Recently, two-dimensional (2D) layered materials such as graphene and transition-metal dichalcogenide (TMDs) have been widely researched owing to their extraordinary physical properties^[1] and great potential in electronics, photonic and optoelectronic applications^[2–13]. Among them, the anisotropic 2D materials with low in-plane symmetry have been immensely attractive due to their excellent application in photodetection^[14–21] and potential in conceptually novel devices^[22–27]. For example, the renascent member of the 2D materials—black phosphorus (B-P), exhibits high in-plane anisotropy due to its different bond angles and lengths along the direction of armchair and zigzag^[17,28,29]. The photocurrent ratio is nearly 0.3 under the illumination of near infrared laser^[17]. Also as a typical 2D in-plane anisotropic crystal, B-P is the pioneering model for other emerging two-dimensional anisotropic materials, like GeP, B-As, SiP and so on^[30–37].

Herein, we summarize the recent research progress on two-dimensional anisotropic materials into three aspects. In the first part, the origin of the in-plane anisotropy of anisotropic materials is discussed by analyzing the crystal structure. In the second part, we introduce typical polarized-Raman configuration for measurements and analyze the angle-dependent Raman spectroscopy of different anisotropic materials. In the final part, we summarize the anisotropy in the electric and photoelectric properties of the representative two-dimensional materials, like B-As^[35,36], B-P^[38], As_0.83P_0.17^[39], GeAs^[40], GeSe^[41], ReS₂^[42], ReSe₂^[43,44]and KP₁₅^[45]. This review offers perspectives and new ideas for the future utilizations of two-dimensional anisotropic materials.

Orthorhombic Black-Arsenic (B-As) (Fig. 1(a))^[35] and Black-Phosphorus (B-P) (Fig. 1(b))^[46] are the representative anisotropic materials belonging to the space group Bmab and Pcmn respectively. The bulk materials are the minerals in black color, so named for black-As and black-P^[36]. In the single layer, each As or P atom are covalently bonded with three adjacent atoms. GeAs (Fig. 1(c)), similar to GaTe structure with the space group of C2/m, is the new 2D intralayer anisotropic material^[47]. In the structure of GeAs, each Ge atoms are coordinated by one Ge atom and three As atoms, and each As atoms are coordinated by three Ge atoms. Therefore, there are two kinds of Ge–Ge bonds parallel and perpendicular to b-axis^[40,47,50]. GeSe is the derivative of B-As and B-P and belongs to Pcmn- space group as shown in Fig. 1(d)^[41]. KP₁₅ is another kind of layered material with fiber-like structure. The left of Fig. 1(e) is the unit cell of KP₁₅, and the right is the triclinic KP₁₅ structure with the space group . As shown in the structure, one layer consists of two antiparallel P tubes, and four P tubes are coordinated by K atoms. Each K atom is coordinated with one [P₁₅]^– cell. The inside of [P₁₅]^– cell exhibits pentagonal P atoms arrangement which causes the highly anisotropic property^[45]. Quasi-1D titanium trisulfide (TiS₃) is shown in Fig. 1(f)^[51]. There are two kinds of Ti-S bonds lengths in the structure, one is 4.97 Å along a-axis and another is 3.43 Å along b-axis^[52]. Contrary to above materials, ReS₂^[53], ReS_2(1–x)Se_2x^[49], and ReSe₂^{[44, 54]} belong to distorted 1T structure. The crystal structure of ReSe₂ is shown in Fig. 1(g), in which diamond-shaped Re₄ clusters along zigzag due to the Peierls transition.

Raman spectroscopy is a fast, nondestructive and high sensitivity tool for the characterization of the lattice structure as well as the electronic, optical and phonon properties of 2D materials^[55–59]. Among them, the angle-resolved polarized Raman spectroscopy is necessary to be utilized to research crystal orientation and phonon anisotropy^[60,61]. For angle-resolved polarized Raman spectroscopy, there are three typical configurations as shown in the Figs. 2(a)–2(c). Fig. 2(a) is a schematic diagram of the most basic configurations for angle-resolved polarized Raman measurements. The polarization of incident laser is rotated with α degree by rotating the half-wave plate with α/2 degree respecting to the fast-axis direction. This configuration is widely used for its time-saving and easy-to-handle advantages. In Fig. 2(b), the laser polarization is fixed along y axis by a polarizer, and the analyzer direction is set to x axis or y axis, which corresponds to generally-used cross- or parallel-polarization configuration, respectively. In the process of measurement, the sample is clockwise rotated around z axis with β angle. The configuration of Fig. 2(c) is equivalent in function to that in Fig. 2(b) but different in geometry, where a half-wave plate is inserted between the edge filter and the objective while the sample is fixed^[62]. This configuration can be a substitution of the former one since it can technically avoid sample moving and be more time-consuming.

ReS₂, ReSe₂ and their alloy ReS_2(1–x)Se_2x are the emerging materials which exhibits a stable distorted 1T phase and strong in-plane anisotropy due to its reduced crystal symmetry. It is essential to research their angular-dependent anisotropy behaviors. The Raman spectra of ReSe₂ with different thicknesses grown on SiO₂ and hBN substrate are shown in the left of Fig. 2(d)^[44]. With the thickness increasing, the peak positions are blue shift (2 cm^–1) due to the decoupled lattice vibrations, which is similar to ReS_2(1–x)Se_2x. The angle-resolved polarized Raman intensity of ReSe₂ at 238 cm^–1 peak has displayed in the right of Fig. 2(d) under the configuration in Fig. 2(b). The periodic changes in intensity give direct illustration of its strong anisotropy. Fig. 2(e) shows the angle-resolved polarized Raman intensity of ReS_2(1–x)Se_2x at 212 cm^–1 (red points) and 406 cm^-1 (blue points) as the composition changes^[49]. For the peak of 212 cm^–1 in ReS_2(1–x)Se_2x, the direction with maximum intensity gradually deviates from b-axis direction (along Re chains) with x increasing. For the ReS_2(1–x)Se_2x crystals, the Raman tensor R of all Raman active modes have the form of . The intensity of Raman mode can be expressed by the function of , where and is the unit polarization vector for scattered light and excitation laser, respectively. Therefore, the intensity of polarized Raman can be written as . All experimental data can thus be well fitted^[55].

As for another layered material KP₁₅ with distinctive shape, its Raman spectra (Fig. 2(f)) include 14 Raman peaks locating at 466.6, 449.0, 408.8, 376.3, 368.4, 351.1, 303.7, 288.5, 124.1, 114.1, 106.8, 90.7, 74.6 and 66.4 cm^-1. The thickness of the measured sample is 373.9 nm. As the most anisotropic one, the angle-dependent Raman intensity of peak 9 is individually extracted and shown in the right of Fig. 2(f). All Raman peaks in Fig. 2(f) follow the function of cos⁶θ. In addition, the crystal of KP₁₅, similar to phosphorene (P), also has anisotropic photoluminescence (PL) properties. In the measurement of polarization-resolved PL spectra, the KP₁₅ samples of 373.9 nm and 2.3 μm are chosen and the results are shown in Fig. 2(g). Four kinds of excitation-detection combinations are taken in the polarization-resolved PL measurements. When the laser polarization is remained constant, the intensity ratio (y-axis/x-axis) is 5.8, which indicates the anisotropic emission property caused by its high anisotropic structure. From the polar plot in Fig. 2(g), it can be observed that the anisotropy of samples with different thickness is diverse from each other, which indicates that the anisotropy of PL spectra also relates to the thickness of the KP₁₅^[45].

GeSe is a typically stable and anisotropic IV−VI chalcogenide. The angle-dependent Raman spectrum of GeSe is shown in the Fig. 3(a) with the corresponding contour color map under the parallel and cross polarization configurations. The contour map visually shows the anisotropy of each peak. The parallel-polarization configuration and cross-polarization configuration correspond to the polarization analyzer before the spectrometer parallel and perpendicular to the laser polarization, as mentioned before. The sample is rotated with a step of ten degrees. There are two Raman peaks around 150 and 188 cm^–1 coming from B_3g mode and A_g mode respectively. Similar to materials with anisotropic absorption such as B-P, one needs to consider the impact of light absorption in the form of the Raman tensor. Additional phase index should be introduced to fit the experimental results. In parallel-polarization configuration, the fitting function of A_g mode is , and that of B_3g mode is . While under the cross-polarization configuration, the fitting function of A_g mode is f²sin²2θ, and that of B_3g is f²cos²2θ^[41].

The anisotropic characteristics of angular-dependent and excitation-dependent Raman spectra of B-P has been thoroughly reviewed in previous work^[61]. Similarly, B-As, a rare chemical form of arsenic, is also reported with extremely anisotropy. The angle-dependent Raman spectrum (Fig. 3(b)) can be used to investigate the anisotropic vibrational properties. The strong Raman peaks are located at 223.6, 230.2 and 257.9 cm^–1, corresponding with out-of-plane A_g¹, in-plane B_2g and in-plane A_g² modes. Among them, the intensity of A_g¹ mode is fitted by the function of (1 + bsin²θ)², where b is a matrix element in the Raman tensor of A_g¹ mode. The intensity of B_2g mode varies as e²sin²(2θ), where e is the Eiler’s number and θ is the angle between the laser polarization and AC direction of crystal. From the polar plot in Fig. 3(b), the A_g¹ peak behave strongest in intensity and B_2g weakest along the direction of armchair, which is consistent with the its electrical behaviors as discussed below.

GeAs is a newly introduced 2D material with high anisotropy. From the Raman spectra taken under three configurations (Fig. 3(c)-left), it can be observed that the non-polarized Raman spectra includes 7 peaks (locating at 147, 174, 242, 256, 274, 283, 307 cm^–1), and the parallel/cross configuration include 6 peaks/2 peaks, which confirms the intrinsic anisotropy of GeAs crystal. Furthermore, the angle-dependent Raman spectra is measured by rotating the sample under non-polarized configuration and shown in the Fig. 3(c)-right. The intensities of angle-dependent of Raman is extracted and shown in polar plot (Fig. 3(d)). In the polar plot, the data can be fitted by the function of , where θ represents the polarized angle and all of , and are fitting parameters^{[40, 63, 64]}.

In addition, Prof. Dai and co-workers have researches the anisotropic Raman response of SnSe, MoTe₂ and WTe₂^[65–67].

The anisotropy along armchair (AC) and zigzag (ZZ) directions also manifest on their photoelectrical properties. For convenience of comparison, the details of a series 2D anisotropic materials are summarized and provided in Table 1. Conduction ratio is defined by dividing the maximum conduction value by the minimum conduction value showing along different orientation. Responsivity is the ratio of photocurrent generated by photoconductive mode to excitation light. Dichroic ratio represents the degree of the discrepancy in response to different polarized light by dividing the maximum photocurrent value by the minimum photocurrent value.

The anisotropic optical properties of B-P crystal have been researched detailly. The anisotropic optical absorptions of visible light and infrared light are measured under the configuration shown in the schematic diagram in Fig. 4(a). The optical absorptions (Fig. 4(b)) shows that more visible photons are absorbed with light polarized along x-axis (0°) than that along y-axis (90°). B-P photodetector with a ring-shaped photocurrent collector is fabricated (Fig. 4(c)-(1)) and its polarization-dependent photoresponsivity is shown in Fig. 4(c)-(2), with illumination from 400 mn to 1700 nm under the polarization along x crystal axis (0°) and y crystal axis (90°) respectively. The photoresponsivity contrast ratio between the two perpendicular directions is as large as 3.5. To clearly observe the anisotropic photoresponse, spatial mapping of photocurrent is obtained (Fig. 4(c)-(3)). It visually demonstrates the difference in intensity of photocurrent along the x-axis and y-axis^[38].

B-As, as a “cousin” of B-P, is reported as high mobilities and anisotropic behaviors. The anisotropic research is mainly focused on the direction of armchair and zigzag. For an anisotropic semiconductor with twofold symmetry in the polar plot, the conductance (S) varies with the θ changing as S_θ = S_maxcos²θ + S_minsin²θ^[35]. From fitting the angle-dependent electrical conductance in Fig. 4(d), the highest conduction is S_max = 24.3 μS along armchair direction, and the weakest is S_max = 3.8 μS along zigzag direction. The anisotropic conduction ratio is as high as 6.4. To further analysis its anisotropic electric properties, the hall device is fabricated to measure the temperature dependent resistance (R) and magnetic dependent conductively (σ) along armchair and zigzag directions. The resistance is sensitive to temperature along zigzag while inert along armchair, with a much higher value along zigzag compared to armchair, as shown in Fig. 4(e)-left. As the same time, the magnetic dependent conductively shows opposite signs along armchair and zigzag. Herein, the longitudinal conductivities can be described as , and the transverse conductivities as . In the Fig. 4(e)-right, the results of magnetic field dependent conductively can be fitted as the function of and . And then, the concentration (n) and mobility (μ) of holes (h) and electrons (e) can be extracted from above equations. The obtained concentration are n_e = 2.0 × 10¹⁶ cm^–3 and n_h = 5.3 × 10¹⁵ cm^–3 while mobility are as high as μ_h^ZZ = 60.7 cm²V^–1s^–1 and μ_e^ZZ = 376.7 cm²V^–1s^–1 along zigzag direction, μ_h^AC = 10 606 cm²V^–1s^–1 and μ_e^AC = 1.5 cm²V^–1s^–1 along armchair direction^[35].

Orthorhombic black-AsP, which is the alloy of B-As and B-P, is fabricated by the Prof. Hu and co-workers^[39]. For the polarization-dependent photocurrent and the polarization-sensitive photocurrent mapping (Fig. 4(g)), researchers focused on the properties along x-axis (armchair direction) and y-axis (zigzag direction). The polarization-dependent photocurrent was measured under the illumination of linear-polarized light. The laser was set to pass a linear polarizer to obtain the linear-polarized light, and the half-wave plate to adjust the polarization direction, then the 20× or 100× microscopy objective to focus. The polarization-sensitive photocurrent mapping is measured by scanning the linear-polarized light over the device. At the dark environment, the conductivity along x-axis is nearly 1.73 times than that along y-axis at V_g= 0 V, which is consistent with previously reported results^[74]. Under the illumination of mid-infrared laser (4.034 μm), the anisotropic photocurrent ratio IP_x/IP_y at V_ds= 1 V is nearly 3.51. The photocurrent was observed to be maximum when the light polarization was along the x-direction and minimum when the light was along the y-direction, similar to the observation in black phosphorus^[39]. The photocurrent anisotropy ratio is as high as γ= (I_pmax– I_pmin)/(I_pmax + I_pmin) ≈ 0.59, which is larger than the ratio of B-P (~0.3)^[17].

GeAs crystal, as a new 2D materials, is reported by its highly anisotropic electricity and photoelectricity properties. The field-effect mobility (Fig. 5(b)) of GeAs transistors are measured with a resolution of 15° under vacuum of 10^–5 Torr. The mobility is calculated by the equation of , where C_ox= 11.6 Nf/cm² corresponds with 300 nm SiO₂ dielectric capacitance, L and W is the channel length and width, G represents the channel conductance, and V_G is the voltage of gate. The anisotropic mobility ratio is as high as 4.8^[47]. From the polarization-resolved absorption spectra (Fig. 5(c)), it can be observed that a linear dichroism photodetection behavior and the dichroic ratio is 1.14/1.42 at 520 nm/830 nm respectively. The direction of the strongest absorption is dominating along b-axis between 400 to 500 nm wavelength while reverses to a-axis after 630 nm wavelength. Comparing the absorption of visible light with near-infrared light, the angle of strongest absorption direction is around 80 degrees. This phenomenon is defined as perpendicular optical reversal phenomenon.

Further, the polarization-resolved photocurrents of GeAs is measured under the schematic configuration in Fig. 5(d), where linear-polarized laser is obtained with the polarizer and its polarization is changed by half-wave plate. By rotating the half-wave plate with α/2 steps, the angle-resolved photocurrents are measured and shown in polar plot with α steps (Fig. 5(e)). The dichroic ratio ( ) is as high as 1.49 at 520 nm laser illumination and 4.4 at 830 nm laser illumination. The fitting curves of polarization-resolved photocurrents follow the function of I_ph(θ) = I_pmaxcos²(θ + φ) + I_pminsin²(θ + φ), where only φ is the adjustable fitting parameter. The perpendicular optical reversal phenomenon is also observed in the photoelectric measurement with the reversal angle is 70°, corresponding with the anisotropic absorption spectra.

To research the source of photocurrent, the spatial mapping of photocurrents is measured with different polarization directions (Fig. 5(f)). Once again, distinct angle difference for linear-polarization mapping was observed around 80° between 520 and 830 nm lasers, corresponding with the reverse angle observed in anisotropic absorption spectra and polarization-resolved photocurrents. Besides, it is can be observed that the photocurrent signals occur in the interface between GeAs nanoflake and electrode, and two contacts have opposite polarity. That is due to the Schottky junction, formed between semiconductor materials and metal electrode, causing the photovoltaic and photothermoelectric effect. It is similar to the Schottky diode^[40].

The distinct anisotropic features of GeSe is manifested in linear-polarization-sensitive photodetectors. The polarization-resolved absorption spectra of GeSe with 49.6 nm thicknesses is probed (Fig. 5(g)). The results show that the absorption ratio , 1.26 and 3.02 at the wavelength of 532, 638 and 808 nm, respectively. There is a polarization peak around the wavelength of 808 nm which corresponds with the electric band structure of GeSe crystal. Further, by measuring the layer-dependent photo response, it is found that the photo response of the 8–16 nm GeSe have the best results. So, the 8.63 nm GeSe is chosen to measure the properties of polarization photodetectors. The colormap (Fig. 5(h)) directly exhibits the relationship between the photo response and the angle of polarized laser under the illumination of 808 nm laser. The polarization photocurrents under 95 mW/cm² illumination and voltage of source–drain of 2 V are measured and shown in polar plot (Fig. 5(i)). The data of polarization photocurrents can be fitted by the function . The dichroic ratio of photo response is at 808 nm laser. The dichroic ratio of absorption and photo response is different, which is possibly due to defect states introduced by the processing fabrication, measuring apparatus error or different thickness samples and so on^[41].

ReSe₂ crystal is different from other hexagonal TMDs, and its anisotropy is introduced by the 1T phase of 1D arrangement of Re chains. From the polarization sensitive transmission spectra in Fig. 6(a), it can be observed that the infrared transmission spectrum with γ = 0° is more dipping than that with γ = 90° at the energy between 1.32 and 1.85 eV. The γ = 0° is defined as the direction of polarization light parallel to the b-axis, and the γ = 90° is defined as the direction of polarization light perpendicular to the b-axis. Besides, the anisotropic transmission ratio at 1.86 eV is 0.66 and 0.98 with γ = 0° and 90°, which demonstrating b-axis absorb more photons. Further, polarization-dependent photocurrent mappings are measured in order to find the source of the photocurrent. It can be seen that photocurrent signals come from the ReSe₂ channel rather than the metal electrodes, which confirms that the influence of Schottky barriers are eliminated^[44]. Next, a series of optical anisotropies of ReS_2(1–x)Se_2x were researched (Fig. 6 (c))^[49]. It can be seen that the mobility of ReSe₂, ReS_0.38Se_1.62, and ReS_1.02Se_0.98 is in the range of 2.12 to 6.16, 1.44 to 5.53, and 1.26 to 8.45 cm² V⁻¹ s⁻¹, respectively^[75]. The maximum mobility of ReS_2(1–x)Se_2x are along b-axis. At the same time, the anisotropic mobility ratios of ReSe₂, ReS_0.38Se_1.62, and ReS_1.02Se_0.98 few-layers are calculated to be 2.9, 3.8 and 5.6, respectively^[76].

In 2017, Prof. Wei and co-workers successfully synthesized the TiS₃ crystal and researched its anisotropic optical properties. The crystal TiS₃ is formed by interacting quasi-1D chains and the weakly coupled Ti–S bond. The Ti–S bond of TiS₃ is nearly 80% less than that of TiS₆ polyhedrons within the chain. This leads to the strong anisotropy in TiS₃. Further, the anisotropic photocurrents are measured with different wavelengths of laser illumination and shown marked linear dichroism. The extinction ratios based on TiS₃ photodetector are calculated to be 2.8, 4.6 and 4.0 under the illumination of 532, 638 and 830 polarized light^[52,77]. In 2018, Andres Castellanos-Gomez and co-works researched the polarization optical properties of TiS₃/Si p–n junction^[48]. In their work, the TiS₃ nanowire is deposited onto PDMS to measure its polarization-sensitive transmittance spectra, as shown in Fig. 6(d). In the transmittance spectra, the 0 degree corresponds to a-axis, and 90 degrees corresponds to b-axis. At 2.32 eV, the transmittance along the a-axis reaches 71%, as the same time, the transmittance along the b-axis is as low as 52%. The polarization-sensitive transmittance of typical wavelengths (500, 600, 700 and 800 nm) are extracted and shown in the polar plot (the inset of Fig. 6(d)), which indicates the in-plane optical properties of TiS₃ crystal. Then, the photocurrents of TiS₃/Si-based device are measured with the 660 nm polarizer laser (Fig. 6(e)). The polarizer photocurrents under –2 and 0 V bias voltage are extracted and shown in the Fig. 6(f).

Furthermore, the anisotropies of electrical in SnSe and Ta₂NiS₅ have been investigated. The condition radio of SnSe can be as high as 3.9^[67]. And the condition radio of Ta₂NiS₅ is 1.78 at 80 K and 1.41 at 293 K^[78].

In this review, we have reviewed several two-dimensional anisotropic materials and related field effect transistors and photodetectors based on recent advances. This review pays special attention and make comparison of the anisotropy in their optical and electrical properties. More anisotropic materials are gradually revealed and can be broadly applicable to various platforms and devices. Polarization-sensitive photodetectors based on such anisotropic crystals have fast, high sensitivity, broad spectrum, high anisotropy ratio and greatly repeated anisotropic properties. We hope this review could guide interested readers to properly utilize their anisotropic behaviors for material synthesis and specific applications.

This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 61622406, 61571415, 11874350, 11434010), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB30000000).