Giant Transport Anisotropy in ReS_2 Revealed via Nanoscale Conducting Path Control
Dawei Li, Shuo Sun, Zhiyong Xiao, Jingfeng Song, Ding-Fu Shao, Evgeny Y. Tsymbal, Stephen Ducharme, Xia Hong
11 Giant Transport Anisotropy in ReS Revealed via Nanoscale Conducting Path Control
Dawei Li, Shuo Sun, Zhiyong Xiao, Jingfeng Song, Ding-Fu Shao, Evgeny Y. Tsymbal, Stephen Ducharme, Xia Hong Department of Physics and Astronomy & Nebraska Center for Materials and Nanoscience, University of Nebraska-Lincoln, Lincoln, Nebraska 68588-0299, USA * Correspondence to: [email protected]
Abstract
The low in-plane symmetry in layered 1T'-ReS results in strong band anisotropy, while its manifestation in the electronic properties is challenging to resolve due to the lack of effective approaches for controlling the local current path. In this work, we reveal the giant transport anisotropy in monolayer to four-layer ReS by creating directional conducting paths via nanoscale ferroelectric control. By reversing the polarization of a ferroelectric polymer top layer, we induce conductivity switching ratio of >1.5 × in the ReS channel at 300 K. Characterizing the domain-defined conducting nanowires in an insulating background shows that the conductivity ratio between the directions along and perpendicular to the Re-chain can exceed 7.9 × . Theoretical modeling points to the band origin of the transport anomaly, and further reveals the emergence of a flat band in few-layer ReS . Our work paves the path for implementing the highly anisotropic 2D materials for designing novel collective phenomena and electron lensing applications. Layered two-dimensional (2D) semiconductors such as black phosphorus and 1T’-rhenium disulfide (ReS ) possess low in-plane symmetry, which leads to a rich spectrum of intriguing electronic and optical phenomena [1], including intrinsic band anisotropy [2], strong anisotropic bound excitons and nonlinear optical responses [3-6], tunable hyperbolic plasmonics [7-9], large optical birefringence [10,11], moiré superlattices [12-14], and multiferroic behaviors [15,16]. The transition metal dichalcogenide (TMDC) ReS is a direct band gap semiconductor, with the band gap ( E g ) varying from 1.43 eV in monolayer samples to 1.35 eV in bulk [17]. It exhibits strong intra-layer anisotropy between the directions along and perpendicular to the Re chains [Fig. 1(a)]. Theoretical studies have shown that the band dispersions lead to strong mobility anisotropy in ReS [18,19], while direct mapping of its angle-resolved transport remains challenging due to the lack of effective strategies to control the local current path [20]. A promising approach to define reconfigurable, directional conduction paths in the 2D semiconductors is to leverage the nanoscale controllable polarization of an adjacent ferroelectric layer. In previous studies, ferroelectric domain patterning has been exploited to impose a wide range of functionalities in TMDCs [21,22], including programmable homo- and hetero-junction states [23,24] and photovoltaic effects [25], nanoscale excitonic modulation [26,27], and nonlinear optical filtering [28]. Combining local polarization writing with the ferroelectric field effect enables the programming of nanoscale conduction paths within an insulating background, which can confine the local current flow in pre-designed directions on the same sample. Unlike lithographically defined nanowires, the nonvolatile field effect approach is clean, reversible, and does not involve uncontrollable sample-to-sample variations. In this work, we exploited nanoscale polarization control of a ferroelectric copolymer poly(vinylidene fluoride-trifluoroethylene) [P(VDF-TrFE)] top layer to probe the transport anisotropy in atomically thin ReS . By characterizing the domain-defined conducting nanowires in the insulating channel [Fig. 1(b)], we mapped out the angle-resolved conductance of monolayer (1L), bilayer (2L), and four-layer (4L) ReS field effect transistors (FETs), which revealed a giant conductivity ratio of 7.9 × between the directions along and perpendicular to the Re-chain. The transport results can be well accounted for by the band anisotropy in conjunction with the electron-phonon scattering, as revealed by our first-principles density functional theory (DFT) modeling, which further points to the emergence of a flat band in the 4L ReS . Our study illustrates a powerful approach for resolving nanoscale electronic signatures of emergent band properties in van der Waals (vdW) materials, as well as presenting a promising material platform for realizing topology and correlation-driven quantum phenomena. Single-layer and few-layer ReS flakes were mechanically exfoliated from bulk single crystals onto the Gel-Films. The layer number is confirmed by atomic force microscopy (AFM) studies combined with the Raman frequency difference ∆ between the modes I and III, and the crystalline orientation of ReS was identified by angle-resolved parallel-polarized Raman scattering measurements (Supplemental Materials) [29]. Selected 1-4L ReS flakes were transferred onto SiO (290 nm)/doped Si substrates pre-patterned with Cr/Au (2 nm/10 nm) electrodes, forming FET devices. Next, we deposited 9 MLs of P(VDF-TrFE) film on top of ReS using the Langmuir-Blodgett (LB) technique [30] followed by a thermal annealing treatment at 135 o C for 80 min (Supplemental Materials). To switch the ferroelectric polarization, a ±11 V DC bias ( V bias ) was applied to a conductive PtIr-coated tip (Bruker SCM-PIC-V2), which was controlled by the NanoMan program. The resulting domain structures were imaged using piezoresponse force microscopy (PFM). The AFM and PFM studies were carried out using a Bruker MultiMode 8 AFM system. The electrical characterization was performed using the semiconductor parameter analyzer (Keysight B1500A) after domain patterning, while the sample was kept in the AFM during the entire process. Figure 1(c) display the PFM phase images taken on a 1L ReS FET, with the P(VDF-TrFE) top layer polarized uniformly in the down ( P down ) and up ( P up ) polarization. In both states, the sample exhibits linear source-drain current-voltage ( I d - V d ) relation, confirming the Ohmic characteristic (Supplemental Materials). Figure 1(d) compares the I d versus back-gate voltage ( V bg ) relation for the as-prepared, no poling state of P(VDF-TrFE) with those in the P down and P up states, showing the P down ( P up ) state accumulates (depletes) electrons in ReS , as expected. The transfer curve in the P up state exhibits hole-doped characteristic, with the off-state current at a comparable level as that of the no poling state. In contrast, the P down polarization of P(VDF-TrFE) introduces a high level of electron-doping in ReS , changing the dominant carrier type from p -type to n -type. In this state, the ReS channel remains highly conductive over the entire V bg –range, showing that the accumulated electron density well exceeds what can be effectively depleted by the SiO back-gate. The current switching ratio between the P down and P up states reaches 5.3×10 at V bg = 7 V. A higher switching ratio may be expected at (cid:3397)7 𝑉 (cid:3409) 𝑉 (cid:2912)(cid:2917) (cid:3409) (cid:3397)40 V , where the 1L ReS becomes so insulating in the P up state that the current level is below the instrument resolution. We also achieved nonvolatile current modulation in the 2L and 4L ReS FET devices (Fig. 1(e) and Supplemental Materials) . We extracted from the transfer curves a high current switching ratio of 1.5×10 at V bg = 12 V, which is among the highest values reported in ferroelectric-gated 2D FETs [31], reflecting the high doping modulation induced by the polarization of P(VDF-TrFE). Even though the fractional change of the doping level is expected to increase with decreasing channel thickness, we find the ferroelectric field effect is the largest in the 4L sample. A likely reason is the thinner samples are highly insulating in the P up state and cannot provide sufficient screening to P(VDF-TrFE). This leads to high depolarization field, so that the polarization cannot be fully switched [21]. To create a directional conducting nanowire, we switched the polarization of P(VDF-TrFE) into the uniform P up state, setting the entire ReS channel in a highly insulating state, and then wrote a line-shaped P down domain between the source and drain. Given the high current switching ratio, the nanowire conductance remains orders of magnitude higher than the insulating background over the entire V bg -range. Writing P down nanowire domains along different orientations thus enables angle-resolved conductance measurements on the same sample. Figure 3 shows the results obtained on a 1L ReS FET using this approach. The b -axis of this sample is perpendicular to the channel orientation [Fig. 2(a)] . We wrote 300-400 nm wide P down nanowires connecting the source and drain electrodes [Figs. 2(b)-2(e)], and mapped out the corresponding conduction of the device. Figure 2(f) shows the corresponding channel sheet conductance 𝜎 (cid:3404) (cid:3013)(cid:3024) (cid:3010) (cid:3279) (cid:3023) (cid:3279) , or 2D conductivity, as a function of V bg for the nanowires. Here L and W are the length and width of the nanowire, respectively, and the angle 𝜃 is defined with respect to the b -axis of ReS . It is evident that there are two distinct transfer characteristics for these four angles. For the nanowire along the directions of 𝜃 (cid:3404) 30 (cid:2925) and (cid:2925) , which are oriented close to the b -axis, the channel remains highly conductive with n -type characteristic over the entire V bg -range. In contrast, for 𝜃 (cid:3404) 75 (cid:2925) and (cid:2925) , which are close to the direction perpendicular to the b -axis, the ReS nanowires exhibit very low conductance, with the channel effectively turned into p -type at 𝑉 (cid:2912)(cid:2917) (cid:3407) 20 𝑉 . At 𝑉 (cid:2912)(cid:2917) (cid:3404) 20 V , ReS exhibits up to 7.9 × -fold change in conductance between the directions of 𝜃 (cid:3404) 30 (cid:2925) and 𝜃 (cid:3404)75 (cid:2925) , which also corresponds to a change of carrier type from electron- to hole-doped behavior. An even larger transport anisotropy is expected between 𝑉 (cid:2912)(cid:2917) (cid:3404) 20 V and 35 V, where the channel is too insulating along 𝜃 (cid:3404) 75 (cid:2925) direction to be measured. To map out the angle-resolved transport, we extracted the conductivity of nanowires in various directions at the same V bg , at which the sample is turned on and electron-doped in all directions. Figures 3(a) shows the polar plot of 𝜎 for the 1L ReS sample. The sheet conductance measured at the angles 𝜃 (cid:3404) 30 (cid:2925) and (cid:2925) differs by a factor of 56. Similar electron conduction anisotropy has been observed in the 2L [Fig. 3(b)] and 4L [Fig. 3(c)] ReS samples (Supplemental Materials). While all samples exhibit high conductance in the vicinity of the b -axis ( 𝜃 (cid:3404) 0 (cid:2925) ) and low conductance when 𝜃 approaches (cid:2925) , the anisotropy is strongly enhanced in the few-layer sample. A giant anisotropic conductance ratio of 1.7 × has been observed in the 4L ReS device between the directions of 𝜃 (cid:3404) 0 (cid:2925) and (cid:2925) [Fig. 3(c)]. Unlike the modulation observed in Fig. 2(f), this change does not involve the change of carrier type, thus reflecting solely the electron transport anisotropy. Note that the observed angular dependence of 𝜎 is not fully symmetric with respect to the 𝜃 (cid:3404) 0° axis, which does not correspond to a mirror plane. As 1T’-ReS belongs to the space group 𝑃1(cid:3364) , it only has an inversion symmetry. The conductance in ReS is determined by the electron mobility 𝜇 (cid:3404) 𝑒𝜏/𝑚 ∗ , where 𝑒 is the electron charge, 𝜏 is the average scattering time induced by defects, impurities, or phonons, and 𝑚 ∗ is the effective mass determined by the band structure 𝐸(cid:4666)𝒌(cid:4667) as 𝑚 ∗ (cid:3404) ℏ (cid:3118) (cid:3105) (cid:3118) (cid:3006)(cid:4666)𝒌(cid:4667)/(cid:3105)𝒌 (cid:3118) . To understand the role of band dispersion on the anisotropic conduction, we performed the first-principles DFT calculations for the band structures of 1L [Fig. 4(a)], 2L [Fig. 4(b)], and 4L [Fig. 4(c)] ReS . The details of the calculation can be found in the Supplemental Materials [32-35]. The result obtained for 1L ReS is consistent with the previous report [20]. For all three layer numbers, the band dispersion along the k x direction ( b -axis) at the CBM exhibits a larger curvature compared with that along the k y direction [Figs. 4(d)-(f)], yielding a lighter 𝑚 ∗ along b -axis ( 𝜃 (cid:3404) 0° ) and a heavier 𝑚 ∗ perpendicular to b -axis ( 𝜃 (cid:3404) 90° ). The anisotropy of the band dispersion, on the other hand, is significantly enhanced with increasing layer thickness of ReS . For all layer thicknesses, the inversion symmetry of the space group 𝑃1(cid:3364) has been preserved in the calculated 𝑚 ∗ (Supplemental Materials). Figures 4(g)-(i) show the normalized ∗ vs. 𝜃 relation superimposed onto the normalized conductance ( 𝜎 (cid:2924)(cid:2925)(cid:2928)(cid:2923) ) data. For 1L ReS , ∗ shows a similar 𝜃 (cid:3398) dependence as the measured 𝜎 , i.e. , the maximum values appear at orientations close to 𝜃 (cid:3404) 0° and and the minimum values appear close to 𝜃 (cid:3404) 90° and 27 directions [Fig. 4(g)]. The variation in ∗ , however, cannot fully account for the relative change in 𝜎 (cid:3041)(cid:2925)(cid:2928)(cid:2923) . Considering that the band anisotropy also affects the election-phonon scattering, we incorporated the contribution of phonon scattering in mobility 𝜇 by using the Takagi formula [36-38]: 𝜇 (cid:3036) (cid:3404) (cid:3032)ℏ (cid:3119) (cid:3004) (cid:3284) (cid:3038) (cid:3251) (cid:3021)(cid:3040) (cid:3284)∗ (cid:3040) (cid:3279)∗ (cid:3005) (cid:3284)(cid:3118) . (1) Here 𝑖 refers to the conduction direction, and 𝑚 (cid:3031)∗ (cid:3404) (cid:3493)𝑚 (cid:3051)∗ 𝑚 (cid:3052)∗ is the density-of-state effective mass for an anisotropic electronic band. The deformation potential constant is defined as 𝐷 (cid:3036) (cid:3404) (cid:3105)(cid:3006) (cid:3271) (cid:3105)(cid:3084) (cid:3284) , where 𝐸 (cid:3023) is the energy of the conduction band minimum (CBM) and 𝜀 (cid:3036) is a strain applied along direction 𝑖 . The 2D elastic modulus along the conduction direction is calculated using 𝐶 (cid:3036) (cid:3404) (cid:2870)(cid:3105) (cid:3118) (cid:3006) (cid:3178)(cid:3173)(cid:3178)(cid:3159)(cid:3170) (cid:3020) (cid:3116) (cid:3105)(cid:3084) (cid:3284)(cid:3118) , where 𝐸 (cid:2930)(cid:2925)(cid:2930)(cid:2911)(cid:2922) is the total energy of ReS and 𝑆 (cid:2868) is the area of the 2D ReS without strain. As shown in Fig. 4(g), the modeled 𝜇 vs. 𝜃 relation shows improved agreement with 𝜎 (cid:2924)(cid:2925)(cid:2928)(cid:2923) (cid:4666)𝜃(cid:4667) , indicating that the anisotropic conductance in 1L ReS is resulted from the convoluted effects of the anisotropic band dispersion and the phonon scattering. On the other hand, we find that 𝜎 (cid:2924)(cid:2925)(cid:2928)(cid:2923) (cid:4666)𝜃(cid:4667) for the 2L [Fig. 4(h)] and 4L [Fig. 4(i)] ReS can be well explained by the calculated ∗ vs. 𝜃 relation. This is because the anisotropy of the conduction band dispersion is significantly enhanced in thicker ReS [Figs. 4(d)-(f)], so that the angular dependence of electron-phonon scattering plays a relatively minor role in the electron transport in 2L and 4L ReS . These findings are in sharp contrast with the previous study of angle-resolved transport in ReS using a circular sample geometry with multiple point-contacts fabricated along various directions [20], where the experimentally extracted anisotropic conductance ratio is significantly smaller than the theoretical prediction. In that approach, the conductance was measured between a pair of oppositely located point-contacts, while the local current path within the sample cannot be controlled. The measurements thus collect current flows over a wide range of angle distributions, making it challenging to quantitatively analyze the directional conduction. What is intriguing is the emergence of a nearly flat band in 4L ReS at the CBM along the k y direction [Fig. 4 (f)], leading to a drastic increase in 𝑚 ∗ for 𝜃 (cid:3404) 90° (Supplemental Materials), which can well account for the giant electron transport anisotropy observed in 4L ReS . Such band dispersion highly resembles what is expected from one-dimensional graphene superlattices [39]. It is thus conceivable to design novel electron lensing applications by integrating few-layer ReS with other isotropic vdW materials, which eliminates the need to form the superlattice potential. The flat band and the associated heavy effective mass also make few-layer ReS a promising platform for hosting collective phenomena, such as magnetism and superconductivity. In summary, we have resolved for the first time the giant transport anisotropy in mono- to few-layer ReS by creating directional conducing paths through the nanoscale ferroelectric control, which reveals a 2D conductivity ratio exceeding 7.9 × between the directions along and perpendicular to b -axis. Our DFT calculations point to the band origin of this intriguing behavior, and revealed the emergence of a flat band in few-layer ReS . We expect our approach to be widely applicable to other anisotropic vdW materials, providing a novel route for resolving nanoscale electronic signatures of emergent band properties and designing collective phenomena and electron lensing applications in vdW heterostructures. Acknowledgements
We thank Xi Huang and Yongfeng Lu for the access to the Raman system. This work was primarily supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0016153 (sample preparation and characterization, FET device fabrication and characterization). S.S. and S.D. acknowledge the support of the Nebraska Center for Energy Research. The work of D.-F.S. and E.Y.T. was supported by the NSF Nebraska Materials Research Science and Engineering Center (MRSEC) Grant No. DMR-1420645 (theoretical modeling). The research was performed in part in the Nebraska Nanoscale Facility: National Nanotechnology Coordinated Infrastructure and the Nebraska Center for Materials and Nanoscience, which are supported by the National Science Foundation under Award ECCS: 2025298, and the Nebraska Research Initiative. References [1] S. Barraza-Lopez, F. Xia, W. Zhu, and H. Wang, Beyond Graphene: Low-Symmetry and Anisotropic 2D Materials, Journal of Applied Physics , 140401 (2020). [2] C. Gong, Y. Zhang, W. Chen, J. Chu, T. Lei, J. Pu, L. Dai, C. Wu, Y. Cheng, T. Zhai, L. Li, and J. Xiong, Electronic and Optoelectronic Applications Based on 2D Novel Anisotropic Transition Metal Dichalcogenides, Advanced Science , 1700231 (2017). [3] X. Wang, A. M. Jones, K. L. Seyler, V. Tran, Y. Jia, H. Zhao, H. Wang, L. Yang, X. Xu, and F. Xia, Highly anisotropic and robust excitons in monolayer black phosphorus, Nature Nanotechnology , 517 (2015). [4] X. Meng, Y. Zhou, K. Chen, R. H. Roberts, W. Wu, J. F. Lin, R. T. Chen, X. Xu, and Y. Wang, Anisotropic Saturable and Excited‐State Absorption in Bulk ReS , Advanced Optical Materials , 1800137 (2018). [5] Q. Cui, R. A. Muniz, J. Sipe, and H. Zhao, Strong and anisotropic third-harmonic generation in monolayer and multilayer ReS , Physical Review B , 165406 (2017). [6] D. Li, C. Wei, J. Song, X. Huang, F. Wang, K. Liu, W. Xiong, X. Hong, B. Cui, and A. Feng, Anisotropic enhancement of second-harmonic generation in monolayer and bilayer MoS by integrating with TiO nanowires, Nano Letters , 4195 (2019). [7] A. Nemilentsau, T. Low, and G. Hanson, Anisotropic 2D materials for tunable hyperbolic plasmonics, Physical Review Letters , 066804 (2016). [8] C. Wang, G. Zhang, S. Huang, Y. Xie, and H. Yan, The Optical Properties and Plasmonics of Anisotropic 2D Materials, Advanced Optical Materials , 1900996 (2020). [9] T. Low, A. Chaves, J. D. Caldwell, A. Kumar, N. X. Fang, P. Avouris, T. F. Heinz, F. Guinea, L. Martin-Moreno, and F. Koppens, Polaritons in layered two-dimensional materials, Nature Materials , 182 (2017). [10] H. Yang, H. Jussila, A. Autere, H.-P. Komsa, G. Ye, X. Chen, T. Hasan, and Z. Sun, Optical Waveplates Based on Birefringence of Anisotropic Two-Dimensional Layered Materials, ACS Photonics , 3023 (2017). [11] N. Papadopoulos, R. Frisenda, R. Biele, E. Flores, J. R. Ares, C. Sánchez, H. S. J. van der Zant, I. J. Ferrer, R. D'Agosta, and A. Castellanos-Gomez, Large birefringence and linear dichroism in TiS nanosheets, Nanoscale , 12424 (2018). [12] Z. Qiu, M. Trushin, H. Fang, I. Verzhbitskiy, S. Gao, E. Laksono, M. Yang, P. Lyu, J. Li, J. Su, M. Telychko, K. Watanabe, T. Taniguchi, J. Wu, A. H. C. Neto, L. Yang, G. Eda, S. Adam, and J. Lu, Giant gate-tunable bandgap renormalization and excitonic effects in a 2D semiconductor, Science Advances , eaaw2347 (2019). [13] Y. Liu, J. N. B. Rodrigues, Y. Z. Luo, L. Li, A. Carvalho, M. Yang, E. Laksono, J. Lu, Y. Bao, H. Xu, S. J. R. Tan, Z. Qiu, C. H. Sow, Y. P. Feng, A. H. C. Neto, S. Adam, J. Lu, and K. P. Loh, Tailoring sample-wide pseudo-magnetic fields on a graphene–black phosphorus heterostructure, Nature Nanotechnology , 828 (2018). [14] R. Plumadore, M. M. Al Ezzi, S. Adam, and A. Luican-Mayer, Moiré patterns in graphene–rhenium disulfide vertical heterostructures, Journal of Applied Physics , 044303 (2020). [15] S. Barraza-Lopez, B. M. Fregoso, J. W. Villanova, S. S. Parkin, and K. Chang, Colloquium: Physical properties of group-IV monochalcogenide monolayers, arXiv:2009.04341 (2020). [16] F. Xia, H. Wang, J. C. M. Hwang, A. H. C. Neto, and L. Yang, Black phosphorus and its isoelectronic materials, Nature Reviews Physics , 306 (2019). [17] S. Tongay, H. Sahin, C. Ko, A. Luce, W. Fan, K. Liu, J. Zhou, Y.-S. Huang, C.-H. Ho, J. Yan, D. F. Ogletree, S. Aloni, J. Ji, S. Li, J. Li, F. M. Peeters, and J. Wu, Monolayer behaviour in bulk ReS due to electronic and vibrational decoupling, Nature Communications , 3252 (2014). [18] J. L. Webb, L. S. Hart, D. Wolverson, C. Chen, J. Avila, and M. C. Asensio, Electronic band structure of ReS by high-resolution angle-resolved photoemission spectroscopy, Physical Review B , 115205 (2017). [19] B. S. Kim, W. Kyung, J. Denlinger, C. Kim, and S. Park, Strong One-Dimensional Characteristics of Hole-Carriers in ReS and ReSe , Scientific Reports , 1 (2019). [20] E. Liu, Y. Fu, Y. Wang, Y. Feng, H. Liu, X. Wan, W. Zhou, B. Wang, L. Shao, and C.-H. Ho, Integrated digital inverters based on two-dimensional anisotropic ReS field-effect transistors, Nature communications , 1 (2015). [21] H. Ryu, K. Xu, D. Li, X. Hong, and W. Zhu, Empowering 2D nanoelectronics via ferroelectricity, Applied Physics Letters , 080503 (2020). [22] X. Hong, Emerging ferroelectric transistors with nanoscale channel materials: the possibilities, the limitations, Journal of Physics: Condensed Matter , 103003 (2016). [23] Z. Xiao, J. Song, D. K. Ferry, S. Ducharme, and X. Hong, Ferroelectric-Domain-Patterning-Controlled Schottky Junction State in Monolayer MoS , Physical Review Letters , 236801 (2017). [24] G. Wu, B. Tian, L. Liu, W. Lv, S. Wu, X. Wang, Y. Chen, J. Li, Z. Wang, S. Wu, H. Shen, T. Lin, P. Zhou, Q. Liu, C. Duan, S. Zhang, X. Meng, S. Wu, W. Hu, X. Wang, J. Chu, and J. Wang, Programmable transition metal dichalcogenide homojunctions controlled by nonvolatile ferroelectric domains, Nature Electronics , 43 (2020). [25] L. Lv, F. Zhuge, F. Xie, X. Xiong, Q. Zhang, N. Zhang, Y. Huang, and T. Zhai, Reconfigurable two-dimensional optoelectronic devices enabled by local ferroelectric polarization, Nature Communications , 1 (2019). [26] C. H. Li, K. M. McCreary, and B. T. Jonker, Spatial Control of Photoluminescence at Room Temperature by Ferroelectric Domains in Monolayer WS /PZT Hybrid Structures, ACS Omega , 1075 (2016). [27] B. Wen, Y. Zhu, D. Yudistira, A. Boes, L. Zhang, T. Yidirim, B. Liu, H. Yan, X. Sun, and Y. Zhou, Ferroelectric-driven exciton and trion modulation in monolayer molybdenum and tungsten diselenides, ACS Nano , 5335 (2019). [28] D. Li, X. Huang, Z. Xiao, H. Chen, L. Zhang, Y. Hao, J. Song, D.-F. Shao, E. Y. Tsymbal, Y. Lu, and X. Hong, Polar coupling enabled nonlinear optical filtering at MoS /ferroelectric heterointerfaces, Nature Communications , 1422 (2020). [29] D. A. Chenet, O. B. Aslan, P. Y. Huang, C. Fan, A. M. van der Zande, T. F. Heinz, and J. C. Hone, In-Plane Anisotropy in Mono- and Few-Layer ReS Probed by Raman Spectroscopy and Scanning Transmission Electron Microscopy, Nano Letters , 5667 (2015). [30] S. Ducharme, S. P. Palto, V. M. Freidkin, and L. M. Blinov, Ferroelectric Polymer Langmuir-Blodgett Films (Academic Press, San Diego, 2002), Vol. 3, Handbook of Thin Film Materials. [31] S. Bertolazzi, P. Bondavalli, S. Roche, T. San, S. Y. Choi, L. Colombo, F. Bonaccorso, and P. Samorì, Nonvolatile memories based on graphene and related 2D materials, Advanced Materials , 1806663 (2019). [32] P. E. Blöchl, Projector augmented-wave method, Physical Review B , 17953 (1994). [33] G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Physical Review B , 1758 (1999). [34] J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Physical Review Letters , 3865 (1996). [35] S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, Journal of Chemical Physics , 154104 (2010). [36] S.-i. Takagi, A. Toriumi, M. Iwase, and H. Tango, On the universality of inversion layer mobility in Si MOSFET's: Part I-effects of substrate impurity concentration, IEEE Transactions on Electron Devices , 2357 (1994). [37] S.-i. Takagi, A. Toriumi, M. Iwase, and H. Tango, On the universality of inversion layer mobility in Si MOSFET's: Part II-effects of surface orientation, IEEE Transactions on Electron Devices , 2363 (1994). [38] S. Poncé, W. Li, S. Reichardt, and F. Giustino, First-principles calculations of charge carrier mobility and conductivity in bulk semiconductors and two-dimensional materials, Reports on Progress in Physics , 036501 (2020). [39] C.-H. Park, Y.-W. Son, L. Yang, M. L. Cohen, and S. G. Louie, Electron Beam Supercollimation in Graphene Superlattices, Nano Letters , 2920 (2008). FIG. 1. (a) Schematic crystal structure of ReS . (b) Device schematic. (c) PFM phase images of a 1L ReS FET with the P(VDF-TrFE) top-gate uniformly polarized in the P down (top) and P up (bottom) states. (d) I d vs. V bg for the 1L ReS FET in (c) in the P down , P up , and no poling states of P(VDF-TrFE). (e) I d vs. V bg for a 4L ReS in different polar states of P(VDF-TrFE). FIG. 2. (a) Optical image of a 1L ReS FET device. Insets: laboratory coordinate system (left) and crystalline axes of ReS (right). (b-e) PFM phase images of P down nanowires created on the uniform P up state background along different 𝜃 directions with respect to b -axis of ReS : (b) 𝜃 (cid:3404) 30 (cid:2925) , (c) 𝜃 (cid:3404) 75 (cid:2925) , (d) 𝜃 (cid:3404) 90 (cid:2925) , and (e) 𝜃 (cid:3404) 150 (cid:2925) . (f) 𝜎 vs. V bg corresponding to the four nanowire orientations shown in (b-e). FIG. 3. Polar plots of 𝜎 of (a) a 1L ReS at V bg = 40 V, (b) a 2L ReS at V bg = -40 V, and (c) a 4L ReS at V bg = 10 V. The dashed lines serve as the guide to the eye. Insets in (b): The corresponding PFM images of directional P down nanowires patterned in the uniform P up domain. The top left image corresponds to the initial state before the nanowire patterning. All scale bars are 3 m. FIG. 4. (a-c) Band structures of (a) 1L, (b) 2L, and (c) 4L ReS . Insets in (a) show the symmetry points in the first Brillouin zone (left), where k x and k y are the same as x - and y -direction in the real space unit cell used for calculation (right). (d-f) The corresponding expanded views near the Γ point. (g) Normalized conductivity 𝜎 norm vs. 𝜃 (left axis) for the 1L ReS in Fig. 3a superimposed with the normalized 1/ m *norm and norm (right axis) . (h and i) 𝜎 norm vs. 𝜃 (left axis) for (h) 2L and (i) 4L ReS superimposed with 1/ m *norm (right axis) ..