifier are used. The photogalvanic current is measured in the unbiased structure via a preamplifier and then is recorded by the lock-in amplifier in phase with the PEM. The wavelength of the light ranges from 810 to 990 nm.
Figure 1(c) shows a schematic diagram to illustrate the origin of the CPGE current induced by inter-band excitation in C 2v point group samples taking into account the splitting of conduction and valence bands in k-space. Firstly, SOC will lift the spin degeneracy and lead to spin splittings in k space both in conduction and valence bands. When a circularly polarized light with photon energy above the exictonic state of ground state of QWs, for example, left-hand circularly polarized light σ +, irradiates obliquely on the sample, the electrons in the first heavy hole subband with the spin s=−3/2 are excited to the first electron subband with the spin s=−1/2, according to the optical selection rules. Then due to spin splitting and optical selection rules, the occupations of carriers in k space will be unbalanced, which will result in spin polarized electric current in real space. Obviously, if the helicity of the light, which irradiates oblique on the sample, is changed from left- to right-hand circularly polarized, the direction of the CPGE current will be reversed. For inter-band excitation, the spin polarized carriers with unbalanced momentum occupation in k space can be produced by two ways: (1) direct formation of free electrons and holes by inter-band transitions, and (2) creation of free carriers through excitons. For undoped insulating semiconductor QWs, the latter one will play a more important role. Take the sample investigated in this experiment as an example, when the sample is under no irradiation, the electron density of the sample is too low to be measured by a Hall system, while the 2D density of the photo-induced carriers is estimated to be at the order of 1010 cm−2 under an irradiation of 285μW at 950 nm at a temperature of 290 K. This indicates that the photogenerated carriers dominate the measured current. Besides, the intensity of the common photocurrent under dc bias is much stronger than that at room temperature (see Fig. 2(b) in [25]), especially for the excitonic state 1H1E, which indicates that the excitonic effect may play an major role in the photocurrent at low temperature. Specifically, the excitons are firstly formed by inter-band excitations, and then the excitons will dissociate to generate free carriers through interaction with phonons, impurity centers or other excitions [26]. Electric field will also lead to the dissociation of the excitons. Because of the optical selection rules and the spin splitting, the electron-hole pairs which make up of the excitons have well defined momentums. When they are dissociated to form free carriers, the momentums of carriers are maintained to some extent leading to a electric current in real space, i.e., CPGE current. It can be seen that the intensity of the CPGE current is associated with the value of spin splittings both in conduction and valence bands. Since the strength of spin splitting is proportional to the SOC of the QWs and the intensity of the SOC in the conduction and valence bands is different, the value of CPGE will reflect the intensity of the effective SOC in the QWs.
Fig. 2 CPGE spectra induced by (a) Rashba- and (b) Dresselhaus-type SOC normalized by the power of the light at different temperatures ranging from 80 to 290 K.
Since the Rashba and Dresselhaus SOC contribute differently to the CPGE current for different crystallographic directions, we can separate the spin splitting induced by Rashba and Dresselhaus SOC according to the method proposed in [4] and [7]. Therefore, using the geometry shown in Fig. 1(a) and 1(b), we can obtain the CPGE current induced by Rashba and Dresselhaus spin splitting, respectively. In the figure, ê denotes the direction of light propagation and êx is its x component. I SIA and I BIA indicate the CPGE current induced by Rashba and Dresselhaus spin splitting, respectively. The incident angle of the light is θ=30 °.
3. Results and discussions
Figure 2(a) and 2(b) show the CPGE spectra induced by Rashba- and Dresselhaus-type SOC, respectively, at different temperatures ranging from 80 to 290 K. They are normalized by the power of the incident light. The common photocurrent spectra I PC under DC bias at different temperatures are also obtained, which are the same with that reported in our previous work [25]. Therefore, they are not shown here. The spectra in Fig. 2(a) are measured under the geometry illustrated in Fig. 1(a), while those in Fig. 2(b) are obtained under the geometry of Fig. 1(b). All of the spectra are shifted vertically for clarity. The thick solid and dashed arrows indicate the energy positions of the transitions 1H1E and 1L1E, respectively. According to 6 band k · p theory, the energy position of 2H1E is at about 885 nm at 80 K. Besides, a large signal emerges at 846 nm at 80 K in Fig. 2(a), whose value decreases with the increasing temperature and nearly drops to zero when the temperature is above 180 K. Its origin is still unclear, and it may be assigned to the transition of 3H1E. We can see from Fig. 2 that the CPGE spectra induced by Rashba-type SOC show similar spectral line-shape with that induced by Dresselhaus-type SOC at 290 K, and the CPGE current of the transition 1H1E has the same sign with that of 1L1E for both SIA- or BIA-induced CPGE spectra at 290 K. These observations are not consistent with the theoretical results reported in [3], which predicted that the SIA- and BIA-induced CPGE spectra showed different spectral lineshapes and there was a sign change in the SIA-induced CPGE spectra in the energy range covering the transitions of 1H1E to 3H1E. Besides, it also predicted that the BIA-induced CPGE current was close to zero at the spectral region corresponding to the transitions 1H1E and 2H1E. These discrepancies may be attributed to the following two reasons: (1) the prediction adopted a infinitely-high-barrier approximation, which may introduce some errors; (2) the prediction did not take into account the excitonic effect, which may play a dominant role in the CPGE spectra of the QW sample. Actually, in our previous work [24], we have proved that the calculated CPGE current had the same sign for 1H1E and 1L1E in GaAs/AlGaAs QWs when the actual height of the barriers was adopted. Besides, it is worth noting that the CPGE current observed in our experiments always presents in the energy positions corresponding to excitonic states of the QWs, which may indicate the dominant role of excitonic effect in the CPGE spectra in our sample. Therefore, theoretical results that are agree well with the experiments may be obtained if both of the actual barrier height and excitonic effect are taken into account.
It can be seen from Fig. 2(b) that, the spectral line-shape of the BIA-induced CPGE current does not change significantly during the temperature range of 80 to 290 K. It is worth mentioning that although the sample temperature can affect both the linear and cubic in k Dresselhaus terms, the influence is small in materials with weak cubic in k spin splitting, and it may play an important role in highly doped QWs and narrow band semiconductors like InAs-based QWs [17]. For the undoped GaAs-based InGaAs/AlGaAs QWs studied here, cubic in k Dresselhaus terms are quite weak, so the influence of temperature on the Dresselhaus terms is small, which may be evident from the weak dependence of the BIA-type CPGE current on temperature. However, the spectral line-shape of the SIA-type CPGE current exhibits a remarkable change when the temperature is changed from 80 to 290 K, especially for 1H1E, whose sign reverses when the temperature is lower than 120 K. There are several reasons which may be responsible for this phenomenon. Firstly, the sign changing behavior of the SIA-type CPGE current at about 120 K may indicate the change of the mechanism of CPGE. Because in addition to the spin-splitting dependent mechanisms of CPGE, there are orbital mechanisms, which are related with an interference of the wavevector odd and even terms in optical transition matrix elements or connected with an interplay of the excitation and scattering processes [27]. Therefore, the sign reversion of the SIA-type CPGE current may indicate the main mechanism of the CPGE changes from spin-splitting related one to the orbital one, or vice versa. Secondly, as mentioned in Sec. 2, there are spin splitting both in the conduction and valence bands, and the spin splitting in valence band may be comparable or even much larger than that in conduction band [28,29]. Thus, the CPGE current generated due to the spin splittings may be proportional to the combinations of corresponding conduction and valence band parameters. If the contributions made by the conduction and valence bands to the CPGE have close magnitudes and opposite signs, a small change in the conduction or valence band parameters can make one or the other contribution dominant resulting in the sign change of the CPGE. Thirdly, since the spin polarization of holes is known to relax much faster than that of electrons, the CPGE current may be mainly governed by the spin splitting of the conduction band. In this case, the sign reversion may be attributed to the sign change of the Rashba parameter α in the conduction band, since under this conditon the CPGE current induced by SIA is proportional to the Rashba parameter α in the conduction band and Rashba-type SOC is an extrinsic effect which can be tuned by electric field [30], strain [24, 31] and asymmetric potential gradients [32]. In what follows, we are going to discuss the possible mechanism that the change of Rashba parameter α influences on the sign reversion of the SIA-type CPGE. According to [24,31], which demonstrated that Rashba-type SOC can be linearly tuned by shear strain εxy, α can be expressed as [33]
Here, a is a constant, and f(U) is a function of the potential U of the QW system, depicting the influence of the asymmetric potential U on the Rashba parameter α. α 0 is the so-called Rashba coefficient, which is related to the band structure of the host crystal [20] and is predicted to be large in materials with a narrow band gap [34]. Since both of the asymmetric potential and the shear strain εxy do not change significantly with temperatures, the sign reversion of the SIA-type CPGE may be mainly attributed to the first term in Eq. (1). It has been reported that the Rashba coefficient α 0 decreases nearly linearly with decreasing temperatures [20]. Besides, at low temperatures (80 – 130 K), the radiation of the light will generate a large number of excitons, which dissociate rapidly under the built-in field and then in turn reduce the built-in field F. Both of the diminishment of the Rashba coefficient α 0 and the built-in electric field will decease the first term in Eq. (1). If the built-in field has an opposite effect on the Rashba parameter α compared with that of shear strain εxy and asymmetric potential U, the reduction of the built-in field at low temperatures may result in the sign reversion of the SIA-type CPGE current.If the CPGE current is governed by the spin splitting of conduction band, the temperature dependence of RD ratio for the transition 1H1E, i.e., α/β versus temperature, can be obtained by I SIA/I BIA under different temperatures. The result is shown in Fig. 3(a) by squares. It can be seen that, as the temperature increases from 80 to 160 K, the RD ratio increases from −6.7 to 17.9, and then it drops to around 8.5 and keeps almost stable at a temperature range of 180 to 290 K. The slight change of the BIA-type CPGE shown in Fig. 2(b) may indicate a weak dependence of Dresselhaus parameter β of conduction band on temperature if the CPGE current is dominated by the spin splitting of conduction band. Thus, the variation of the RD ratio with temperatures may be mainly attributed to the change of the Rashba parameter α with temperatures. As we mentioned above, there are three factors contributing to the Rashba SOC, i.e., shear strain εxy, electric field and the asymmetric potential along the z direction. Since there is no external shear strain applied to the sample, and the residual shear strain is supposed to be quite small, the main contribution may come from the built-in electric field and the asymmetric potential. The built-in electric field is measured to be about 12.6 kV/cm [23], and the large degree of asymmetry in the potential induced by the strong segregation effect of indium atoms in the QWs is proved by the result of reflectance-difference spectroscopy in our previous work [23]. However, the Rashba coefficient α 0 shows a nearly linear dependence on temperatures according to [20], but in our experiment the RD ratio does not follow this trend. Therefore, the temperature dependence of RD ratio observed in our experiments should not be attributed to the diminishment of the Rashba coefficient α 0 with decreasing temperatures. However, it may be owing to the reduction of the built-in field in low temperatures. What is more, the RD ratio does not change significantly when the temperature is above 180 K, which indicates the built-in electric field is becoming stable at this temperature range. This is because the excitonic effect is weakened in this temperature range, which can be evident from the slight change of the common photocurrent I PC intensity with temperatures. In addition, a maximum is present at about 160 K for the RD ratio, and the reason is still unknown. Besides the reason of the variation of the built-in electric field with temperatures, another reason may contribute to the sign reversion of RD ratio, i.e., the interplay between electrons an holes at different temperatures. There are interactions between electrons and holes whether they combine to form excitons or dissociate to be free carriers. These interactions may be stronger in the undoped insulating QW samples than that in doped counterparts, since in the undoped ones, the exctionic effect are much stronger and the electrons and holes are of the same number. These interactions may change the momentum relaxation time and the momentum distribution of the carriers, and what is more, the interaction strength will change with temperatures, which may result in the sign reversion of RD ratio. No matter which kind of mechanisms is dominant, the excitonic effect seems to play a significant role. Thus, it can be inferred from Fig. 2 that the excitonic effect do not greatly influence the Dresselhaus-type CPGE, but it will significantly affect the Rashba-type CPGE.
Fig. 3 Temperature dependence of (a) RD ratio and (b) the ratio of I SIA and I PC for the transition of 1H1E (filled squares) and the calculated results of αe (filled circles). The inset of (b) shows the temperature dependence of τ 0.
The common photoinduced current under DC bias I PC can be expressed as
where e is the elementary charge, S is the cross sectional area of the current, μ is the mobility of electrons, E is the applied in-plane electric field, and N 0 = (n↑ +n↓) is the density of the photoinduced electrons (n↑ and n↓ are the density of the spin-up and spin-down electrons, respectively). According to [25], N 0 can be written as N 0 = Gτ 0. Here G is the generation rate of spin-up electrons and τ 0 is the recombination lifetime of the photoinduced electrons. The CPGE current induced by Rashba-type SOC can be written as where τp is the momentum relaxation time of the photoinduced electrons, and is the degree of the circular polarization. In our experiment, P c = 1. αe is proportional to α, and it has the same dimension with electric field E. Therefore, αe can be interpreted as the effective electric field experienced by the spin polarized carriers induced by Rashba-type SOC. Here the contribution of holes has been neglected, since the spin polarization of holes is known to relax much faster than that of electrons. Combining Eqs. (2) and (3), we have Since our sample is an intrinsic InGaAs/AlGaAs QWs with negligible electron-electron scattering, τp can be expressed as τp = m * μ/e [20], where m * is the effective electron mass, and it can be adopted as m * = 0.06m 0 in InGaAs/AlGaAs QWs (m 0 is the free electron mass) [35]. It is expected that μ changes linearly with T −1 for a nondegenerate two-dimensional electron system, that is, μ = A/T [20]. Thus, we have . The mobility of electrons in InGaAs/AlGaAs QWs is measured to be 5952 cm2/(V·s) at 300 K and 22315 cm2/(V·s) at 80 K. Thus, by linear fitting we obtain A=178.6 m2KV−1s−1. The electric field E applied in the experiment to measure I PC is about 150 V/cm. Therefore, if the value of τ 0 is known, one can calculate the value of αe from the ratio of I SIA and I PC. Figure 3(b) shows the value of I SIA/I PC for the transition of 1H1E under different temperatures (filled squares). Thus, using the τ 0 value reported in [36], which is also shown in the inset of Fig. 3(b), we obtain the value of αe under different temperatures, as shown in Fig. 3(b) by filled circles. It can be seen that, the Rashba-type effective electric field αe firstly increases when the temperature is decreased from 290 to 200 K, and then it decreases with the decreasing temperatures. Finally, a sign reversion occurs at temperatures of 80 and 100K. This special temperature dependent behavior of αe is closely related to the variations of the Rashba parameter α with temperatures, and they may have the same reasons.4. Conclusion
In conclusion, we have experimentally investigated the spin photocurrent spectra induced by Rashba- and Dresselhaus-type CPGE at inter-band excitation in InGaAs/AlGaAs QWs in a temperature range of 80 to 290 K. It is found that, for the transition of 1H1E, Rashba-type CPGE shows a sign reversion with deceasing temperatures, while the sign of the Dresselhaus-type CPGE remains unchanged. The possible reasons for the sign reversion of the Rashba-type CPGE are discussed. The temperature dependence of the ratio of Rashba and Dresselhaus spin-orbit coupling coefficients are extracted, which increases from −6.7 to 17.9. The possible reasons for the special temperature dependence of RD ratio are discussed. Finally, a model is developed to extract the temperature dependence of Rashba-type effective electric field. Our results demonstrate that excitonic effect will significantly influence the Rashba-type CPGE, but it will have little effect on Dresselhaus-type CPGE when temperatures are changed.
Acknowledgments
The work was supported by the National Natural Science Foundation of China (No. 60990313, No. 61006003, No. 61306120, No. 61474114, No. 11574302), the 973 program ( 2012CB921304, 2013CB632805), Natural Science Foundation of Fujian (Grant No. 2014J05073) and Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics (No. KF201405).
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