⇦Chinese Physics Letters, 2023, Vol. 40, No. 11, Article code 117102 Ferroelectricity and Large Rashba Splitting in Two-Dimensional Tellurium Yao Wang (王垚)1,2†, Zhenzhen Lei (雷珍珍)1†, Jinsen Zhang (张金森)1, Xinyong Tao (陶新永)1, Chenqiang Hua (华陈强)3,4*, and Yunhao Lu (陆赟豪)3 Affiliations 1College of Materials Science and Engineering, Zhejiang University of Technology, Hangzhou 310014, China 2Moganshan Research Institute at Deqing County Zhejiang University of Technology, Huzhou 313000, China 3School of Physics, Zhejiang University, Hangzhou 310027, China 4Zhongfa Aviation Institute of Beihang University, Hangzhou 311115, China Received 27 August 2023; accepted manuscript online 10 October 2023; published online 7 November 2023 †They contributed equally to this work.
*Corresponding author. Email: huachenqiang@zju.edu.cn Citation Text: Wang Y, Lei Z Z, Zhang J S et al. 2023 Chin. Phys. Lett. 40 117102    Abstract Two-dimensional (2D) ferroelectric (FE) systems are promising candidates for non-volatile nanodevices. Previous studies mainly focused on 2D compounds. Though counter-intuitive, here we propose several new phases of tellurium with (anti)ferroelectricity. Two-dimensional films can be viewed as a collection of one-dimensional chains, and lone-pair instability is responsible for the (anti)ferroelectricity. The total polarization is determined to be $0.34 \times 10^{-10}$ C/m for the FE ground state. Due to the local polarization field in the FE film, we show a large Rashba splitting ($\alpha_{\scriptscriptstyle{\rm R}} \sim 2$ eV$\cdot$Å) with nonzero spin Hall conductivity for experimental detection. Furthermore, a dipole-like distribution of Berry curvature is verified, which may facilitate a nonlinear Hall effect. Because Rashba-splitting/Berry-curvature distributions are fully coupled with a polarization field, they can be reversed through FE phase transition. Our results not only broaden the elemental FE materials, but also shed light on their intriguing transport phenomena.
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 DOI:10.1088/0256-307X/40/11/117102 © 2023 Chinese Physics Society Article Text Since the successful experimental exfoliation of graphene,[1] a variety of two-dimensional (2D) materials have been proposed theoretically and synthesized experimentally.[2-12] Since the $z$-axis direction is confined to the sub-nanometer scale, the properties of 2D materials can be different from their bulk counterparts[13,14] and thus they are promising for high-speed nanodevices. In contrast to the significant depolarization effect in ABO$_{3}$ perovskite films, stable antiferroelectric/ferroelectric (AFE/FE) orders have been demonstrated in many 2D systems, such as improper ferroelectrics, sliding ferroelectrics, and moiré ferroelectrics.[15-25] It is worth noting that all these reported 2D FE materials are based on compounds with two or more elements, whereas elemental FE systems were rarely reported.[26,27] Recently, AFE and FE orders have been predicted in single-element group-V monolayers.[28] The underlying physics of the in-plane polarization is related to the weak and anisotropic $sp$-orbital hybridization, leading to buckled structure without inversion symmetry. Furthermore, stable FE properties have been proposed in monolayer/multilayer Te flakes, where the localized lone pair due to the multivalency nature of Te is key to trigger FE phase transition.[29,30] Interestingly, through scanning tunneling microscopy (STM) and Kelvin probe force microscopy (KPFM) measurements, Gou et al. observed the FE state and domain wall in buckled monolayer Bi,[31] which is the first documented experiment to show single-element ferroelectricity. These successes compel us to explore more elementary FE/AFE systems with versatile properties, including controllable spin-splitting, coupled topological order and combined magnetism. In nature, Te has an inversion asymmetric bulk structure with multivalent metalloid properties, which may facilitate the separation of positive and negative charge centers.[29] To date, many works have been carried out about Te systems, such as new allotropes, multivalence, charge-governed phase manipulation, spin-orbit coupling (SOC) splitting, band topology, and semiconductor-to-metal transition in nanoribbons.[32-40] Among them, the intriguing properties of Te, including large SOC and metalloid properties, compel the exploration of more FE/AFE structures. In this Letter, we propose a new phase of chained one-dimensional (1D) Te with large spin-splitting and construct several 2D structures based on this 1D system. We show that these 2D Te systems exhibit in-plane (anti)ferroelectricity and the FE configuration is in the ground state. The in-plane atomic displacement breaks the centrosymmetry and leads to spontaneous polarization with the transition barrier of about 0.2 eV/u.c. (u.c. denotes unit cell) through the centrosymmetric phase. The calculated value of spontaneous polarization is about $0.34 \times 10^{-10}$ C/m, which is comparable to that of previously reported 2D FE materials,[28,41] and the estimated transition temperature is about 40 K. Furthermore, clear band-splitting is observed according to the spontaneous breaking of inversion symmetry, where the Rashba effect is controllable under an electric field since it is combined with the spontaneous polarization. Reversible Berry-curvature distribution is also discussed regarding a possible nonlinear Hall effect. Our findings demonstrate several new single-element FE/AFE materials with intriguing properties. Computational Details and Methods. All theoretical calculations were performed based on density-functional theory (DFT) methods implemented in the Vienna ab initio Simulation Package (VASP).[42] The Perdew-Burke-Ernzerhof realization of the generalized gradient approximation was used for the exchange correlation.[43] The project augmented wave method was employed to model the ionic potentials.[44] The energy cutoff of the plane wave was set to be at 500 eV. The vacuum space along the $z$-direction was larger than 18 Å so as to separate the periodic images. The thresholds of total energy and optimization were $10^{-6}$ eV and 0.001 eV/Å, respectively. The Brillouin zone was gridded with $8 \times 1 \times 1/8 \times 8 \times 1$ $k$-mesh for 1D chain/2D film, respectively, which was increased to $17 \times 1 \times 1$ and $17 \times 17 \times 1$ for self-consistent calculations. For all systems, van der Waals (vdW) correction with a DFT-D3 approach was adopted to capture the intercell-chain interactions.[45] Phonon spectra were calculated using density functional perturbation theory (DFPT) to check the dynamic stability and a $4 \times 4 \times 1$ supercell was used.[46] Ab initio molecular dynamics (AIMD) was studied with the NVT ensemble, as implemented in the VASP code. The formation energy reads \begin{align} E_{\rm formation}=E_{\rm total/atom}-E_{\rm bulk\,Te/atom}, \tag {1} \end{align} where $E_{\rm total/atom}$ is the total energy of 1D-Te chain and 2D-Te films per atom, respectively. $E_{\rm bulk\,Te/atom}$ denotes the energy of bulk Te per atom. The binding energy is defined as \begin{align} E_{\rm binding}=\frac{E_{\rm total}-{nE}_{\rm chain}}{n}, \tag {2} \end{align} where $E_{\rm total}$ is the total energy of bulk Te or 2D Te. $E_{\rm chain}$ is the energy of single 1D chain with $n$ denoting the number of Te chains. According to the Kubo formula,[47,48] the spin Hall conductivity can be written as \begin{align} \sigma_{x y}^{{\rm spin}\,z}&(\mu,\omega)=\hslash \int_{\rm BZ} {\frac{d^{3}k}{(2\pi)^{3}}\sum\limits_n f_{n\boldsymbol{k}}}\notag\\ &\times\sum\limits_{m\neq n} \frac{2\mathrm{Im}[\langle nk|\hat{j}_{x}^{{\rm spin}\,z}|mk\rangle\langle mk|-e\hat{v}_{y}|nk\rangle]}{(\epsilon_{n\boldsymbol{k}}-\epsilon_{m\boldsymbol{k}})^{2}-(\hslash \omega +i\eta)^{2}}, \tag {3} \end{align} where $n$ and $m$ are band indexes; $\epsilon_{n}$ and $\epsilon_{m}$ are the eigenvalues; $f_{n\boldsymbol{k}}$ is the Fermi-Dirac distribution function with respect to the chemical potential $\mu$; BZ denotes the first Brillouin zone; $\hat{j}_{x}^{{\rm spin}\, z}=\frac{1}{2}\{\hat{S}_{z},\hat{v}_{x}\}$ is the spin current operator and $\hat{S}_{z}=\frac{\hslash}{2}\hat{\sigma}_{z}$ is the spin operator; $\hat{v}_{y}=\frac{1}{\hslash }\frac{\partial H(\boldsymbol{k})}{\partial k_{y}}$ is the velocity operator, and the frequency $\omega$ and $\eta$ are set to zero in the direct-current (dc) clean limit. The Berry-phase method was employed to evaluate the polarization of 2D Te.[49] The ferroelectric switching pathway was obtained by using the climbing-image nudged elastic band (CINEB) method.[50] The Berry curvature was obtained by Wannier 90.[51] VASPKIT was used for the preprocessing of structural data[52] and the atomic configurations were visualized through VESTA.[53] The Te structures here can be realized through global optimization and searching approach as implemented in the Crystal Structure Analysis by Particle Swarm Optimization (CALYPSO) code.[54] Square-Like Te Chain. First, we start with a new phase of chained 1D Te. According to the $s^{2}p^{4}$ configuration[30] and large $s$–$p$ separation of Te, the bonding behavior is usually considered to be dominated by $p$ electrons.[32,34,55] Accordingly, we construct a square-like Te (s-Te) chain along the $x$-direction via the CALYPSO method[54] and the optimized structure is shown in Fig. 1(a), where each atom is bonded to two adjacent Te atoms. Compared to the standard Te-chain (1D $\alpha$-Te), both systems have similar formation energy, i.e., 0.45/0.50 eV/atom for 1D s-Te and $\alpha$-Te, respectively (see Table 1). One-dimensional s-Te holds a $P2_{1}$ space group (SG), which is a chiral SG containing only one screw rotation symmetry, i.e., the two-fold rotation symmetry of the $x$-axis ($C_{2x}$) followed by a translation along the $x$-direction. This symmetry is close to the $P2$ SG of 1D $\alpha$-Te and both are chiral. The dynamic stability of 1D s-Te is investigated using a phonon spectrum prior to establishing the electronic properties, as shown in Fig. 1(b). Except for the chiral-rotation mode at $\varGamma$, all the vibration modes are positive, indicating probable stability with the support of the substrate or encapsulation [see Fig. S1 in the Supporting Information for a similar phonon spectrum of 1D $\alpha$-Te].
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Fig. 1. (a) Top view and side view of 1D s-Te. (b) Phonon spectrum of 1D s-Te. Bottom mode at $\varGamma$ is imaginary, representing a chiral-rotation mode along $x$-direction (see inset for the snapshot of this mode). Band structures of 1D s-Te (c) without SOC and (d) with SOC. $S_{x}$ component is projected (see $S_{y}$/$S_{z}$ in Fig. S2).
We then focus on the electronic properties of 1D s-Te. When SOC is excluded, each band has a two-fold degeneracy, and it is an indirect-gap semiconductor with both the conduction band minimum (CBM) and valence band maximum (VBM) located near $X$ [see Fig. 1(c)], conforming to the coordination number of two for 1D s-Te. After the inclusion of SOC, significant band-splitting is found near $X$ in the band structure since Te is a heavy element, as illustrated in Fig. 1(d). As a result, the band gap decreases from 1.21 to 1.05 eV due to the large splitting near $X$. This band-splitting in 1D s-Te can also be understood through the symmetry analysis discussed above, from which it is clear that 1D s-Te is inversion asymmetric, and SOC can naturally split the degenerate bands. Two-Dimensional Te Film. As reported previously, 1D $\alpha$-Te chains can be connected to form 2D $\alpha$-Te through quasi-vdW interactions.[32] Thus, we construct a 2D s-Te film (denoted as phase A) by stacking the 1D s-Te chains along the $y$-direction, as shown in Fig. 2(a), with the optimized lattice constants of 6.05/6.00 Å along the $x$/$y$-directions, respectively. This 2D s-Te film inherits the $P2_{1}$ SG symmetry of the 1D parent, which is reflected by the asymmetric charge distribution [electron localization function] in Fig. S3(a). According to the stacking rule from 1D to 2D, we can reasonably define two typical Te–Te interactions, i.e., intra/inter-chain interactions, which are naturally expected to be different from the aspect of symmetry. Indeed, as illustrated in Fig. 2(b), we find stronger bonding/antibonding strengths for intra/inter-chain interactions by calculating the crystal orbital Hamiltonian population (COHP).[56] In addition, it is clear to see the difference between intra/inter-cell bonds along the $x$-direction intuitively, and COHP results demonstrate the stronger bonding strength for the intercell Te–Te interaction [see Fig. S4(a)]. These results indicate the possible (anti)ferroelectricity in 2D s-Te along the $x$ and/or $y$ directions. According to the 2D structure and uneven bonding strength, a highly symmetric structure (phase B) is constructed, as illustrated in Fig. 2(c). Different from the $P2_{1}$ SG, it now has $P4/nmm$ SG with mirror symmetries ($M_{x}$/$M_{y}$) along the $x/y$-directions as well as inversion symmetry, which naturally enforces the intra/inter-chain interactions to be the same [Fig. S4(c)]. This highly symmetric structure could be unstable and may trigger structural distortions due to the lone-pair-like charge-distribution [Fig. S3(c)].[28,32] Therefore, we calculate the corresponding phonon spectrum [Fig. 2(d)] to explore the possible distortion, and unsurprisingly, it is dynamically unstable with four distinct soft-modes near $\varGamma$ and the BZ boundary. In particular, the $\lambda_{1}$ and $\lambda_{2}$ modes directly lead to the aforementioned phase A and one new structure [denoted as phase C in Fig. 2(e)], respectively. This new phase C is 12 meV/u.c. lower in energy than phase A (see Table 2). Interestingly, the chain formed in phase C is along the [110] direction now with SG $Abm2$. This SG has broken the inversion symmetry, resulting in non-symmetric charge distribution compared to that of phase B (Fig. S3). From the COHP results in Figs. 2(f) and S4(b), phase C exhibits different intra/inter-cell and intra/inter-chain interactions along the $x/y$-directions, respectively, similar to phase A. The correspondence between soft modes and non-symmetric structures as well as the non-equivalent bonds compels the exploration of possible (anti)ferroelectricity in these 2D Te systems.
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Fig. 2. (a) Top/side views of stacked 2D s-Te (phase A). Single unit cell is marked by the dashed line. (b) COHP results for intra/inter-chain interactions in (a). (c) Top/side views of highly symmetric phase B. Dashed lines represent the mirror symmetries. (d) Phonon spectrum of phase B. Here $\lambda_{1}$, $\lambda_{2}$, $\lambda_{3}$, and $\lambda_{4}$ indicate the soft optical modes. Inset denotes the Brillouin zone. (e) Top/side views of phase C. Single unit cell is marked by the dashed lines. (f) COHP results for intra/inter-chain interactions in (e).
In addition to the BZ center, we find one soft mode near $X$ ($\lambda_{3}$) and another one near $M$ ($\lambda_{4}$). As shown in Fig. S5, $\lambda_{4}$ exhibits a special vibration mode and the corresponding distortion is not stable during structural optimization. For the $\lambda_{3}$ mode near $X$, one new phase D with a $2 \times 1 \times 1$ supercell is constructed and it is illuminating to see that this structure is similar to phase A, as shown in Fig. S6(a). In particular, phase D is the anti-distorted version of phase A along the $x$ direction. After the energy comparison, we find that phase C is the ground state, which is 227 and 8.0 meV/u.c. lower in energy than phases B and D, respectively (see Table 2).
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Fig. 3. (a) Calculated phonon spectrum for phase A. (b) Calculated phonon spectrum for phase C. Small imaginary modes around $\varGamma$ originate from the calculation-method error and this negligible part thus can be neglected.
Table 1. Energy comparison between different systems.
System $E_{\rm formation}$
(eV/atom)		 $E_{\rm binding}$
(eV)		 Synthesized
Bulk Te $-1.51$ Yes
1D $\alpha$-Te 0.50 Yes
1D s-Te 0.45 Not yet
Monolayer $\alpha$-Te 0.30 $-$0.62 Yes
Bilayer $\alpha$-Te 0.17 $-1.$01 Not yet
2D s-Te (phase C) 0.34 $-$0.62 Not yet
2D s-Te (phase A) 0.34 $-$0.61 Not yet
To confirm the energetic stability, the binding and formation energies are calculated. The binding energy for phase C is $-$0.62 eV, similar to $-0.62$/$-1.01$ eV for mono/bilayer $\alpha$-Te (see Table 1). The calculated value of the formation energy is 0.34 eV/atom, which is also comparable to 0.30/0.17 eV/atom for mono/bilayer $\alpha$-Te, as listed in Table 1, indicating that 2D s-Te can probably be synthesized experimentally. As shown in Fig. 3, the phonon spectra for phases A and C are calculated with negligible imaginary modes, demonstrating their dynamic stability.
Table 2. Energy comparison between proposed Te structures. The energy of phase C is set as a reference value for comparison.
Structure Energy (meV/u.c.)
Phase A 12
Phase B 227
Phase C 0
Phase D 8
Ferroelectricity and Antiferroelectricity. Next, we verify the ferroelectricity and antiferroelectricity in 2D Te structures. For details, we define the parameters $d/h$ for these structures to label the local displacements along the $x/y$ axes (Fig. 4). Obviously, the local displacements are nonzero, and $d$ is non-equivalent to $h$ for phase A. By reversing all the displacements together ($d$ goes to $-d$, and $h$ goes to $-h$), phase A$'$ can be achieved with the same energy. When $d/h$ goes to zero, the structure will transition back to phase B. Using the CINEB method, it is demonstrated that phase B is the saddle point in the double-well feature pathway, and the transition barrier is $\sim$ 0.20 eV/u.c. from phase A to A$'$ through B. The existence of (anti)ferroelectricity is strongly suggested by the double-well feature. It should be noted that the net displacement for phase A/A$'$ is compensated although the local ones are nonzero, and thus we refer to phase A/A$'$ as the AFE structure. Our Berry-phase calculations indeed give us zero polarization of phase A/A$'$, conforming to the above analysis.
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Fig. 4. Top views of two degenerate structures: (a) AFE phase A and (b) A$'$. (c) Switching pathway and energy barrier for phase A/A$'$. Top views of two degenerate structures: (d) FE phase C and (e) C$'$. Purple circles are indicated for reference. Large arrows denote the directions of the polarization field for phase C/C$'$. (f) Switching pathway and energy barrier for phase C/C$'$.
Similarly, we find nonzero local displacements for phase C/C$'$, but $h$ is now equivalent to $d$ in magnitude, leading to a net displacement vector along the [$\bar{1}$10]/[1$\bar{1}$0] direction, which is perpendicular to the chain direction. CINEB calculations reveal that the local minimum is phase C/C$'$, which is $\sim$ 0.23 eV/u.c. lower than the highly symmetric phase B. This structure can therefore be described as FE structure with a net polarization value of $0.34 \times 10^{-10}$ C/m and direction along [$\bar{1}$10]/[1$\bar{1}$0]. The underlying physics of this spontaneous polarization can be clearly illustrated by the asymmetric charge redistribution along the [$\bar{1}$10] direction in phase C (Fig. S3), which leads to a separation of positive and negative charge centers, resulting in the emergence of polarization, similar to the results reported previously.[32] For phase D in Fig. S6(a), the displacements along $y$ cancel well with each other, forming the anti-polar distortion as an AFE one (like phase A). For parameters along $x$, the displacements also cancel well with each other, resulting in a net polarization of zero. Therefore, phase D is also AFE, which connects two original chains together and forms the special chain along $x$. Next, we calculate the thermal stability of FE films and evaluate the transition temperature $T_{\rm c}$ through AIMD since $T_{\rm c}$ is the critical factor for practical applications of non-volatile devices. The base temperatures used here vary from 20 K to 70 K. During the AIMD process, we monitor the structural distortions, which are directly related to the local polarization. The results are summarized in Fig. S7. It is found that the structure of FE monolayer remains stable with intact configurations at 30 K. At higher temperature, especially above 50 K, the structure starts to distort. In particular, at 70 K, the system begins to collapse. Thus, we can conclude that the transition temperature (lower limit) is $\sim$ 40 K for the FE structure.[28,32,57] Reversible Rashba Splitting and the Berry Curvature. According to the symmetry of FE Te film, the band degeneracy should decrease when SOC is included, due to the intrinsic polarization field. Figure 5(a) shows the band structure when SOC is not considered, and FE monolayer is a semiconductor with direct band gap of 0.57 eV. When SOC is included, the band gap becomes indirect and decreases to 0.48 eV, which is ascribed to the large band-splitting near the VBM and CBM. We demonstrate below that the SOC-induced spin-splitting is controllable under the FE phase transition, and this band-splitting is Rashba splitting with an in-plane polarization field.
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Fig. 5. (a) Band structure of phase C without SOC. (b) Band structures of phase C with SOC included. (c) Band structures of phase C$'$ with SOC included. Inset is the close-up view of the CBM around point $M$. Red/blue lines represent the $S_{z}$ component pointing upwards/downwards. Other spin components ($S_{x}$/$S_{y}$) are found to be zero (Fig. S8). (d) Calculated spin Hall conductivity near the CBM. CBM is set at zero for reference. (e) Berry-curvature distributions for phase C corresponding to (b). (f) Berry-curvature distributions for phase C$'$ corresponding to (c).
Interestingly, the bottom conduction band is apparently split with SOC and this band-splitting induces the local spin-polarization near the band edge [see Figs. 5(b) and 5(c)], which resembles the Rashba effect in 2D systems when inversion symmetry is broken with the external/intrinsic electric field.[58-61] Following the Rashba model (see Note I in the Supporting Information), we can obtain an effective Rashba Hamiltonian in the form of $-E_{\rm IP}k_{y}\sigma_{z}$, when the $k_{z}$ component is deleted due to the 2D space. Here, $E_{\rm IP}$ and $\sigma_{z}$ represent the in-plane polarization field and spin Pauli matrix, respectively. Clearly, only the $S_{z}$ component is retained according to the Rashba model. More interestingly, if the in-plane polarization field changes its direction, the effective Rashba Hamiltonian will be $-E_{\rm IP}k_{y}$($-\sigma_{z}$), which means that spin reversal has occurred. These characteristics are in excellent agreement with the DFT-calculated bands in Figs. 5(b) and 5(c) and Fig. S8 in the Supporting Information. Therefore, an external electric field or other methods can be utilized not only to tune the polarization direction of the Te film, but also to control the spin polarization of carriers, which is significant for the development of spintronic nanodevices. It should be emphasized that the Dresselhauss contribution and Zeeman-type splitting can be excluded, based on the band-splitting behavior (also see Note II in the Supporting Information). We also calculate the Rashba parameter $\alpha_{\scriptscriptstyle{\rm R}}$ according to the equation, $\alpha_{\scriptscriptstyle{\rm R}} = 2E_{\scriptscriptstyle{\rm R}}/k_{0}$, where $E_{\scriptscriptstyle{\rm R}}$ is the Rashba-splitting energy and $k_{0}$ is the corresponding momentum shift [see inset in Fig. 5(c)]. The estimated $E_{\scriptscriptstyle{\rm R}}$ and $k_{0}$ near the CBM are 31.9 meV and 0.032 Å$^{-1}$, respectively, leading to a large value of $\alpha_{\scriptscriptstyle{\rm R}}$ (2.0 eV$\cdot$Å). This $\alpha_{\scriptscriptstyle{\rm R}}$ is much larger than that of a heavy metal surface.[62-64] For the AFE phase in Fig. S9, we find similar band splitting, which is intriguing for nano-spintronics. As shown in Fig. 5(d), we calculate the spin Hall conductivity ($\sigma_{\rm s}$) near the CBM and it is clear that $\sigma_{\rm s}$ gradually increases. For example, $\sigma_{\rm s}$ is $\sim$ 10$\hslash /e$ ($\Omega\cdot$cm$^{-1}$) at 0.3 eV above the CBM, which is comparable to that of metal dichalcogenides,[65,66] also indicating the possible detection in low-temperature transport experiments through inverse spin Hall effect.[67-69] From the band geometry, the valence and conduction bands near $M$ mimic the massive Dirac cone, especially when SOC is excluded. According to the valley properties of gapped graphene and 2H-MoS$_{2}$ family,[70,71] this band geometry may carry local Berry curvature. Thus, we compute the distributions of Berry curvature for phases C and C$'$ in Figs. 5(e)–5(f). Indeed, Berry curvature is nonzero near $M$ and has a dipole-like distribution along the [110] direction for phase C. As previously reported, the Berry-curvature dipole may lead to the nonlinear Hall effect in the transport measurements.[72,73] More interestingly, the distribution is fully reversed when polarization is inverse for phase C$'$, demonstrating the strong coupling between polarization and distribution of Berry curvature, which possibly leads to the sign change of nonlinear Hall contribution. In summary, we propose new phases of chained Te in 1D and 2D forms, based on first-principles calculations, which are energetically and dynamically stable. In particular, the stacking of 1D chains together can yield 2D Te films with different intra/inter-chain and intra/inter-cell interactions, directly leading to local polarization. According to DFT calculations, the FE structure is demonstrated to be in the ground state, and the transition barrier is experimentally available. Due to strong SOC of Te, we find large spin-splitting in both 1D and 2D Te systems due to the broken inversion symmetry. More interestingly, this spin splitting of FE-Te can be reversed when the structure is under an inversion operation (e.g., through an external electric field). Our discovery not only expands the family of elemental FE materials, but also demonstrates controllable spin-splitting, providing perspectives for realizing conceptual spintronic/non-volatile devices. Acknowledgments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11904317 and 12204029), the Funding of Leading Innovative and Entrepreneur Team Introduction Program of Zhejiang (Grant No. 2020R01002), and the Natural Science Foundation of Zhejiang Province (Grant Nos. LY23E020010 and LQ23A040013). 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