Gate voltage control of helicity-dependent photocurrent and polarization detection in (Bi1&#x2212;xSbx)2Te3 topological insulator thin films

Shenzhong Chen; Jinling Yu; Jinling Yu; Xiyu Hong; Kejing Zhu; Yonghai Chen; Yonghai Chen; Shuying Cheng; Yunfeng Lai; Ke He; Ke He; Qikun Xue

doi:10.1364/PRJ.494932

1. INTRODUCTION

Polarization is more than a physical property of light, which can carry and distinguish information. The state of polarization characterizing electric field oscillation is important in imaging, display, and information storage [1–4]. For example, when light interacts with materials such as organic molecules with chiral structures the change of the polarization state can reflect their chemical and physical information like the structure symmetry, chemical composition, and other properties [1]. Thus, optical chirality detection is essential for modern optoelectronic applications, such as biomedical sensing, quantum communications and computing, liquid crystal displays, astronomy, and telecommunications [2,3,5,6]. The conventional polarization detection solutions normally require a combination of phase retarders, polarizers, quarter-wave plates, and rotating optomechanical components [4,7,8]. This is because the common semiconductors used to make photodetectors lack an intrinsic chiral response, which increases the difficulties and cost in the miniaturization and integration of devices. Using intrinsically chiral materials as a substitute can be one direction to avoid the installation of bulky and rigid optical elements. Halide perovskites have been found to be one of the promising polarization materials that meet the need for low cost, flexibility, tunable polarization sensitivity, and superior optoelectronic properties [9–15]. More recently, metamaterials demonstrate the capability to manipulate polarization states as well, which has been applied to fabricate ultracompact optical elements for direct chirality detection [16–20]. Nevertheless, a photodetector made by intrinsically chiral materials or metamaterials requires too much of a fabrication effort.

Topological insulators (TIs) may be one of the favorable materials for intrinsic solid-state polarization detection devices with easier integration. Much attention in condensed-matter physics has been recently directed toward understanding the electronic properties of spin-polarized carriers in 3D topological insulators. The 3D TIs have metallic surface states showing linear dispersion over the insulating bulk states. In these systems, the resulting spin-polarized carriers have spins locked perpendicular to their linear momentum due to the time-reversal invariant protecting them from backscattering of any nonmagnetic impurity [21–31]. Hence, the carriers in the surface states with one spin orientation flow in a particular direction. The spin-momentum locking in the topological surface states offers a unique opportunity for spintronic, optic, and optoelectronic applications [32–36]. Until now, optical methods have been adopted as one of the main approaches to control the spin-polarized currents in 3D TIs [37–41]. In particular, circularly polarized light can induce a directional helicity-dependent photocurrent in 3D TIs, which is one of the most notable manifestations of the electronic chirality of surface states [42,43]. However, these polarization-dependent photocurrents can be generated by the circular photogalvanic effect (CPGE), the linear photogalvanic effect (LPGE), and the photon drag effect [36,42,44–48], which prevent it from direct chirality detection of the elliptical polarized light. If one can differentiate these photocurrents to obtain the CPGE and LPGE currents separately under the polarization detection, it will make the 3D TIs promising in chirality detection or Stokes parameter analysis [49].

In this paper, we report a strategy for linear and circular polarization detection using a topological insulator ${({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3}$ thin film, which does not require complex microfabrication and additional optical elements. We first performed a comprehensive experimental study of the photocurrent response for polarized light incident on the 3D TI ${({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3}$ thin films and found that the photoresponses of the circularly and linearly polarized light are both dependent on the incident angle of the light. Further studies of the incident angle dependence of the photocurrents allowed us to extract the different components of the polarization-dependent photocurrents, including the CPGE, LPGE, circular photon drag effect (CPDE), and linear photon drag effect (LPDE). On this basis, we realized the circular polarization detection by comparing the measured photocurrents to the calibrated results under two measurements at opposite incident angles. In addition, the accuracy of circular polarization detection can be enhanced by back gating. What is more, the linear polarization of the light can also be detected when applying proper back gating; hence, the Stokes parameters can be obtained by measuring the photocurrent on different detection modes. To the best of our knowledge, the method we have proposed to realize intrinsic optical chirality detection by a single device is new, and offers a promising platform based on topological insulators for optoelectronic applications and photodetection technologies.

2. EXPERIMENTAL DETAILS

The samples used in the experiment to investigate the helicity-dependent photocurrents and the polarization detection are ternary topological insulator ${({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3}$ thin films named BST. The ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ thin films with thicknesses of 10- and 20-quintuple layers (QL) and the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3}$ thin films are grown on insulating ${SrTiO}_{3}$ (STO) substrates with molecular beam epitaxy. The BST films are manually cut into Hall-bar shapes with indium contacts deposited on the surface of the BST films. The 2D electron densities determined by Hall measurements are $n = 0.56 \times 10^{13} {cm}^{- 2}$ , $3.17 \times 10^{13} {cm}^{- 2}$ , and $3.94 \times 10^{13} {cm}^{- 2}$ for the 7-, 10-, and 20-QL samples at 77 K, respectively. The samples are mounted on an optical cryostat with a 1 Pa low-pressure chamber after bonding in the air. This cryostat also allows for the variation of the temperature in the range of 77–300 K.

A diode-pumped solid-state continuous wave laser with a wavelength of 1064 nm was adopted as the radiation source. The laser passed through a chopper (229 Hz), a polarizer, and a quarter-wave plate, and then illuminated the center of the sample, as shown in Fig. 1(a). The photocurrent was first amplified/filtered by a current preamplifier and then measured by a lock-in amplifier at the chopping frequency. After passing a lens with a focus of 20 cm, the light spot with a diameter of about 0.8 mm was focused on the sample. An optical attenuator was adopted to change the light power illuminated on the sample.

Fig. 1. (a) Schematic diagram of the device structure and measurement geometry. (b) Photocurrent as a function of the phase angle $φ$ of the 10-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ sample when the light spot is illuminated at oblique incidence of $θ = 30 °$ . The solid line (black) is the fitting curve using Eq. (1). The dotted lines (purple and blue) and the dashed line (red) are the photocurrent induced by linearly and circularly polarized light, respectively. The dash-dotted line (green) indicates the polarization-independent current $D$ .

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To investigate the dependence of the photocurrent in BST on incident angles, we changed the incident angle $θ$ from $- 40 °$ to $+ 40 °$ with the laser beam incident in the $x − z$ plane and the photocurrent measured along the $y$ direction, as shown in Fig. 1(a). To extract the polarization-dependent photocurrent from the total photocurrent, we fit the polarization state dependent photocurrent to [26,41,47]

J_{total} = C \sin 2 φ + L_{1} \sin 4 φ + L_{2} \cos 4 φ + D,

where

φ

is the angle between the initial plane of polarization and the optical axis of the quarter-wave plate. The coefficient

C

of

\sin 2 φ

represents the helicity-dependent photocurrent induced by CPGE or CPDE. The

L_{1}

and

L_{2}

terms indicate the photoresponses due to linearly polarized light, which may originate from the LPGE or LPDE. The

D

term is the polarization-independent current, which arises from the photovoltaic effect or the Dember effect [42,50,51].

Besides, the measurements of the back gate tuning of the polarization-dependent photocurrent in 3D TIs are performed by applying a direct current gate voltage to the drain contact and the back gate of the insulating ${SrTiO}_{3}$ substrate. All measurements under back gating are carried out at a temperature of 77 K. For the ionic liquid gating modulated CPGE measurement, the ionic liquid (DEME-TFSI) is dropped on the surface of the sample and then covered by a quartz coverslip.

3. RESULTS AND DISCUSSION

A. Polarization-Dependent Photocurrents Analysis

To use the electronic chirality of the topological surface states for polarization detection, let us first investigate the light incident angle dependence of the photocurrent in 3D TI BST thin films. This is because the dependence of the photocurrent on the incident angle may provide an important parameter that can be adopted to detect the polarization state of light.

At a certain incident angle, the measured photocurrent can be well fitted by Eq. (1) to extract each term of the polarization-dependent photocurrents, and the typical fitting result is shown in Fig. 1(b). By fitting, we can determine the helicity-dependent photocurrent $C$ , and the photocurrent induced by linearly polarized light, i.e., $L_{1}$ and $L_{2}$ , of the 7-, 10-, and 20-QL BST samples at different incident angles, as shown in Fig. 2.

Fig. 2. Dependence of the coefficients (a) $C$ , (b) $L_{1}$ , and (c) $L_{2}$ on the light incident angle ( $θ$ ), which are extracted by fitting Eq. (1) to the polarization-dependent photocurrent of the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3}$ , 10-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ , and 20-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ samples. The solid curve in (a) is the fitting curve by using $J_{y}^{CPGE} + J_{y}^{CPDE}$ expressed by Eq. (2). The solid curves in (b) and (c) represent the fitting curve by using Eq. (7) and Eq. (8), respectively.

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Figure 2(a) shows the helicity-dependent photocurrent (HDPC), which includes CPGE and CPDE, as a function of incident angle $θ$ in the 7-, 10- and 20-QL BST samples under an ungated condition. The results are obtained by fitting Eq. (1) to polarization-dependent photocurrents measured at different light incident angles. Note that the HDPC in BST varies as an odd function of $θ$ . This should be attributed to the generation mechanism of the CPGE and CPDE with the inversion asymmetry of the topological surface states. The CPGE current arises from the asymmetric excitation of states in $k$ space due to the transfer of the angular momentum from photons to free carriers, ignoring the linear momentum transfer of photons [26,41,42,50]. However, the CPDE current is due to the transfer of both linear and angular momenta from the photons to the free carriers [44,52]. Besides, the CPGE and CPDE are both restricted by crystal symmetry [41,42,44,52]. The bulk states of 3D TIs belong to $D_{3 d}$ symmetry, and they will not generate CPGE and CPDE due to inversion symmetry [41]. For the surface states with a reduced symmetry of $C_{3 v}$ , the CPGE current that flows perpendicular to the incident plane is proportional to $\sin θ$ , while that from CPDE is proportional to $\sin 2 θ$ [41], which can be expressed by [41,50,53]

J_{y}^{CPGE} = \frac{A_{CPGE} \sin θ \cos^{2} θ}{n_{ω} (\cos θ + \sqrt{n_{ω}^{2} - \sin^{2} θ}) (n_{ω}^{2} \cos^{2} θ + \sqrt{n_{ω}^{2} - \sin^{2} θ})},

J_{y}^{CPDE} = \frac{A_{CPDE} \sin 2 θ \cos^{2} θ}{n_{ω} (\cos θ + \sqrt{n_{ω}^{2} - \sin^{2} θ}) (n_{ω}^{2} \cos^{2} θ + \sqrt{n_{ω}^{2} - \sin^{2} θ})} .

Here, $θ$ is the incident angle, and $n_{ω}$ is the refractive index of the BST films, which is adopted to be 6 [26]. $A_{CPGE}$ and $A_{CPDE}$ are the coefficients proportional to the spin-orbit coupling (SOC) strength of the sample. The fitting curve using $J_{y}^{C} = J_{y}^{CPGE} + J_{y}^{CPDE}$ is shown by a solid line in Fig. 2(a). Note that the experimental data can be well fitted by the theoretical phenomenological formula, and by fitting, we obtain $J_{y}^{CPGE} / J_{y}^{CPDE}$ , which is about 6.34, 4.62, and 2.11 for the 7-, 10- and 20-QL samples, respectively. This indicates the dominance of CPGE over CPDE in all these samples. Therefore, we mainly focus on CPGE in the following discussion. At a certain incident angle, the HDPC of the 7-QL sample shows an opposite sign to that of the 10- and 20-QL samples. This is because the HDPC is dominated by the bottom surface states, while that of the 10- and 20-QL samples are dominated by the top surface states, which is confirmed by the CPGE measurement under the front and back illuminations (see the discussion below).

Then we move to find the origin of the linear polarization-dependent components $L_{1}$ and $L_{2}$ , since they are important for polarization detection. Figures 2(b) and 2(c) show the dependence of the $L_{1}$ and $L_{2}$ components on the incident angle, respectively. The solid symbols indicate the experimental data. Note that the $L_{1}$ term shows an odd function of $θ$ while the $L_{2}$ term varies as an even function of $θ$ for all the samples.

The linear polarization-dependent photocurrent can be attributed to LPGE or LPDE. Now let us separate these two photocurrents, since the separation of LPGE and LPDE will be helpful in polarization detection. To generate LPGE, the system should have inversion symmetry breaking. Therefore, the surface states with $C_{3 v}$ symmetry in BST will generate LPGE, while the bulk states, which belong to $D_{3 d}$ symmetry, will not generate LPGE. The LPGE current can be described by the phenomenological equation [45]

J_{y}^{LPGE} = - χ E_{0}^{2} t_{p} t_{s} \sin θ_{0} \sin 4 φ + χ^{'} {(t_{0} E_{0})}^{2} \cos θ_{0} \cos 4 φ .

Here,

χ

and

χ^{'}

are the linearly independent components of the third-rank tensor at oblique incidence and normal incidence, respectively.

E_{0}

is the electric field amplitude of the light wave.

t_{0} = 2 / (n_{ω} + 1)

is the amplitude of the transmission coefficient for normal incidence, and

n_{ω}

is the refractive index of the BST films.

θ_{0}

is the refraction angle related to

θ

by

\sin θ_{0} = \sin θ / n_{ω}

.

t_{s}

and

t_{p}

are the amplitudes of the Fresnel transmission coefficients for the s- and p-polarized lights, respectively. This equation reveals that the LPGE will contribute to both

L_{1}

and

L_{2}

terms.

The LPDE has a different origin compared to the LPGE because it results from a dynamical alignment of carrier momenta without the requirement for inversion asymmetry [36]. The LPDE can be generated in the bulk states as well as in the surface states. With the LPDE considered, the $L_{2}$ component induced by linearly polarized light flowing along $y$ direction can be expressed as [36]

J_{y}^{L_{2}} = - \frac{E_{0}}{2} \cos 4 φ [(χ^{'} - T_{z} q \cos θ) (t_{s}^{2} + t_{p}^{2} \cos^{2} θ) + T_{∥} q t_{p}^{2} \sin^{2} θ \cos θ] .

Here,

T_{z}

,

T_{∥}

, and

χ^{'}

are the coefficients representing the photon drag effect at normal incidence, the photon drag effect at oblique incidence, and the photogalvanic effect at normal incidence, respectively.

q

is the magnitude of the photon wave vector. However, if we fit Eq. (4) to the incident angle dependent

L_{2}

terms, we can only obtain the fitting value of

χ^{'} - T_{z} q \cos θ

and

T_{∥}

, and we cannot separate each component of

T_{z}

and

χ^{'}

. To differentiate the LPGE and LPDE contributions, we should further analyze the microscopic theory of the photon drag effect [36]. In 3D TIs system, it has been found that

T_{z}

will be substantially smaller than

T_{∥}

at the high radiation frequency of incident light, since they have different frequency dependences. The relation between

T_{z}

and

T_{∥}

can be expressed as [36]

\frac{T_{z}}{T_{∥}} \sim \frac{1 + {(ω τ_{t r})}^{2}}{{(ω τ_{t r})}^{2}} \frac{ε_{F}}{m_{0} v_{0}^{2}},

where

ω = 2 π f

is the angular frequency of the radiation electric field of the light,

τ_{t r}

is the transport relaxation time,

ε_{F}

is the energy of Fermi level,

m_{0}

is the mass of the electron, and

v_{0}

is the Dirac Fermion velocity. Equation (5) demonstrates that, because the radiation magnetic field affects elastic scattering weaker than the electric field,

T_{z}

is substantially smaller than

T_{∥}

[36]. This is because

m_{0} v_{0}^{2} \sim 10 eV

, resulting in the factor

ε_{F} / m_{0} v_{0}^{2}

to be on the order of

10^{- 1}

to

10^{- 2}

for BST samples [36].

Therefore, the contribution from $T_{z}$ to the LPDE can be neglected at a high radiation frequency of incident light for $λ = 1064 nm$ . Thus, Eq. (4) can be reduced to

J_{y}^{L_{2}} = - \frac{E_{0}}{2} \cos 4 φ [χ^{'} (t_{s}^{2} + t_{p}^{2} \cos^{2} θ) + T_{∥} q t_{p}^{2} \sin^{2} θ \cos θ] .

By fitting Eq. (6) to the incident angle dependence of the

L_{2}

term, we find that the fitting value of

χ^{'}

is significantly smaller than that of

T_{∥}

, which suggests that the LPGE contribution at normal incidence (

χ^{'}

) can be neglected. Based on the discussion above,

L_{1}

and

L_{2}

components can be phenomenologically expressed as

L_{1} = γ \sin θ \sin 4 φ,

\begin{array}{l} L_{2} = τ \sin^{2} θ \cos θ \cos 4 φ . \end{array}

Here,

γ = - χ E_{0}^{2} t_{p} t_{s}

and

τ = - \frac{E_{0}}{2} T_{∥} q t_{p}^{2}

, which are related to the LPGE and LPDE, respectively. The solid lines in Figs. 2(b) and 2(c) show that these two functions fit well, confirming that the

L_{1}

term is contributed by the LPGE and the

L_{2}

term mainly comes from the LPDE. In addition, the

L_{1}

and

L_{2}

terms of the 7-QL sample show opposite signs to that of the 10- and 20-QL samples. This should be attributed to the fact that the photocurrent of the 7-QL sample is mainly dominated by the bottom surface, while those of the 10- and 20-QL samples are mainly contributed by the top surface, which is confirmed by the analysis in the following discussion.

B. Gate Tuning of the Polarization-Dependent Photocurrents

Electrostatic gating is one of the best methods to manipulate the helicity-dependent photocurrent of the topological surface states by tuning its chemical potential. We find it is also a potent tool to tune the photodetection performance of 3D TIs. Now we discuss the deep tuning of different polarization-dependent photocurrents by electrical gating.

The dependence of the CPGE and LPGE on back gate voltages, which are shown in Fig. 3, is obtained by fitting Eq. (1) to the polarization-dependent photocurrent. Figure 3(a) shows that the CPGE currents of both the 10- and 20-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ samples are linearly tuned by the back gate voltage. Meanwhile, the sheet resistances of the 10- and 20-QL samples are linearly tuned by the back gate voltage, as shown in Fig. 4(a), and their monotonic decrease reveals that the carrier type of the two ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ samples is n-type [51,54]. This linear dependence indicates that the Fermi level is always above the Dirac point at all the back gate voltages we adopted. The negative gating brings down the Fermi level of the surface states, suppressing the scattering between the surface-Dirac electrons and the bulk state electrons, and the positive gating raises the Fermi level into the conduction band, enhancing this kind of scattering [47,51]. As a result, the CPGE current of the two ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ samples changes linearly with the back gating.

Fig. 3. Dependence of (a) CPGE and (b) LPGE currents of the 10- and 20-QL BST samples on the gate voltage, measured under $θ = - 30 °$ at 77 K. (c) Dependence of the CPGE, LPGE, and LPDE currents on the gate voltage for the 7-QL BST sample measured at the incident angle $θ = - 30 °$ at 77 K. (d) Dependence of the value of $| C | / (| C | + | L_{1} | + | L_{2} |)$ on the gate voltage, which is the ratio of $| C |$ to the sum of the absolute values of the polarization-dependent photocurrents $(| C | + | L_{1} | + | L_{2} |)$ .

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Fig. 4. Dependence of the sheet resistance on the gate voltage for (a) the 10- and 20-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ samples and (b) the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3}$ sample at 77 K. The inset shows the schematic drawing of the position of Fermi level for the BST samples under different back gate voltages.

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Figure 3(c) shows that the CPGE current of the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3}$ sample reaches its peak value at $V_{b g} \approx - 30 V$ . Besides, the value of $| C | / (| C | + | L_{1} | + | L_{2} |)$ , which is the ratio of $| C |$ to the sum of the absolute values of the polarization dependent photocurrents, and the sheet resistance of the 7-QL sample also achieve their maximum values at $V_{b g} \approx - 30 V$ , as shown in Fig. 3(d) and Fig. 4(b), respectively. This phenomenon suggests that the Fermi level of this 7-QL sample is tuned across the Dirac point under the back gating [54]. At a back gate voltage of $- 30 V$ , the Fermi level is located at the Dirac point, in which the scattering between the surface-Dirac electrons and the bulk state electrons is minimum, leading to the maximum CPGE current. As the back gate voltage deviates from $- 30 V$ , the Fermi level will move toward the bulk bands, as shown in the inset of Fig. 4(b). Then, the scattering between the surface-Dirac electrons and the bulk state electrons increases, leading to a drop in the CPGE current [49].

Moreover, it can be seen from Fig. 3(a) that the CPGE current in the 20-QL BST sample is more effectively tuned by the back gate voltage, which may indicate that the CPGE current mainly comes from the top surface states. This is because the back gating will more effectively tune the Fermi level of the bottom surface states than that of the top surface states. As a result, the tuning effect of the top surface states will be less significant in the thicker sample compared to the thinner one.

To confirm our speculation, we measured the CPGE currents under the front and back illuminations. Figure 5(a) shows the experimental geometry, and Figs. 5(b), 5(c), and 5(d) show the CPGE current under the front and back illuminations of 1064 nm light for the 10-, 20-, and 7-QL samples, respectively. The experiment is carried out at room temperature. Since the top surface states show an opposite spin helicity to that of the bottom surface states, their CPGE current will also present opposite signs [55,56].

Fig. 5. Light incident angle dependence of the CPGE current under the front and back illuminations at room temperature for the 10- and 20-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ samples. (a) Schematic illustrations of the CPGE measurement under the front and back illuminations. (b)–(d) Dependence of the CPGE current on the incident angle under the front and back illuminations for the 10-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ sample, the 20-QL ${({Bi}_{0.9} {Sb}_{0.1})}_{2} {Te}_{3}$ sample, and the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3}$ sample. The solid lines are the fitting curves using Eq. (2a).

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In Fig. 5(b), the CPGE current of the 10-QL sample under front illumination shows an opposite sign to that under the back illumination. This phenomenon indicates that the top surface states play the dominant role under the front illumination while the bottom surface states dominate the CPGE under the back illumination, which can be explained by the phenomenological analysis. Specifically speaking, the CPGE for the surface states of BST with $C_{3 v}$ symmetry can be expressed by $J_{y}^{CPGE} = γ_{y x} {\hat{e}}_{x} E_{0}^{2} P_{circ}$ . Here, $J_{y}^{CPGE}$ is the CPGE current flowing along the $y$ direction, $γ_{y x}$ is the second-rank pseudo-tensor for $C_{3 v}$ point group, and ${\hat{e}}_{x}$ is the unit vector pointing in the direction of the light propagation [50]. Under the front and back illumination geometries, the ${\hat{e}}_{x}$ remains the same for a certain incident angle. Therefore, if the sign of the CPGE current reverses under opposite illuminations, the dominant contribution of the CPGE must switch from the top surface states to the bottom surface states, or vice versa. Since the light intensity that reaches the top surface is stronger under the front illumination than that under the back illumination, it can be inferred that CPGE in the 10-QL BST is dominated by the top surface states under front illumination. Because the CPGE current of the 20-QL sample shows the same sign as that of the 10-QL sample under the same incident angle, while that of the 7-QL sample shows an opposite sign, the CPGE current of the 20- and 7-QL samples should be mainly contributed by the top and the bottom surface states, respectively, in the case of front illumination. The results of CPGE currents under the front and back illuminations confirm that the CPGE of both the 10- and 20-QL samples is dominated by the top surface states, which is consistent with the observation of the back gate tuning of the CPGE current in the 10- and 20-QL samples.

In addition to the CPGE current being successfully tuned by the back gate voltage, the LPGE current can also be modulated by back gating, as shown in Fig. 3(b). The back gating dependence of the LPGE currents illustrates that the LPGE of BST can be effectively tuned by the gating voltage. It can be seen that the amplitude of the LPGE increases with an increase in the back gate voltage. This is because as the back gate voltage increases, the Fermi level moves upward, leading to the increase of the carrier density and stronger scattering of carriers [49,57]. Since LPGE is due to the asymmetry scattering of free carriers on phonons, static defects, or other carriers in non-centrosymmetric media [50], the stronger scattering of carriers will increase the LPGE. The unchanged sign of the LPGE current of the 10- and 20-QL samples under back gating agrees with the gate voltage dependence of their resistance. The fact that the CPGE and LPGE currents of the thinner film are more tunable confirms that the CPGE and LPGE in the 10- and 20-QL samples are mainly contributed by the top surface states, since it is more difficult to tune the Fermi level of the top surface states in the thicker films by back gating. This result is consistent with that observed in the CPGE measurements under the front and back illuminations.

Furthermore, we also tune the CPGE current of the BST by the ionic liquid top gate. Ionic liquid gating has higher carrier density tunability than conventional top gating [41]. This is because the ionic liquid has a very high dielectric constant and, when forming an electric double-layer transistor, an extremely high electric field can be achieved within the ionic liquid. Besides, the ionic liquid is transparent, and thus can be used for photoelectric experiments [58].

The dependence of the CPGE current of the 20-QL sample on ionic liquid gating voltages is shown in Fig. 6(c), with the experimental setup illustrated in Fig. 6(a). The gating voltage is applied between the Au gate electrode and the indium electrode on the 20-QL BST film. When applying a positive gating voltage, the Fermi level moves upward, as shown in Fig. 6(b). This will lead to larger scattering between the surface-Dirac electrons and the bulk state electrons. As a result, the CPGE current decreases. Similarly, the negative gating voltage will move down to the Fermi level and reduce the scattering, which will increase the CPGE current. Figure 6(c) shows that the dependence of the CPGE current on the top ionic liquid gating has the same trend as that under the back gating. This phenomenon further confirms that the CPGE of BST is mainly contributed by the top surface states, since the top gating mainly tunes the top surface states. It can be also seen from Fig. 6(c) that the CPGE can be more effectively tuned by top ionic liquid gating compared to the back gating, because obtaining the same tuning effect requires smaller gating voltages under ionic liquid gating.

Fig. 6. (a) Schematic diagram of the device structure and measurement geometry for the modulation of the CPGE by ionic liquid gating. (b) Schematic drawing of the band structure and the Fermi level position of the BST thin film under different ionic liquid voltages. (c) Comparison of the gating voltage dependence of the CPGE current under the back and top gatings for the 20-QL BST sample measured at $θ = - 30 °$ .

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C. Polarization and Stokes Parameters Detection

The complete polarization state can be described by a set of independent Stokes parameters including the total intensity $S_{0}$ , two linear components $S_{1}$ and $S_{2}$ , and the chiral component $S_{3}$ . In addition to Stokes parameters, a fully polarized light can also be described by using the geometrical parameters of an ellipse, including the amplitude $A$ , the azimuthal angle $ψ$ , and the ellipticity angle $φ$ . The relation between the Stokes parameters and the geometrical ellipse parameters can be described as [18]

S_{0} = A^{2},

S_{1} = A^{2} \cos 2 ψ \cos 2 φ,

S_{2} = A^{2} \sin 2 ψ \cos 2 φ,

S_{3} = A^{2} \sin 2 φ .

Notably, the four independent Stokes parameters can be obtained by measuring the three parameters

A

,

ψ

, and

φ

. Obviously, if we can differentiate the circularly-polarized and linearly-polarized photocurrents induced by the detecting light, the Stokes parameters can be easily obtained. This can be achieved by separately using linear and circular polarization-sensitive photodetectors but requires the fabrication of multiple polarization detectors. In this paper, we find an approach to implement both the linear and circular polarization measurements by using a single 3D TIs thin film device.

In an ideal situation with no linear polarization photoresponse, circular polarization detection can be realized by comparing the measured photocurrent to the calibrated photocurrent to detect the degree of chirality. Specifically, in this case, for a calibrated chirality photodetector, the dependence of the total photocurrent $I_{total}$ , the helicity-dependent photocurrent $I_{C} = C \sin 2 φ$ , and the polarization-independent current $I_{D}$ on light power is obtained. Then, the relation between the value $I_{total} / I_{D}$ and the degree of chirality, i.e., $\sin 2 φ$ , can be abstracted. For the calibrated chirality photodetector, the relation between the $I_{D}$ and the light power is known. Therefore, the $I_{D}$ can be determined from the measured photocurrent under a certain light power. By comparing the measured $I_{total} / I_{D}$ to the calibrated $I_{total} / I_{D}$ , one can obtain the degree of chirality of the light.

However, the contribution from the additional linear polarization photoresponse prevents it from the accurate quantification of the circular component for light with arbitrary polarization states. To resolve the circular polarization detection using a device with a large linear polarization response, the research about the incident angle dependence of the polarization-dependent photocurrents could be the key. As demonstrated previously, the $C$ , $L_{1}$ terms change as an odd function of incident angle, indicating that reversing the incident $θ$ can lead to a huge change of the circular polarization response to the polarization-independent baseline. By comparing the measured photocurrent under opposite incident angles to the calibrated results, the ellipticity angle $φ$ can be determined. Figure 7 shows an example of determining the ellipticity angle $φ$ by this method with the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3} / STO$ sample. In Fig. 7, the solid lines are the dependence of the ratio $I_{total} / (I_{C} + I_{D})$ of the 7-QL sample under $θ = \pm 30 °$ on the phase angle $φ$ , measured at 77 K under an illumination of 1064 nm laser of 110 mW with $V_{b g} = - 30 V$ . These photocurrents are used as the calibrated values, denoted as $I_{total}^{cal} / (I_{C}^{cal} + I_{D}^{cal})$ . Then, by dividing the measured photocurrent, denoted as $I_{total}^{mea}$ , under $θ = \pm 30 °$ to the calibrated $I_{C}$ and $I_{D}$ at different phase angles $φ$ , we obtain the ratio $I_{total}^{mea} / (I_{C}^{cal} + I_{D}^{cal})$ , as illustrated by the dashed lines in Fig. 7. There are four intersections between the solid and short dashed lines. The intersection coordinates at $φ = 35 °$ are the only common intersection gained under both the positive and negative incident angles, which suggests that the ellipticity angle $φ$ is 35°.

Fig. 7. Dependence of the ratio $I_{total} / (I_{C} + I_{D})$ of the measured and calibrated photocurrent on the phase angle $φ$ under incident angle $θ = \pm 30 °$ . The photocurrent is measured under the light illumination with a power of 110 mW at 77 K and back gate voltage of $V_{b g} = - 30 V$ . The intersections of the ratio $I_{total}^{mea} / (I_{C}^{cal} + I_{D}^{cal})$ and $I_{total}^{cal} / (I_{C}^{cal} + I_{D}^{cal})$ are marked out at $φ = 35 °$ , 128°.

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It is worth mentioning that the reason for applying a back gate voltage of $- 30 V$ is that at $V_{b g} = - 30 V$ the value of $| C | / (| C | + | L_{1} | + | L_{2} |)$ reaches the maximum, as shown in Fig. 3(d), which can improve the accuracy of the circular polarization detection. We set the ratio $I_{total} / (I_{C} + I_{D})$ as the comparing target because its correlation with CPGE is higher than $I_{total}$ and thus can enhance the detection accuracy.

Figures 8(a) and 8(b) show the dependence of the fitting parameters $C$ , $D$ , $L_{1}$ , and $L_{2}$ on the incident light power for the 7-QL sample. Note that the photocurrent components $C$ , $D$ , $L_{1}$ , and $L_{2}$ show a linear dependence on the light power. Figure 8(c) shows the dependence of the photoconductance on the incident light power in the 7-QL sample, which almost changes linearly with the light power. By measuring a photoconductance under an illumination of a light at $V_{b g} = - 30 V$ , the light power can be easily obtained by the calibrated photoconductance. As a result, the Stokes parameter $S_{0}$ can be obtained by the photoconductance measurement [49]. Comparing our polarization detection method to the one realized in ${Bi}_{2} {Te}_{2} Se$ thin films, which separates the circular polarization from the linear polarization by obtaining the differential photocurrent at different bias voltages [49], our method is of wider applicability for 3D TIs thin films. The reason is that their method is easier to implement only when the LPDE is negligible, so that the LPGE current will not be amplified by the bias because of the instantaneous nature of the LPGE. However, besides the LPGE, the LPDE may also show up in 3D TIs [36,41,59], which will make the linear polarization-dependent photocurrent also change with the bias. For example, we observed the considerable LPDE current in our ${({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3}$ thin films. As a result, if we apply the bias voltages to the ${({Bi}_{1 - x} {Sb}_{x})}_{2} {Te}_{3}$ thin films, it will be hard to separate the photoresponse of circular polarization from that of the linear polarization. The polarization detection strategy we proposed can be applied to all kinds of 3D TIs materials. To sum it up, our method for polarization detection is better in applicability for 3D TIs thin films.

Fig. 8. Dependence of the fitting parameters $C$ , $D$ , $L_{1}$ , and $L_{2}$ on the incident light power in the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3}$ thin film under an incident angle (a) $θ = - 30 °$ and (b) $θ = 30 °$ at 77 K. (c) Dependence of the photoconductance on incident light power in the 7-QL ${({Bi}_{0.8} {Sb}_{0.2})}_{2} {Te}_{3}$ thin film.

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For further confirmation, we also use the 10- and 20-QL BST samples to detect the ellipticity angle. We find that the ellipticity angle can also be successfully detected by the 10- and 20-QL samples, but the 7-QL sample shows a better detection accuracy compared to the 10- and 20-QL samples. This is because the ratio of the helicity-dependent photocurrent to the sum of the absolute values of the polarization-dependent photocurrents $| C | / (| C | + | L_{1} | + | L_{2} |)$ is larger in the 7-QL sample. Besides, for the 7-QL sample, the detection accuracy is better when applying a back gate voltage of $- 30 V$ because the value of $| C | / (| C | + | L_{1} | + | L_{2} |)$ reaches the maximum at $V_{b g}$ of $- 30 V$ . This phenomenon further confirms that the larger proportion of helicity-dependent photocurrent will improve the detection accuracy of the ellipticity angle.

Based on the method mentioned above, we can obtain the ellipticity angle $φ$ and the light power $A^{2}$ ; hence, we also can obtain the complete polarization states by full-Stokes detection after characterizing the azimuthal angle $ψ$ . To obtain the azimuthal angle $ψ$ , we use the linear polarization detection mode, in which the CPGE (or CPDE) should be almost turned off and the LPGE (or LPDE) currents will play the dominate role. It can be seen from Fig. 3(c) that, to almost turn off the CPGE (or CPDE), one should apply a back gate voltage of 260 V. Under $V_{b g} = 260 V$ , the CPGE (or CPDE) is almost turned off. This is because the chemical potential is tuned to the warping region at the conduction band edge where the spin texture is not strictly locked to its momentum, and the electrons are also easily scattered to spin-degenerated states by bulk phonons [51,56].

Figure 9 shows the dependence of the photocurrent, with the polarization-independent current $D$ being subtracted, on the angle of the quarter-wave plate $α$ , which is measured under the same condition as that on the ellipticity angle detection except that the back gate voltage is applied. Considering that $ψ = 2 α$ , we fit the calibrated photocurrent with the equation $J = 0.15 \sin (4 α + β) + 0.06 \cos (4 α)$ . Here, the angle $β$ is a fitting parameter, which represents the angle between the $a$ axis of the lattice and the $y$ axis. This is because the LPGE is related to the lattice orientation [57], but the LPDE is not related to the lattice symmetry. Therefore, the $\cos (4 α)$ term does not contain any additional angle parameter [36]. By fitting, we obtain $β = 0.03 π$ . The measured photocurrent for linear polarization detection is then used to determine the phase angle $α$ within 0° to 90°, by comparing the measured results with the calibrated photocurrent under the opposite light incident angles. For linear polarization detection, it is more reasonable to calculate the ratio $I_{total} / (I_{LPGE} + I_{D})$ as the comparing target. Finally, the azimuthal angle $ψ = 2 α$ can be substituted into Eqs. (9)–(12) and $\tan (2 ψ) = S_{2} / S_{1}$ to determine the Stokes parameters $S_{1,2}$ . Thus, we demonstrate a way to use the 3D TI BST thin film as an effective miniature single-device for chirality and polarimetry detection.

Fig. 9. Dependence of the photocurrent, with the polarization-independent current $D$ being substrated, on the angle of the quarter-wave plate $α$ in the 7-QL BST sample. The photocurrent is measured under a light power of 110 mW and a back gate voltage of 260 V at 77 K.

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4. CONCLUSION

In conclusion, we have demonstrated a single device based on 3D TI BST thin films for optical chirality and polarimetry detection. Tuning the back gate voltages can switch the detector to different operating modes for linear or circular polarization detection, respectively. The investigations of the microscopic origin and the gate voltage tuning effect of different components of the polarization-dependent photocurrents in BST thin films provide the theoretical support for polarization detection. Combining the measurements of photocurrents under opposite light incident angles enables chiral photodetectors with a thin film device, and increasing the proportion of the helicity-dependent photocurrent in the total photocurrent by back gating can enhance the detection accuracy. The full Stokes parameters can be extracted by incorporating the measured linear polarization state on the same device. Therefore, the polarization detection method proposed in this work shows potential to be an effective way for chirality and polarimetry detection and can be used in a wide spectrum of applications from biomedical molecules to screening polarimetric imaging.

Funding

National Natural Science Foundation of China (62074036, 61674038, 11574302); Foreign Cooperation Project of Fujian Province (2023I0005); Open Research Fund Program of the State Key Laboratory of Low-Dimensional Quantum Physics (KF202108); National Key Research and Development Program of China (2016YFB0402303); Foundation of Fujian Provincial Department of Industry and Information Technology (82318075).

Disclosures

The authors declare no conflicts of interest.

Data Availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Gate voltage control of helicity-dependent photocurrent and polarization detection in (Bi_1−xSb_x)₂Te₃ topological insulator thin films

Abstract

1. INTRODUCTION

2. EXPERIMENTAL DETAILS

3. RESULTS AND DISCUSSION

A. Polarization-Dependent Photocurrents Analysis

B. Gate Tuning of the Polarization-Dependent Photocurrents

C. Polarization and Stokes Parameters Detection

4. CONCLUSION

Funding

Disclosures

Data Availability

REFERENCES

Data Availability

Cited By

Figures (9)

Equations (13)

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