⇦Chinese Physics Letters, 2017, Vol. 34, No. 11, Article code 117203 Circular Photogalvanic Effect in the Weyl Semimetal TaAs * Kai Sun(孙开)1,3†, Shuai-Shuai Sun(孙帅帅)1†, Lin-Lin Wei(尉琳琳)1,3, Cong Guo(过聪)1, Huan-Fang Tian(田焕芳)1, Gen-Fu Chen(陈根富)1,2, Huai-Xin Yang(杨槐馨)1,3**, Jian-Qi Li(李建奇)1,2,3** Affiliations 1Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 2Collaborative Innovation Center of Quantum Matter, Beijing 100084 3School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049 Received 11 September 2017 *Supported by the National Basic Research Program of China under Grant Nos 2015CB921300, the National Key Research and Development Program of China under Grant Nos 2016YFA0300300, 2017YFA0504703 and 2017YFA0302900, the National Natural Science Foundation of China under Grant Nos 11604372, 11474323 and 11774391, the Strategic Priority Research Program (B) of the Chinese Academy of Sciences under Grant No XDB07020000, and the Scientific Instrument Developing Project of the Chinese Academy of Sciences under Grant No ZDKYYQ20170002.
†Kai Sun and Shuai-Shuai Sun contributed equally to this work.
**Corresponding author. Email: hxyang@iphy.ac.cn; ljq@aphy.iphy.ac.cn Citation Text: Sun K, Sun S S, Wei L L, Guo C and Tian H F et al 2017 Chin. Phys. Lett. 34 117203 Abstract Weyl semimetal (WSM) is expected to be an ideal spintronic material owing to its spin currents carried by the bulk and surface states with spin-momentum locking. The generation of a sizable photocurrent is predicted in non-centrosymmetric WSM arising from the broken inversion symmetry and the linear energy dispersion that is unique to Weyl systems. In our recent measurements, the circular photogalvanic effect (CPGE) is discovered in the TaAs WSM. The CPGE voltage is proportional to the helicity of the incident light, reversing direction if the radiation helicity changes handedness, a periodical oscillation therefore appears following the alteration of light polarization. We herein attribute the CPGE to the asymmetric optical excitation of the Weyl cone, which could result in an asymmetric distribution of photoexcited carriers in momentum space according to an optical spin-related selection rule. DOI:10.1088/0256-307X/34/11/117203 PACS:72.40.+w, 71.20.-b, 72.25.Fe © 2017 Chinese Physics Society Article Text Weyl semimetals (WSMs) have attracted broad interest in both theoretical and experimental fields because of their remarkable transport phenomena, potential applications, and emergent condensed matter realizations of the Weyl fermion. WSMs feature an electron band structure with two-fold degenerate bulk band crossing points (Weyl nodes) in three-dimensional (3D) momentum space, and a linear dispersion relation applies in all three momentum space directions as the momentum moves away from the Weyl nodes.[1-4] WSM has been regarded as an excellent material for studying spin currents. It was recently suggested that a large intrinsic spin Hall conductivity in TaAs WSM can be used to generate and detect spin currents that mediate intrinsically via the bulk and surface states with spin-momentum locking, which exhibit a large Berry curvature and strong spin-orbit coupling.[5,6] From the broken inversion symmetry and linear energy dispersion, a significant photocurrent generated by circularly polarized (CP) photons in the WSM was also predicted theoretically.[7] Absorption of the CP photons can generate a spin-polarized charge current, or spin current, through the asymmetric distribution of carriers in the momentum space imposed by an optical spin-related selection rule. This photoinduced phenomenon referred to as the circular photogalvanic effect (CPGE), potentially reveals the nature of charge-spin interchange mechanism and the energy band in terms of its observable helicity-dependent photoresponse,[8] which has been systematically investigated in some novel systems, such as the Dirac topological insulator of (Bi$_{1-x}$Sb$_{x}$)$_{2}$Te$_{3}$ thin films,[9,10] the electric-double-layer transistors WSe$_{2}$,[11] and the (In)GaAs/AlGaAs quantum wells.[12-14] In this study, we report the experimental observation of a CPGE in TaAs, which can be considered as a direct reflection of the topological characteristics of the WSM. A photoinduced spin-polarized electric current generated by CP light is found to produce an observable CPGE voltage in TaAs, which essentially derives from an asymmetric optical excitation of the Weyl cone with linear dispersion associated with spin following an optical spin-related selection rule. This CPGE voltage is modulated by the helicity of the incident light and hence oscillates periodically with changing polarization with period $\pi$. A high-quality TaAs single-crystalline sample was synthesized using the chemical vapor transport method.[15] TaAs crystallizes in a body-centered-tetragonal NbAs-type structure displaying non-centrosymmetry with space group $I4_{1}md$, in which the $c$ axis is perpendicular to the $a$–$b$ plane (Fig. 1(a)). The lattice parameters are $a=b=3.4348$ Å and $c=11.641$ Å. Single-crystal x-ray diffractometry confirms that the TaAs single crystals grow along the [001] zone axis direction, and the average stoichiometry was determined from energy-dispersive x-ray spectroscopy. Figure 1(b) shows an experimental schematic diagram of the TaAs sample under laser irradiation, and the measurements were performed at room temperature. The crystal was polished into a rectangular sample (1.2 mm $\times$ 0.3 mm $\times$ 0.08 mm) and electrodes were located along the $y$ direction on the opposing side faces of the cuboid sample (Fig. 1(b)); the $x$ and $y$ directions are parallel to the $a$ and $b$ crystal orientations of TaAs, respectively. The CPGE voltage was measured using a high-stability voltmeter. A linearly polarized 300-fs (pulse length) laser beam was generated from a 100-kHz (repetition rate) source at a wavelength of 520 nm. The laser beam passed through a polarizing beam splitter cube attached to a beam quality detector that was used to accurately monitor the position of the central beam. The beam then irradiated the (001) surface of the sample at an out-of-plane incident angle of $\theta$ (the angle between the wave vector of light and the $x$–$y$ plane) and an in-plane angle of $\alpha$ (the angle between the in-plane component of the wave vector and the $y$ axis) as illustrated in Fig. 1(b). The rotatable half and quarter wave plates were used to modulate the polarization of the incident laser.
cpl-34-11-117203-fig1.png
Fig. 1. (Color online) (a) Crystal structure of TaAs featuring non-centrosymmetric space group $I4_{1}md$. (b) Schematic view of the experimental configuration and the CPGE under the incident $\sigma^{+}$ CP light. The electrodes are located along the $y$ direction. The photovoltage $V_{y}$ was measured with an out-of-plane light incident angle $\theta$ to the $x$–$y$ plane ((001) surface) and an in-plane angle of $\alpha$. The helicity of the laser light was modulated by a rotatable quarter-wave plate with a rotation angle of $\phi$. The short black arrows indicate spin orientations, and green arrows indicate spin-polarized electric currents satisfying the optical spin-related selection rule.
With the wave plate rotating the polarization of the laser beam irradiating the TaAs crystal from 0$^{\circ}$ to 180$^{\circ}$, the photovoltage follows the periodic change in polarization of the incident light. Figure 2(a) shows the photovoltage as a function of the rotation angle $\phi$ of the optical axis for a half-wave plate. At 45$^{\circ}$ and 135$^{\circ}$, the photovoltage reaches two maxima with the same amplitudes. The photovoltage is well fitted by a sine function with period $\pi/2$ and well explained as a linear photogalvanic effect (LPGE) that is independent of spin orientation. The occurrence of an LPGE without a CPGE has been confirmed with measurements of the linear polarization in which the CPGE is forbidden.[8] Excitations with linearly polarized light generate spin-unpolarized charge currents that are associated with the anisotropy of processes such as photoexcitation, scattering, and recombination of the carriers. The LPGE is potentially associated with an anisotropic distribution of the current derived from an asymmetry in the scattering of free carriers from phonons, static defects or other carriers in homogeneous non-centrosymmetric samples.[16] For a centrosymmetric system, the microscopic principle of detailed balancing for photoexcited carriers suggests that the probability (denoted $P_{kk'}$) of an electron transition from the state with momentum $k'$ to a state with momentum $k$ is equal to the probability of the reverse transition, $P_{kk'}=P_{k'k}$, and therefore produces a symmetric momentum distribution for electrons. In a non-centrosymmetric system such as TaAs, $P_{kk'}\ne P_{k'k}$, it can be caused by inelastic scattering of carriers from asymmetric centers, excitation of impurity centers with an asymmetric potential, and the hopping mechanism acting between the asymmetrically distributed centers.[17] This violation of the principle of the detailed balancing generates an asymmetric momentum distribution for the electrons in nonequilibrium, which results in the appearance of the photovoltaic effect with uniform illumination.[18] An asymmetry in the excitations in momentum space establishes a preferred momentum direction for the excited carriers that is essential for the existence of the LPGE.[19,20] As the momentum relaxes, the photoexcited carriers move along their own momentum directions that depend on the polarization direction. Thus a small spatial displacement of the carriers is generated, producing a photovoltage proportional to the intensity of light and its polarization angle. The dependence of the photovoltage on rotation angle $\phi$ of the optical axis for a quarter wave plate (Fig. 2(b)) shows two maxima with notably different amplitudes at 45$^{\circ}$ (higher peak) and 135$^{\circ}$ (lower peak), respectively. For light helicity between the right-hand and left-hand, as in the measurements of the helicity dependence of the photovoltage, both CPGE and LPGE can simultaneously appear in systems without a center of inversion.[8] Based on the relative phase information extracted from the original data, the obtained photovoltage (measured by electrodes along the $y$ direction) fits the formula: $V_{y}=C\sin (2\phi)+L\sin (4\phi)+V_{\rm o}$, where $\phi $ is the rotation angle of the optical axis of the quarter wave plate with respect to the polarized plane of the laser beam, $\sin (2\phi)$ is the coefficient of helicity of the incident light, $C$ is the amplitude of the CPGE voltage and is sensitive to CP light, $L$ is the amplitude of the LPGE voltage, and $V_{\rm o}$ is a constant photoinduced bias voltage (background voltage), which is potentially derived from asymmetric electrodes and the inhomogeneous distribution of photoexcited carriers.[21,22] The photovoltage $V_{y}$, mainly includes two components: an oscillation term with period $\pi$, $V_{\rm CPGE}=C\sin (2\phi)$ (blue curve), corresponding to the spin-mediated CPGE voltage, and an oscillation term with period $\pi/2$, $V_{\rm LPGE}=L\sin (4\phi)$, corresponding to the LPGE as discussed above.[11,23] The $V_{\rm CPGE}$ component satisfies the CPGE amplitude expression $j_{\rm CPGE}=\gamma\eta I\cos\theta\sin (2\phi)$, which directly indicates the helicity of the generated $V_{\rm CPGE}$,[8,11] where $\eta $ is the absorbance, $\gamma $ is a matrix element related to spin, orbital and symmetry, $I$ is the incident light intensity, and $\theta $ is the incident angle. Note that the direction and magnitude of $V_{\rm CPGE}$ strongly depend on the circular polarization of the incident light. Here $V_{\rm CPGE}$ reverses its direction, when the radiation helicity changes handedness from left-hand to right-hand, and forms a perfect sine curve with period $\pi$ that precisely corresponds to the period of the incident CP light (Fig. 2(b)). As expected, the peak and trough of the $V_{\rm CPGE}$ curve appear at 45$^{\circ}$ for $\sigma^{+}$ CP light and at 135$^{\circ}$ for $\sigma^{-}$ CP light. The other values, as observed in the ranges of 0$^{\circ}$ to 45$^{\circ}$, 45$^{\circ}$ to 90$^{\circ}$, 90$^{\circ}$ to 135$^{\circ}$, and 135$^{\circ}$ to 180$^{\circ}$, correspond to photoexcitations of right- or left-handed elliptic polarizations, the helicity-dependent features of which can also be recognized.
cpl-34-11-117203-fig2.png
Fig. 2. (Color online) Photovoltage in TaAs as a function of rotation angle $\phi$ of (a) the half wave plate and (b) the quarter wave plate. Here $\sigma^{+}$ and $\sigma^{-}$ represent the CP light in opposite chiralities.
In general, photoinduced heat gradients in the sample are expected to produce a bulk thermoelectric current background in addition to any photoexcitation. To isolate the photoresponse, we varied the heat gradient between the electrodes by sweeping the laser spot across the sample along the $y$ direction at a fixed circular polarization of $\sigma^{+}$ ($\phi =45^{\circ}$) as illustrated in Fig. 3(a). Undoubtedly, the temperature of the sample surface would increase under persistent illumination, and it inevitably results in a heat gradient that generates a background thermoelectric current, which contributes to the measured photovoltage.[24,25] The photovoltage switches its polarity as the laser spot is swept across the sample and performs a symmetric profile with a nonzero finite value at the center of the sample at which the thermoelectric current is minimum owing to the symmetric heating gradient. Hence, all experimental data in this study are obtained at the center of the sample where the sample is evenly heated. We compare the magnitudes of photovoltage at different incident angles as shown in Fig. 3(b), further inferring the electronic state spin distribution. This is carried out to verify whether the spin-mediated photovoltage is produced by the electron states in the Weyl cone with linear dispersion associated with spin.[24] As in a spin-orbit coupling system, the electrons with spin polarizations aligned or anti-aligned to the wave vector would be preferentially excited by left- or right-circularly polarized light, respectively. Under oblique incident light in the $x$–$z$ plane ($\theta=60^{\circ}$, $\alpha=90^{\circ}$), the photovoltage is clearly helicity-dependent and is generated transverse to the light scattering plane (the $x$–$z$ plane) as illustrated in Fig. 1(b).[24,26] The opposite spin polarizations that are driven by different helicities must be asymmetrically distributed along the $y$ direction in momentum space and have a spin component in the $x$–$z$ plane (incident plane). When the light is obliquely incident in the $y$–$z$ plane ($\theta=60^{\circ}$, $\alpha=180^{\circ}$), the electrodes still lie in the light scattering plane ($y$–$z$ plane) and just barely measure the transverse photovoltage (along the $x$ direction). Therefore, the measured intensity of the photovoltage decreases considerably, indicating that the electrons involved in producing CPGE have spins that are locked perpendicular to their linear momentum, which is considered as a characteristic feature of a chiral spin structure in the helical cone.[26] Under normally incident irradiation ($\theta=90^{\circ}$, $\alpha=90^{\circ}$), the intensity of the photovoltage from the sample is evidently much smaller than that of oblique incidence in the $x$–$z$ plane ($\theta=60^{\circ}$, $\alpha=90^{\circ}$) as shown in Fig. 3(b). Essentially, it indicates a difficulty for in-plane spin polarizations that are perpendicular to the direction of light propagation ($z$ direction) to interact with normally incident CP photons. These incident angle-dependent results indicate that the helicity-dependent CPGE voltage stems from an asymmetric optical excitation of the Weyl cone with a counter-propagating distribution of opposite spins. Analogous with the behavior of opposite electric charges when driven by a constant electric field, electrons with different spin orientations are driven differently by CP light. The direction of the spin-polarized current is determined by the helicity of the light and can be reversed by switching the helicity from right-handed to left-handed. The microscopic working mechanism of the CPGE can be generalized as a selective photoexcitation of the spin-polarized electrons with CP light in accordance with the optical selection rule. A specific CP light ($\sigma^{+}$) with specific incident direction (incident angle) excites the Weyl cone that provides the required asymmetric spin distribution in momentum space, yielding an interaction between the momentum- and spin-selective electron states in the Weyl cone and incident CP photons. This selective photoexcitation induces interband transitions with a probability that is both momentum- and spin-dependent, and the optical transition is allowed for the selective orientation but forbidden for the opposite. The absorption of CP photons brings about asymmetric excitations along the drive direction as illustrated in Fig. 4(a). An optical excitation with a specific CP light ($\sigma^{+}$) drives only one side of a single Weyl node. In the case of a pair of Weyl nodes, CP light drives opposite sides of the opposite-chirality Weyl nodes, inducing a nonzero total photocurrent contributed from different Weyl nodes in terms of the finite tilted Weyl cone in TaAs.[7] The electron states can be asymmetrically depopulated in the momentum space, which converts the spin currents associated with the Weyl cone into a net spin-polarized electrical current, and results in the observed CPGE.
cpl-34-11-117203-fig3.png
Fig. 3. (Color online) (a) Photovoltage as a function of laser-spot position. The data are obtained by moving the laser spot along the $y$ direction of the sample at a fixed circular polarization of $\sigma^{+}$ ($\phi=45^{\circ}$), as shown in the inset. (b) Photovoltage as a function of rotation angle $\phi$ of the quarter wave plate at different incident angles $\theta$ and $\alpha$: $\theta=60^{\circ}$, $\alpha= 90^{\circ}$ ($x$–$z$ plane); $\theta=60^{\circ}$, $\alpha=180^{\circ}$ ($y$–$z$ plane); $\theta=90^{\circ}$, $\alpha=90^{\circ}$ (normal incidence).
Note that $V_{\rm CPGE}$ is strongly correlated with the laser spot intensity. From the helicity dependence of the photovoltage under different laser intensities as shown in Fig. 4(b), the amplitude of $V_{\rm CPGE}$ ($C$) scales linearly with laser fluence (see inset of Fig. 4(b)), as mentioned above, $j_{\rm CPGE}=\gamma \eta I\cos\theta \sin (2\phi)$. It demonstrates that the amplitude of $V_{\rm CPGE}$ is directly proportional to the radiation intensity.[8,11] This feature essentially is consistent with the excitation mechanism involved with the interaction between electrons and injected photons, and indicates a transfer of linear momentum from the incident photons to the excited electrons.
cpl-34-11-117203-fig4.png
Fig. 4. (Color online) (a) Schematic diagram of spin-polarized electrical current induced by optically driving the Weyl cone with $\sigma^{+}$ CP light. (b) Photovoltage as a function of rotation angle $\phi$ for laser intensities ranging from 5 mW to 40 mW. Inset: linearity in the amplitude of the CPGE voltage ($C$) with incident laser intensity.
In conclusion, a CPGE induced by CP photons is found in the TaAs WSM. The CPGE voltage varies sinusoidally with period $\pi$ associated with the polarization of the incident light. It is exactly proportional to the optical helicity and reverses direction on changing the radiation helicity. Moreover, the photovoltage follows the changes of incident angles, revealing that the helicity-dependent CPGE voltage potentially arises from the asymmetric optical excitation of the Weyl cone with a counter-propagating distribution of opposite spins. These behaviors are well interpreted as photoinduced transitions with both momentum- and spin-dependent probability. It leads to an asymmetric distribution of the photoexcited carriers in the momentum space that obeys an optical spin-related selection rule. Furthermore, the CPGE voltage amplitude ($C$) increases monotonically with increasing the intensity of the incident CP light. Underlying this behavior is an excitation related to the interaction between electrons and injected photons. It can be expected that the CPGE in the Weyl material may provide a new approach for developing high-speed photoelectric devices with low-energy consumption. References Weyl Semimetal Phase in Noncentrosymmetric Transition-Metal MonophosphidesA Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs classObservation of Weyl nodes in TaAsExperimental Discovery of Weyl Semimetal TaAsStrong Intrinsic Spin Hall Effect in the TaAs Family of Weyl SemimetalsTopological surface states and Fermi arcs of the noncentrosymmetric Weyl semimetals TaAs, TaP, NbAs, and NbPPhotocurrents in Weyl semimetalsSpin photocurrents in quantum wellsEnhanced photogalvanic current in topological insulators via Fermi energy tuningCircular photogalvanic effect on topological insulator surfaces: Berry-curvature-dependent responseGeneration and electric control of spin–valley-coupled circular photogalvanic current in WSe2Excitation wavelength dependence of the anomalous circular photogalvanic effect in undoped InGaAs/AlGaAs quantum wellsSpectra of Rashba- and Dresselhaus-type circular photogalvanic effect at inter-band excitation in GaAs/AlGaAs quantum wells and their behaviors under external strainCircular photogalvanic effect induced by monopolar spin orientation in p -GaAs/AlGaAs multiple-quantum wellsObservation of the Chiral-Anomaly-Induced Negative Magnetoresistance in 3D Weyl Semimetal TaAsBulk photovoltaic effect in noncentrosymmetric crystalsSpectra of circular and linear photogalvanic effect at inter-band excitation in In0.15Ga0.85As/Al0.3Ga0.7As multiple quantum wellsLinear photogalvanic current excited in sillenite crystals by femtosecond laser pulsesObservation of the photoinduced anomalous Hall effect in GaN-based heterostructuresSpin photocurrents in (110)-grown quantum well structuresControl over topological insulator photocurrents with light polarizationIdentification of Helicity-Dependent Photocurrents from Topological Surface States in Bi2Se3 Gated by Ionic Liquid
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