Abstract
Spin photocurrent spectra induced by Rashba and Dresselhaustype circular photogalvanic effect (CPGE) at interband excitation have been experimentally investigated in InGaAs/GaAs/AlGaAs step quantum wells (QWs) at room temperature. The Rashba and Dresselhausinduced CPGE spectra are quite similar with each other during the spectral region corresponding to the transition of the excitonic state 1H1E (the first valence subband of heavy hole to the first conduction subband of electrons). The ratio of Rashba and Dresselhausinduced CPGE current for the transition 1H1E is estimated to be 8.8±0.1, much larger than that obtained in symmetric QWs (4.95). Compared to symmetric QWs, the reduced well width enhances the Dresselhaustype spin splitting, but the Rashbatype spin splitting increases more rapidly in the step QWs. Since the degree of the segregation effect of indium atoms and the intensity of buildin field in the step QWs are comparable to those in symmetric QWs, as proved by reflectance difference and photoreflectance spectra, respectively, the larger Rashbatype spin splitting is mainly induced by the additional interface introduced by step structures.
Keywords:
Circular photogalvanic effect spectroscopy; Reflectance difference spectroscopy; Rashba and Dresselhaus spin splitting; Inplane optical anisotropyBackground
Recently, spintronics has attracted much attentions due to its significant role in both fundamental research and possible device applications [110]. The most critical issues for realizing spintronic devices are the generation and manipulation of spinpolarized carriers in lowdimensional systems [2,11]. Spinorbit coupling (SOC) and the resulting spin splitting in a twodimensional system have been used to create and manipulate spinpolarized carriers in nonmagnetic materials without external magnetic field [1,1214]. There are two kinds of SOC according to different sources of inversion asymmetry: Dresselhaus SOC induced by the bulk inversion asymmetry (BIA), [15] and Rashba SOC induced by structure inversion asymmetry (SIA) [16]. These two terms can interfere with each other and result in an anisotropy of spin splitting. They can cancel each other when the Rashba and Dresselhaus terms have equal strength, which will lead to a zero spin splitting in certain k directions. [2] Therefore, it is important to control the value of these two components for spintronic device applications. The Rashba SOC can be tuned by external field [17], uniaxial strain [18,19], and the asymmetric potential gradients in the quantum wells (QWs) [7,8,20], while the Dresselhaus SOC is determined by the materials and the size quantization of the electron wave vector k along the growth direction z, that is, = (π/w)^{2} for an infinitely high potential well of width w[9]. Nowadays, there are lots of theoretical [21,22] and experimental investigations [7,20] concerning the influence of the asymmetric potential gradients on the spin splitting of the electrons. However, there is seldom report investigating the influence of the asymmetric gradients on the spin splitting when both the electron and holes are involved. Circular photogalvanic effect (CPGE) is an effective experimental tool to measure spin splitting in lowdimensional semiconductor system at room temperature [10], which is induced by unbalanced occupation of carriers in momentum space excited by circularly polarized light as a result of SOC and optical selection rules [4,23]. Spin photocurrent spectra of CPGE excited by interband transition, which is firstly observed by Bel’kov et al. [24], are a powerful tool to investigate the spin splitting when both the electron and holes are involved, especially when excitonic effect is dominant [19]. Besides, CPGE current with interband resonance excitation shows much stronger intensity than that with innerband excitation [5]. Thus, some unmeasurable features in the innerband excitation may be detectable by this highly sensitive interband resonance excitation. Step QW structure will not only destroy the structure inversion symmetry by a step potential, but also introduce an additional interface compared to symmetrical QWs. Therefore, step QW structure is of fundamental interest in the study of asymmetric gradientinduced and interfaceinduced Rashba spin splitting [22].
In this paper, we use CPGE spectra at interband excitation to study the Rashba and Dresselhaus spin splitting in an undoped asymmetric In_{0.15}Ga_{0.85}As/GaAs/AlGaAs step QWs. For an undoped QWs with high crystal quality, the excitonic effect will play a dominant role in the photocurrent spectra. In this case, both of the electron and holes will contribute to the photocurrent [25]. We separate the CPGE spectra induced by Rashba and Dresselhaus spin splitting, respectively, and we find that the Rashba and Dresselhausinduced CPGE spectra are quite similar with each other during the spectral region corresponding to the transition of the excitonic state 1H1E (the first valence subband of heavy hole to the first conduction subband of electrons). The ratio of the CPGE current induced by Rashba and Dresselhaus spin splitting for the transition of 1H1E is much larger than that in the symmetric QWs reported in our previous work (i.e., 8.8 vs 4.95). Although the reduced well width enhances the Dresselhaustype spin splitting compared to the symmetric QWs, the Rashbatype spin splitting in the asymmetry step QWs increases more rapidly. By using reflectancedifference spectrum and photoreflectance spectrum, we find that the degree of the segregation effect of indium atom and the intensity of the buildin field in the step QWs are comparable to those in symmetric QWs. So, the larger Rashba SOC may be mainly induced by the one more interface present in the step structures.
Methods
The sample studied here is asymmetric In_{0.15}Ga_{0.85}As/GaAs/Al_{0.3}Ga_{0.7}As step QWs grown on (001) SIGaAs substrate by molecular beam epitaxy. After a 2,000Å buffer layer is grown, ten periods of 50 Å In_{0.15}Ga_{0.85}As/50 ÅGaAs/100 Å Al_{0.3}Ga_{0.7}As are grown. The grown temperature of In_{0.15}Ga_{0.85}As and Al_{0.3}Ga_{0.7}As are 540°C and 580°C, respectively. Then, 500Åthick Al_{0.3}Ga_{0.7}As layer and 100Å GaAs cap layer are deposited. All epilayers are intentionally undoped and the InGaAs layers are fully strained since their thickness is far below the critical thickness. The sample is cleaved along [110] and [10] (denoted as the x^{′} and y^{′} directions, respectively) into a square of 5 mm × 5 mm with four pairs of ohmic contacts 4 mm apart along the x^{′}, y^{′} and diagonal directions, respectively, as shown in figure one(a) in [26]. The ohmic contacts are made by indium deposition and annealed at about 420°C in nitrogen atmosphere.
For optical interband excitation, a supercontinuum laser source combined with a monochromator is used providing radiation of wavelength in the range between 800 and 950 nm. The supercontinuum laser provides 5ps pulses with a repetition rate of 40 MHz and an average power of 4 W. Then, the monochromatic light with a linewidth of 1.5 nm goes through a polarizer and a photoelastic modulator (PEM) to yield a periodically oscillating polarization between right (σ^{}) and left (σ^{+})hand circularly polarized light. The light spot on the sample is rectangular of 2 × 3.8 mm with a power of about 150 µW at 950 nm (see figure one(a) in [26]). The photogalvanic current is measured in the unbiased structures at room temperature via a preamplifier and then is recorded by a lockin amplifier in phase with the PEM. Besides, in order to normalize the data thus enabling a better comparison between BIA and SIA, a common photocurrent j_{0} under direct current (dc) bias is also measured by a chopper and a lockin amplifier. Thus, we can use the common photocurrent j_{0} as the denominator for normalizing the CPGE current to eliminate the influences of the anisotropic carrier mobility and carrier density in different directions [26].
For QWs of zinc blende structures grown along the [001] direction, which belongs to C_{2v} point group symmetry, the Rashba term of the spinorbital Hamiltonian can be written as [2]
while the Dresselhaus term is
Here, σ is the Pauli spin matrix, k is the inplane wave vector, α (or β) is the Rashba (or Dresselhaus) spinorbital parameter, and the coordinate system is x∥ [100] and y∥ [010]. These two Hamiltonians will interfere with each other and result in anisotropic spin splitting in kspace. We can separate the spin splitting induced by Rashba and Dresselhaus terms according to the method suggested in [4,7], since the Rashba and Dresselhaus terms contribute differently for particular crystallographic directions. Thus, we can use the geometries shown in Figure 1, i.e., named as geometry CPGEI shown in Figure 1b and geometry CPGEII shown in Figure 1c,d, to separate the CPGE current induced by Rashba and Dresselhaus SOC, respectively. In the figures, denotes the direction of light propagation, and j_{R} and j_{D} indicate the CPGE current induced by Rashba and Dresselhaus spin splitting, respectively [4,7,26]. Thus, we can obtain j_{R} and j_{D} directly from geometry CPGEI and obtain the sum and difference of j_{R} and j_{D} from geometry CPGEII. Therefore, the j_{R} and j_{D} can be obtained separately by the geometry CPGEI and CPGEII, respectively, and then be compared to each other to see whether they are selfconsistent [26].
Figure 1. The schematic diagram of the experimental geometries and the spectra of the normalized CPGE current. The schematic diagram for geometries CPGEI (a) and CPGEII (b and c). The spectra of the normalized CPGE current obtained by geometry CPGEII at different angles of incidence (d). The thin lines indicate the sum of j_{R} and j_{D} by the geometry shown in (b), and the thick lines indicate the difference of j_{R} and j_{D} obtained by the geometry shown in (c). All of the spectra are shifted vertically for clarity.
In order to get the knowledge of the symmetry of the QW system, we perform reflectancedifference spectrum (RDS) measurement. RDS is an interfacesensitive and nondestructive technique [27,28], and it can precisely measure the inplane optical anisotropy (IPOA) between the [110] and directions. Both of bulklike and interfacelike symmetry reduction effects can introduce IPOA into the (001)grown zinc blende QWs. The former one can be induced by electric field [29,30], compositional variation across the QWs, uniaxial strain [31,32], and the atomic segregation effect [28], while the latter one can be introduced by anisotropic interface structures [31] and anisotropic interface chemical bonds [33]. Therefore, from the RDS measurement, one can obtain the symmetry properties of QWs. The setup of our RDS is the same as that used in [27], from which we can obtain the relative reflectance difference between [110] and [10] directions, i.e., . Besides, the reflectance spectrum ΔR/R can be obtained simultaneously during RDS measurements [27,32]. Here, R is the reflectivity of the sample, and ΔR/R is the reflectivity difference of the sample with and without QW layers. To estimate the value of internal field in the sample, we perform PR measurement. The setup of the PR system is the same as that used in [26].
Results and discussion
Figure 1d shows the normalized CPGE current obtained by geometry CPGEII at different angles of incidence. All of the spectra are shifted vertically for clarity. The thin lines indicate the sum of j_{R} and j_{D} obtained by the geometry shown in Figure 1b, and the thick lines are the difference of j_{R} and j_{D} obtained by the geometry shown in Figure 1c. It should be noted that the CPGE spectra are only normalized by the common current j_{0} at the peak located near 908 nm, which corresponds to the transition of excitonic state 1H1E as discussed below. Thus, we can eliminate the influences of the anisotropic carrier mobility and carrier density in different directions and do not incorporate the spectra dependence signal of j_{0} into the CPGE spectra. The power of the exciting light is kept constant during the spectra region between 800 and 950 nm, so it is not necessary to normalize the CPGE spectra by the power of the excitation light. Then, from Figure 1d, we can easily deduce the spectra of the SIA and BIAinduced CPGE current, which is shown in Figure 2 by thick solid lines. The dotted lines in Figure 2a is the SIAinduced CPGE current obtained by CPGEI shown in Figure 1a. Unfortunately, the BIAinduced CPGE current is too small to be detected by geometry CPGEI. From Figure 2a, we can see that the data obtained by the two geometries are consistent with each other. Figure 3 shows the intensity of the CPGE current induced by SIA (squares) and BIA (circles) as a function of angle of incidence corresponding to the transition of the excitonic state 1H1E (at about 908 nm). The solid lines are the fitting results according to the following equation:
Figure 2. The normalized SIA and BIAinduced CPGE current measured at different angles of incidence.(a) The normalized SIAinduced CPGE current obtained by geometry CPGEII (thick solid lines) and by geometry CPGEI (dotted lines). (b) The normalized BIAinduced CPGE current obtained by geometry CPGEII. All of the spectra are shifted vertically for clarity.
Figure 3. The magnitude of CPGE current as a function of angle of incidence. The squares and circles symbols indicate the CPGE current of the excitonic state 1H1E induced by SIA and BIA, respectively. The solid lines are the fitting results.
which describes the dependence of the CPGE current on the angle of incidence θ obtained theoretically [2,34]. Here, , E_{0} is the electric field amplitude of the incident light, κ is the absorption coefficient, γ = α or β, P_{circ} is the degree of circular polarization, i.e., , and n is the refractive index of the QWs material. It can be seen from Figure 3 that the experimental data agree well with the phenomenological theory of CPGE. In the fittings, n is adopted to be 3.55 according to [35], and the parameter A is fitted to be 1,232 ± 15 and 140 ± 10 for SIA and BIAinduced CPGE current, respectively. Thus, we can obtain α/β = 1,232 ± 15 / (140 ± 10) = 8.8 ± 0.1, much larger than the value obtained in symmetric InGaAs/AlGaAs QWs (4.95) investigated in our previous work [26]. This indicates that SIA is the dominant mechanism to induce spin splitting in the step InGaAs/GaAs/AlGaAs QWs. The normalized CPGE signal induced by BIA is estimated to be 0.26 ± 0.01 at an incident angle of 40 °, which is larger than that obtained in the symmetric InGaAs/AlGaAs QWs (0.22 ± 0.01) reported in our previous work [26]. This can be attributed to the size quantization effect of the electron wave vector k along the growth direction z, since the effective well width is reduced in the step QWs compared to the symmetric QWs, and the Dresselhaustype spin splitting increases with decreasing well width of QWs according to [9]. Although the Dresselhaus SOC is enhanced in step QWs, the Rashba SOC increases more rapidly, which results in larger RD ratio in the step QWs. In order to find out the reason for the strong Rashbatype spin splitting, we further perform PR and RDS measurements.
Using the method that has been used in [26], we can estimate the intensity of the internal field to be 12.3 ± 0.4 kV/cm, which is comparable to that in the symmetric QWs (12.6 kV/cm). The imaginary part of RD spectrum Δr/r is shown in Figure 4, which also shows the spectrum of the common photocurrent under dc bias (denoted as j_{0}), the reflectance spectrum ΔR/R, and the spectra of normalized CPGE current induced by SIA and BIA, respectively. By comparing them with each other and performing the theoretical calculation using sixband k·p theory, we can identify the energy position related to the transitions of the excitonic states 1H1E, 2H1E, and 1L1E, as indicated by the arrows in Figure 4. It can be seen that the peak located near 908 nm in the CPGE spectra is related to the transition of the excitonic state 1H1E in the QWs. From the photoconductivity signal j_{0}, the 2D density of the photoinduced carriers corresponding to the transition 1H1E is estimated to be about 5 ×10^{10}cm^{2}. It also shows that, for the excitonic state 1H1E, the CPGE current induced by SIA has the same sign with that induced by BIA, which is also observed in the symmetric InGaAs/AlGaAs QWs [26] and the GaAs/AlGaAs QWs [19]. This phenomenon is different from that predicted in [3], which shows that the BIAinduced CPGE current is close to zero for the transition of 1H1E. This discrepancy may be attributed to the following two reasons: (1) the prediction is based on the infinitely highbarrier approach, which may introduce some errors; (2) the prediction does not take into account the excitonic effect, which will dominate in the interband resonant transition of undoped QWs [19]. There are two ways for the generation of the spinpolarized carriers that form the CPGE current: (1) the direct formation of free electrons and holes, i.e., the direct excitation of electrons from the valence band to the conduction band and (2) the creation of free carriers through excitons [25,36]. Having a neutral charge, excitons themselves cannot contribute to the CPGE current, so they must dissociate in order to make a contribution to the spin photocurrent. There are three mechanisms for the dissociation of excitons to produce free carriers: interaction with (1) phonons, (2) impurity centers, and (3) excitons. The first and the second one are predominant at temperature above and below 70 K, respectively [25,36]. When the excitons make a dominant contribution to the spin photocurrent, the maxima of the photocurrent is always corresponding to the exciton absorption lines. However, for a CPGE current in which the excitons do not play a dominant role, the peak position does not necessarily locate at an energy position which is exactly corresponding to the transition of the excitons [3,5]. Besides, the excitonicrelated CPGE current is expected to be much larger than that of the common CPGE, due to its larger absorption coefficient. What is more, the excitonic spin photocurrent is anticipated to show strong temperature dependence effect. Since the excitonic effect is much stronger in low temperature, we expect stronger intensity of the excitonic spin photocurrent in low temperature. The CPGE signal related to the transitions of 2H1E and 1L1E have not been observed in the step QW system, and one of the possible reasons is the weak intensity of the excitation light. It is expected that the CPGE current corresponding to the transition of 1L1E should show the same sign and similar line shape as that of 1H1E, but with lower intensity due to its lower transition probability. The spectra dependence of the CPGE current for the transitions of 1H1E and 1L1E have been observed in the GaAs/AlGaAs QWs [19], and they show the same sign and similar line shape. The CPGE current of the transition of 2H1E is expected to be very weak and difficult to be observed, since it is a forbidden transition with a very low transition probability.
Figure 4. The comparison of different spectra in the In_{0.15}Ga_{0.85}As/GaAs/Al_{0.3}Ga_{0.7}As step QWs measured at room temperature. The spectrum of common photocurrent under dc bias (denoted as j_{0}), the imaginary part of RD spectrum Δr/r, reflectance spectrum ΔR/R, and the normalized CPGE current induced by SIA and BIA in the step QWs.
For interband excitation of undoped QWs investigated in our case, both electrons and holes may contribute to the CPGE current. Which one plays a dominant role is closely related to their spin relaxation time. The spin relaxation time of electrons in an undoped GaAs/AlGaAs QWs with a well width of 7.5 nm is measured to be 70 ps [37], while that of holes is reported to range from 4 ps [38] to as long as 1,000 ps [39] depending on the doping levels, temperature, and quantum well structures. A recent experiment investigation on ptype QWs concludes that the spin relaxation time of holes should be at least 100 ps and approaching the nanosecond (ns) range at a temperature of 4 K [40]. Besides, a more recent theoretical analysis found that the spin relaxation time can be of the same order of magnitude for electrons and holes for quantum dots with large lateral dimensions [41]. This qualitative conclusion should be of some relevance also for QWs [42]. Therefore, we suppose that the electrons and holes may contribute to the observed CPGE current at the same order.
From the RDS spectrum Δr/r and the reflectance spectrum ΔR/R, we can obtain the degree of polarization (DP) for the transitions 1H1E and 1L1E by [26,27]:
Here, DP is defined as , in which M_{[110]} is the transition probability when the light is polarized along the [110] direction. In the meantime, we can use k·p theory, as described in [26], to simulate the DP value theoretically. Specifically speaking, we treat the hole mixing induced by the shear strain ε_{xy}, the electric field, atomic segregation, and anisotropic interface structures as perturbation, and the perturbation Hamiltonian H^{′} can be written as [26,33,43,44]
and [43]
for the basis 3/2,3/2 >,3/2,1/2 >,3/2,1/2 >,3/2,3/2 >,1/2,1/2 >, and 1/2,1/2 >. Here b and D are the BirPikus deformation potentials, F is the electric field along the [001] direction, d_{14} is the piezoelectric constant, ε_{ij} denotes the symmetric strain tensor, z = z_{0} (z_{1} or z_{2}) is the location of the interfaces of QWs (see the inset in Figure 5), P_{1} (P_{2} or P_{3}) is the interface potential parameter describing the effect of C_{2v} interface symmetry at interface located at z_{0} (z_{1} or z_{2}) [27], x_{1} and x_{2} are the concentrations of In and Al, respectively, with the assumption that the value of the interface potential is proportional to the components of In or Al elements at interface [27], and l_{1} (l_{2} or l_{3}) is the segregation length of the indium atoms in interface located at z_{0} (z_{1} or z_{2}). The segregation model developed by Muraki [45] is adopted, which assumes that the segregation lengths of the indium atoms on the interfaces to be equal. The energies and wave functions of the holes and electrons are calculated by sixband and twoband k·p theory, respectively. Then, the anisotropic transition spectrum and the averaged transition spectrum M () are simulated using the following equation [26]:
Figure 5. The calculated anisotropic transition probabilityΔM and the average transition probabilityM. The vertical lines and arrows indicate the transition positions of 1H1E, 2H1E, and 1L1E. The inset shows the calculated energy band alignment of In_{0.15}Ga_{0.85}As/GaAs/Al_{0.3}Ga_{0.7}As step QWs with segregation length of indium atoms l = 2.8 nm and internal field F = 12.3 kV/cm. E_{c}, E_{lh}, E_{hh}, and E_{so} represent the energy band alignment of the electron band, lighthole band, heavyhole band, and the spinorbit splitoff band, respectively.
Here, Γ is the linewidth of the transition, and E_{nm}(P_{nm}) is the energy (probability) of the transition between nE (the nth conduction subband of electrons) and mLH (the mth valence subband of light holes) or between nE and mHH. Thus, by fitting the theoretical calculated DP with that obtained by experiments, we can determine the structure parameters of the QWs, such as the interface potential parameters P_{i} (i = 1, 2, 3), segregation length of atoms l_{i} (i = 1, 2, 3), and anisotropy strain ε_{xy}.
Using Equation 4, we can estimate the DP values of the transition for the excitonic states 1H1E and 1L1E to be 0.5 % ± 0.5% and 6.3 % ± 0.5%, respectively. In order to calculate the theoretical DP value of the transitions of the QWs, we should first estimate the interface potential P_{0} for an ideal InAsAl_{0.3}Ga_{0.7}As, GaAsInAs, and AlAsGaAs interfaces, respectively. Using the perturbed interface potential, the averaged hybrid energy difference of interface, and the lattice mismatch models, and then adding them up, we can obtain the value of P_{0} for an ideal InAsAl_{0.3}Ga_{0.7}As interface to be 639 meV Å [46]. The P_{0} at GaAsInAs and AlAsGaAs interfaces are reported to be 595 and 400 meV Å [27,47], respectively. Since the InAsonAl_{0.3}Ga_{0.7}As interface tends to be an ideal and abrupt interface, we adopt P_{1} = P_{0}. Due to the segregation effect of indium atoms at the GaAsonInAs interface, P_{2} may not be equal to P_{0}. Therefore, we treat P_{2} as a fitting parameter. According to [27], the interface potential P_{3} for AlAsonGaAs interface is fitted to be 440 meV Å, due to the anisotropic interface structures. Thus, adopting P_{1} = 639 meV Å, P_{3} = 440 meV Å, and internal electric field F = 12.3 kV/cm (obtained by PR measurements) and treating the interface potential P_{2} and the segregation length l_{1} = l_{2} = l_{3} = l as fitting parameters, we fit the theoretical calculated DP value to that of experiments. When we adopt P_{2} = 650 meV Å, l = 2.8 nm, the DP values of the transition 1H1E and 1L1E can be well fitted, and the main features of the RD spectrum are all well simulated (see Figure 5, ΔM∝Δr/r). The large segregation effect of indium atoms and the strong internal field reduce the step well into an irregular well, as shown in the inset of Figure 5. This will result in large Rashba spin splitting according to [8,26]. However, we find that the intensity of the internal field and the segregation length of the indium atoms for the step QWs are comparable to those in symmetric QWs, which indicate that the Rashba SOC induced by these two factors are at the same scale and they are not the main reasons for the larger Rashba spin splitting in the step QWs. On the other hand, the interface in QWs will also introduce Rashbatype spin splitting, which is related to some band discontinuities in valence bands at heterointerfaces [22,48]. Since the step QW structures will introduce one additional interface compared to symmetric QWs and this additional interface will introduce additional Rashba spin splitting, the larger Rashba spin splitting in the step QWs may be mainly induced by this interface Rashba effect. It is worth mentioning that the interface or the segregation effect alone will not necessarily lead to larger Rashba spin splitting, and only when they are combined with large electric field or the presence of a Hartree potential gradient in the asymmetric system will finally result in a significant spin splitting [48].
Conclusions
In conclusion, we have experimentally investigated the spin photocurrent spectra induced by Rashba and Dresselhaustype CPGE at interband excitation in InGaAs/GaAs/AlGaAs step QWs at room temperature. It is found that the line shape of CPGE spectrum induced by Rashba SOC is quite similar to that induced by Dresselhaus SOC during the spectral region corresponding to the transition of the excitonic state 1H1E. The ratio of Rashba and Dresselhausinduced CPGE current for the transition of the excitonic state 1H1E is estimated to be 8.8 ± 0.1, much larger than that reported in the symmetric QWs in our previous work (i.e., 4.95 in [26]). We also find that, compared to symmetric QWs, the reduced well width in the step QWs enhances the Dresselhaustype spin splitting, while the Rashbatype spin splitting increases more rapidly. Since the intensity of the buildin field and the degree of the segregation effect in the step QWs are comparable to those in symmetric QWs, which are evident from RDS and PR measurements, the larger Rashba spin splitting in the step QWs are mainly induced by the additional interface introduced by step structures.
Abbreviations
BIA: bulk inversion asymmetry; CPGE: circular photogalvanic effect; DP: degree of polarization; IPOA: inplane optical anisotropy; PEM: photoelastic modulator; PR: photoreflectance; QWs: quantum wells; RDS: reflectancedifference spectrum; SIA: structure inversion asymmetry; SOC: spinorbit coupling; 1H1E: the first valence subband of heavy hole to the first conduction subband of electrons.
Competing interests
The authors declare that they have no competing interests.
Authors’ contributions
JY conducted the experiments and wrote the paper. YC designed the experiments and performed the sample fabrications. SC, YL, and QZ assisted with the measurements and analysis. All authors contributed through scientific discussions and read and approved the final manuscript.
Acknowledgements
The work was supported by the National Natural Science Foundation of China (No. 60990313, No. 61006003, No. 61306120), the 973 program (2012CB921304, 2013CB632805), the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry (Grant No. LXKQ201104), the fund of Key Laboratory of Optoelectronic Materials Chemistry and Physics, Chinese Academy of Sciences (2008DP173016), and the Foundation of Fuzhou University of China (Grant No. 022498).
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