Introduction

Low-dimensional ferroelectrics, with spontaneous charge polarizations tunable by external electric fields, have drawn extensive interest in nanoelectronics, for applications such as transistors, memories, and sensors1,2,3. The direction of the spontaneous polarization is important to determine possible applications. The out-of-plane ferroelectricity is preferred to realize memory miniaturization with high integration density and low power consumption1,4,5,6, compared with the in-plane one. Usually, ferroelectrics are insulators with low carrier mobility and large band gaps1,5,6,7,8,9. For functional nanodevices, an effective strategy is to construct heterostructures by combining ferroelectric gate insulators and channel semiconductors10,11,12,13,14,15,16 to make ferroelectric field-effect transistors (Fe-FETs). However, leakage current and charge trapping usually exist at the interface, limiting application prospects. A material that is both a high-mobility semiconductor and out-of-plane ferroelectric could make an ideal transistor/memory nanodevice and overcome the above disadvantages17,18,19,20. Such a material requires a highly anisotropic lattice structure with different properties. Recently, a two-dimensional (2D) ferroelectric semiconductor α-In2Se3 has been used as the channel material to compose a Fe-FET17. The spontaneous out-of-plane polarization can tune the in-plane electronic transport via a gate voltage to give rise to a nonvolatile resistive switching, achieving a self-gated Fe-FET (SF-FET). Until now, many efforts have been made to explore ferroelectric semiconductors using compound 2D materials (such as α-In2Se3)17,18,21 and emerging moiré superlattices (such as twisted MoS2 bilayers)19,22,23.

Ferroelectricity is mainly found in compounds with non-centrosymmetric structures18,22,23,24,25,26,27,28, which are unexpected in elemental crystals. Generally, elemental materials possess centrosymmetric structures without local electronegativity differences, thereby lacking spontaneous electric polarizations7,28,29. To date, it has been a challenge to realize single-element ferroelectrics. Recently, tellurium (Te) has drawn significant interest as a 2D single-element semiconductor30,31, due to its outstanding electrical conductivity32,33,34, one-dimensional chain structure35,36,37, and strong spin–orbit coupling (SOC)38,39. Theories have predicted that layered Te possesses a broken symmetry and can be a ferroelectric semiconductor7. The interlayer interaction between adjacent Te chains drives the atomic displacement accompanied by charge transfer, separating the charge centers and leading to spontaneous electric polarization. However, until now, there has been no experimental evidence to support such a prediction. Most recent studies have focused on the Te nanosheets40, whose highly stable structure and strong electrostatic screening may limit the reversal of dipoles. Another form of Te is the nanowire with a relatively low barrier height of atomic displacement41,42, providing a possible route to achieve ferroelectricity.

In this work, we report room-temperature vertical ferroelectricity in quasi-one-dimensional Te nanowires and at the edges of Te nanosheets. The ferroelectric hysteresis and ___domain switching are observed by piezoresponse force microscopy (PFM). Using spherical aberration corrected scanning transmission electron microscopy (Cs-corrected STEM), we attribute the vertical ferroelectricity to the atomic displacement perpendicular to the atomic chains within Te nanowires, verified by density functional theory (DFT) calculations. Furthermore, the Te nanowire can be used as a ferroelectric semiconductor channel to construct a SF-FET with a h-BN gate dielectric. By adjusting the remnant polarization (Pr) of Te nanowires to regulate their vertical depolarization field, SF-FETs exhibit continuous-variable resistive states with fast speed and high-density storage. These capabilities offer a solution for in-memory computing, particularly in artificial intelligence applications that leverage ferroelectric properties.

Results

Quasi-one-dimensional Te nanowires were synthesized with a width of 30~300 nm and a height of 5~30 nm using a substrate-free solution method (section “Methods” and Supplementary Fig. 1), and were identified by Raman spectra (Supplementary Fig. 2a). The surface morphology and cross section of a representative Te nanowire probed through atomic force microscopy (AFM) and scanning electron microscopy (SEM) are shown in Fig. 1a. It shows a triangle-like cross section with clean surfaces and neat edges, indicating the high crystal quality. The STEM image shows a unique chiral chain lattice in Fig. 1b. Each Te atom is bonded to two nearest neighbors, forming helical chains along the c-axis direction (which is the long axis of the nanowire). Those chains are stacked in a hexagonal array through van der Waals bonds between adjacent atomic chains. Note that the Te nanowire shows an inclined plane along the b-axis at the edge. It can be thought to be formed by multiple Te atomic layers stacked along the \(\vec{e}\) direction (perpendicular to b–c plane). Layer-center atoms (LCAs) in each single Te chain show relative off-center displacements, thereby giving rise to a non-centrosymmetric lattice structure of the inclined plane at the edge (the right in Fig. 1b and Supplementary Notes 1, 2). As is well known, the breaking of symmetry is an important premise of ferroelectricity.

Fig. 1: Polar structure and ferroelectric polarization.
figure 1

a AFM, SEM, TEM topographical images and the AFM height profile of a Te nanowire on a SiO2/Si wafer. b STEM images of the Te nanowire viewed along b- and c-axes (lower left insets here as well as in (a) show axes projected into the image planes; left and right insets show atomic lattice models). e is the epitaxial direction of inclined stepwise planes. c Ferroelectric switching pathway of 4L Te from α- to α′-state calculated using the NEB method. Insets display the atomic structures of α and α′, representing two opposite polarization states, as well as the paraelectric nonpolar β-state. d Differential charge density (Δρ) of 4L Te for α-, β- and α′-states. Here Δρ = ρ(tot) − ρ(c-Te) − ρ(n-Te), where ρ(tot) is the total charge density, ρ(c-Te) is the charge density of the LCAs (c) and ρ(n-Te) is the charge density of the neighboring (n) Te atoms. Red and blue colors represent the charge accumulation and depletion, respectively. The isosurface values in α- (α′-) and β-states are set to 0.007 and 0.006 e/bohr3, respectively. The arrows denote the polarization direction. Dotted rectangular boxes in (c) and (d) indicate the smallest repeatable unit in the periodic lattice. e Calculated polarization per layer for the α-state Te with different number of layers.

Full size image

Considering the experimental case, we used DFT to simulate the ferroelectric characteristics of few-layer Te (Supplementary Table S1 and Note 3), focusing on modeling the off-center displacement of LCAs at the inclined edge (which as discussed below would give a vertical polarization component measured in our experiment). To model the layers near and parallel to the inclined edge and stacked along the \(\vec{e}\) direction of the Te nanowire, we performed detailed calculations for a 4-layer (4L) Te sheet in three different states. The atomic structures of the α-, β-, and α′-state in a 4L Te are plotted in the left, middle, and right insets in Fig. 1c, respectively. The β-state Te has the space group P21/m and is centrosymmetric, while the space group of the α (α′)-state Te is reduced to P21. The α- and α′-states Te are energetically degenerate with the opposite displacement (about ±0.41 Å) of their LCAs. The climbing image nudged elastic band (NEB) calculations show that the two stable structures of non-centrosymmetric α- and α′-state are connected through an extremum energy point with the centrosymmetric β-state, implying the possible existence of ferroelectricity. The calculated ferroelectric switching pathway of 4L Te from α- to α′-state in Fig. 1c shows that the energy barrier between the non-centrosymmetric and centrosymmetric states is about 67 meV/layer. We also calculated energy barriers for different numbers of Te layers (Supplementary Fig. 3). The differential charge densities are calculated to investigate the physical mechanism of the existence of polarization in the α- and α′-states Te (Fig. 1d), with the red and blue colors denoting the electron density charge accumulation and depletion regions, respectively. For the β-state 4L Te, the charge distribution is centrosymmetric around the LCAs, resulting in the positive and negative charge centers canceling each other to give a zero net polarization. In contrast, the differential charge densities of the α- and α′-states show charge redistributions between the LCAs and their neighboring atoms. For the α- (or α′-) state layered Te, the negative charge center moves to the right (or left) side of the positive charge center due to more charge accumulating at the right (or left), resulting in the emergence of nonzero polarization pointing from right (or left) to left (or right). Figure 1e shows the calculated spontaneous polarization per layer as a function of the number of layers for α-state Te. We do not calculate a monolayer as it has only the β-state as the stable state and it alone cannot make a meaningful nanowire with inclined edges7. The 2D polarization density is about (2.1~2.4) × 10−10 C/m per layer and slightly increases with increasing number of layers below 8 layers. Apparently, the polarization starts to decrease with further increasing number of layers beyond 8 layers. Our calculations strongly support the existence of ferroelectricity within the layer (perpendicular to the Te chains), thus along the b-axis of the single-element Te nanowire giving rise to a vertical (perpendicular to the a–c plane and substrate) polarization component. Given that Te nanowires are van der Waals materials with one-dimensional chain structures, their crystal structures along both the a-axis and b-axis can be likened to stacked layers of Te atoms, exhibiting the similar atomic arrangements. Our few-layer model can apply to the Te layers parallel to the a direction (e.g., near the bottom surface of the Te nanowire), implying a polarization along the a-axis can also exist. However, as the number of Te atomic layers increases along either the a-axis or b-axis, the bandgap of Te decreases, posing challenges to sustaining spontaneous polarization. A narrow bandgap can induce electrostatic screening due to high carrier density, leading to the disappearance of the depolarization field and hindering the maintenance of ferroelectric polarization.

Vertical PFM was performed to investigate the spontaneous electric polarization of the Te nanowire. Te nanowires were transferred onto an Au-coated silicon substrate for the contact-mode PFM measurement. Figure 2a obtained on a representative Te nanowire, shows that the piezoresponse peaks at a resonance frequency of ~365 kHz, and the intensity is linear with the amplitude of the AC drive voltage (VAC) as shown in the inset in Fig. 2a. It verifies the existence of electric dipole moment and piezoelectricity with an effective piezoelectric coefficient d33 of ~3.1 pm/V in the Te nanowire. Both phase hysteresis and butterfly amplitude loops are observed in Fig. 2b, c, respectively. ON- and OFF-field PFM method is used to identify the ferroelectricity (Supplementary Fig. 2b and Note 4), which shows the typical hysteresis shapes caused by the switching of ferroelectric domains20. In addition, various driving voltage (VAC) (Supplementary Fig. 4 and Note 5) and opposite poling voltages (Supplementary Fig. 5 and Note 6) are employed to entirely preclude the interference of the charge adsorption/desorption process in PFM measurements. The thickness dependence of ferroelectricity is studied (Supplementary Fig. 6 and Note 7). It is important to clarify that the thickness refers to the height of Te nanowires, which directly corresponds to the vertical measurement scale at the boundary of the Te nanowire/nanosheet. Considering the layered structure of Te nanowires along the a–c plane, this height to some extent corresponds to the number of layers. It is found that the ferroelectricity of Te nanowire decreases with increasing thickness and vanishes at thickness over 49 nm. This is due to the narrowing of its bandgap, which leads to higher carrier density and induces electrostatic screening, preventing the observance of ferroelectric polarization. For comparison, Te nanowires were also transferred to an N-doped conductive silicon substrate to exclude the possible effect of substrates, showing a similar ferroelectric hysteresis (Supplementary Fig. 7). PFM is used to identify the distribution of polarization within the Te nanowire, reflecting its local ferroelectric ___domain structure (Fig. 2d). The phase and amplitude mappings correspond well to each other, overlaid on the three-dimensional (3D) topography (Fig. 2d and Supplementary Fig. 8). The ferroelectric ___domain pattern shows a strong contrast between upward (orange) and downward (olive) polarizations with ___domain walls along the chain direction in the Te nanowire. Such a ___domain structure can be attributed to the opposite off-center ion displacements between the two inclined edges (Supplementary Fig. 9). The narrow olive belt at the right edge may result from a slight bend at the end of the edge (Fig. 1a, lower right). For a ferroelectric, off-center ion displacements are tunable by mechanical or electric driving, thereby reversing the ferroelectric domains. Here, the reversal of domains is evaluated after electrical poling using a DC bias applied to the proximal tip. We investigate the reversal of the ferroelectric ___domain in the Te nanowire by “poling” with opposite DC bias (±2.5 V) applied in Fig. 2e, f. It is worth noting that ferroelectricity can still be observed in Te nanowires with even narrower diameters, down to 44.9 nm (Supplementary Fig. 10). This significant reduction in scale limit for maintaining ferroelectricity can enable the achievement of ultrahigh data storage density in ferroelectric storage systems, successfully overcoming the major challenge of poor storage density. Additionally, to verify the intrinsic ferroelectricity, the broken inversion symmetry of Te nanowires/nanosheets was confirmed by SHG measurements (Supplementary Figs. 11, 12 and Note 8). It is noteworthy that the height of Te nanowire increases significantly and its shape changes after poling, which may be attributed to the nonvolatile electrostriction (Supplementary Fig. 13 and Note 9). The orientation of ferroelectric polarization is switchable with the external electric field. Our results demonstrate that the ion displacements at the inclined edge give rise to a vertical component of electric polarization that can be locally detected and controlled by an external field. The ferroelectric polarization reversal with a saturation polarization (Ps) of ~0.02 μC/cm2 was directly confirmed by measuring the typical polarization-electric field (P–E) hysteresis loop in a compressed tablet made from Te nanowires (Supplementary Fig. 14).

Fig. 2: Ferroelectric hysteresis and ___domain switching.
figure 2

a Piezoresponse vs frequency under different VAC for the Te nanowire on an Au-coated silicon substrate, measured at a representative ___location on the inclination edge, showing a resonance peak around 365 kHz. Inset shows the linear dependence of piezoresponse amplitude on VAC with an effective piezoelectric coefficient d33 of ~3.1 pm/V. Phase–voltage hysteresis loops and amplitude–voltage butterfly loops measured by vertical ON-field (b) and OFF-field (c) PFM, where DC bias voltage (VDC) is applied to the tip before (“OFF-field”) or during (“ON-field”) the AC drive. Phase mapping (OFF-field) measured by vertical PFM before electric poling (d), after poling at +2.5 V (e), and after poling at −2.5 V (f), overlaid on the 3D topography image of the nanowire (width ~300 nm, thickness ~18.9 nm). The area of Te nanowire is marked by the cyan dashed line. VDC = 0 V for (a) and (b–f) were measured with VAC = 1.5 V driving on the resonance frequency.

Full size image

The origin of the ferroelectricity in Te nanowires implies the importance of the inclined edge. Besides the Te nanowire, one can synthesize Te nanosheet by a similar substrate-free solution process. Therefore, it is intriguing to investigate the usually neglected edge ferroelectric responses of Te nanosheets. Figure 3a shows the SEM and AFM images of a Te nanosheet with a width of ~1.2 μm and a thickness of ~15 nm. An inclined edge of the Te nanosheet is shown in Fig. 3b, providing a possible platform to investigate edge ferroelectricity. It is intriguing that the effective piezoelectric coefficient (d33) at the edge was found to be ~80% higher than that inside (Fig. 3b and Supplementary Fig. 15a). The difference in piezoelectric responses between the edge and inside is also reflected by the resonance frequencies, which are about 371 kHz (edge) and 391 kHz (inside), respectively. We note that the existence of piezoelectric resonance itself does not necessarily imply ferroelectricity. The edge electric polarization of the Te nanosheet is also investigated using the vertical PFM in Fig. 3c. The phase hysteresis loops were measured at different locations along the edge indicated by double arrows in Fig. 3c. It is observed that vertical ferroelectricity has been identified in the whole edge region. The coercive field decreases gradually as the tip climbs up the edge. The PFM phase hysteresis cannot be observed with the tip approaching the highest position, for the tip has already been placed in the inner region. Our results show that the ferroelectricity emerges only at the edge of the Te nanosheet. In comparison, for Te nanowires with a width of 20–300 nm, the top surface is full of inclined steps, causing ferroelectricity in all regions. To control the ferroelectric ___domain near the edge of the Te nanosheet, we used a biased tip above the local ___domain to apply an electric field while scanning the Te nanosheet. The PFM phase images are overlaid on 3D topography of the nanosheet after DC bias poling in Fig. 3d–f. We observe the post-polling shift of the ___domain wall, demonstrating the switching of ferroelectric polarization induced by the external electric field. The dark region, corresponding to the ferroelectric ___domain, tends to shrink after a positive poling of +2.5 V (Fig. 3e), but expands after a negative poling (Fig. 3f). Due to symmetry breaking in Te nanosheets/nanowires, ferroelectric polarization primarily occurs at the boundaries, aligned along the atomic plane of surface at these boundaries. Therefore, at the edges of Te nanosheets, the ferroelectric polarization tends to align parallel to the inclined Te layer along the b-axis, forming the domains.

Fig. 3: Edge ferroelectricity in a Te nanosheet.
figure 3

a Upper and lower: SEM and AFM topographical images of a Te nanosheet (height of ~15 nm) on an Au-coated silicon wafer. b Values of d33 at the different marked positions (overlaid on an AFM topograph) of the Te nanosheet, showing that d33 at the edge is about 80% higher than that inside of the nanosheet. c OFF-field PFM phase hysteresis loops from the edge to the inside of 2D Te nanosheet, showing ferroelectric ___domain with edge width <200 nm. Upper part is a schematic height profile of the edge and vertical arrows mark locations where individual PFM traces were measured. Vertical PFM phase mapping before electric poling (d), after poling at +2.5 V (e), after poling at −2.5 V (f), overlaid on 3D topography image of the Te nanosheet. c–f were measured with VAC = 1.5 V driving on the corresponding local resonance frequency.

Full size image

Given that Te is a p-type semiconductor (Supplementary Fig. 16)33,34,35,39,41,42, a ferroelectric Te nanowire can be used as the channel material of a SF-FET via its vertical spontaneous electric polarization. Figure 4a shows a SF-FET device composed of a Te nanowire as the channel material and a h-BN layer as the top gate dielectric. The optical and STEM images of Te-nanowire and Te-nanosheet SF-FET devices are exhibited in Supplementary Figs. 17 and 18, respectively. The Te-nanowire SF-FET possesses a typical (p-type) field-effect behavior, as shown by the transfer curves in Fig. 4b and Supplementary Fig. 19, where a gate voltage (Vg) sweeps to vary the carrier density. As a reference for the transport characteristic of a transistor, effective extrinsic field-effect mobility (\({\mu }_{{{\rm{FE}}}}\)) values of ~135 and ~220 cm2 V−1 s−1 for the backward and forward gate voltage sweeps, respectively, can be extracted from the maximum transconductance (gm) (Fig. 4b, lower). These values are comparable to the high-mobility FETs based on few-layer black phosphorene43 and few-layer MoS244. It is most intriguing to observe the resistance–Vg (Rds–Vg) hysteresis (Fig. 4b, upper) originating from the switching of vertical electric polarization. This provides strong evidence supporting the ferroelectricity of the Te nanowire, and suggests a potential application for resistive memories. For comparison, we have also investigated the field effect of Te nanosheet that shows a much smaller hysteresis behavior. The vertical ferroelectricity exists only at the edge, so the spontaneous polarization is not large enough to gate the entire Te nanosheet. In addition, we note that both Te nanowire and nanosheet exhibit clockwise loops in Rds–Vg, different from a regular Fe-FET13,17. For the self-gated device, the external electric field (Eex) opposed the internal remnant electric field (Ein) induced by the spontaneous polarization, thereby causing competition and balance between them. To clarify this hysteresis behavior, we studied the resistive response to multiple on/off operations of a pulsed gate voltage (Vp) as shown in Fig. 4c. It is observed that Rds increases sharply when Vp is applied, but decreases to a level even lower than the initial resistance once Vp is removed (so supply voltage Vg = 0 V again). Additional and even lower resistive states can be obtained at zero Vg after more Vp pulses with increasing amplitudes. Further details on the resistive switching performance of SF-FET after various continuous voltage or pulsed voltage (Vp) can be found in Supplementary Figs. 20–22 and Note 11. SF-FET demonstrates excellent nonvolatile resistive switching performance, showcasing continuous-variable resistive states (>16) with good stability, long-term retention (>105 s), and fast speed (<20 ns). To interpret this effect, a schematic diagram is provided to describe the gating process and the band structures for high resistive state (HRS) and low resistive state (LRS) in Fig. 4d, where the band energy is obtained from the DFT calculations (Supplementary Figs. 23 and 24). In the case of continuous application of positive Vg or Eex, the Rds increase is mainly determined by Eex because of Eex >> Ein. In the absence of Eex, Ein has an opposite direction to Eex, thus has a similar effect to a negative Vg or Eex that attracts more mobile holes to the (p-type) channel and gives rise to Rds lowering (LRS, Fig. 4d, right upper), explaining the lower Rds reached after positive Vp observed in Fig. 4c. The Te SF-FET device enables a nonvolatile resistive memory with multilevel high and low resistance states. Figure 4e shows Rds–Vp hysteresis loops at different pulse durations. Despite the pulse duration range of 20 ns~10 μs, the device shows almost the same nonvolatile resistive states. It is intriguing that the fast switching was even obtained within 20 ns. Such a fast resistive switching is consistent with the speed of ferroelectric polarization reversal (≤20 ns), giving the strong evidence to support the vertical ferroelectricity in the whole Te nanowire45. We have simulated the Rds–Vg and Rds–Vp hysteresis loops (Supplementary Fig. 25 and Note 11), which align with our experimental results. Additionally, the measurement of the depolarization field (Supplementary Fig. 26 and Note 12), the Pr in Te nanowires (with a thickness of ~24 nm) is ~0.026 μC/cm2. Pr–Vp hysteresis loops were also measured by varying the temperature and pulse amplitudes (Supplementary Fig. 27). These loops exhibited negligible changes, confirming that the resistive switching does not stem from charge absorption/desorption. Figure 4f shows the stable Vp dependence of the resistance. The device has a high HRS/LRS resistance ratio of nearly 100. After several pulsed voltages are applied, the Ids–Vds curves still remain almost linear but have different slopes (inset in Fig. 4f). Continuous-variable resistive states are achieved by pulsed gate voltages and are attributed to the moving and switching of multi-domains. To eliminate the interference from oxidation reactions, energy dispersive spectroscopy analysis was conducted on both Te and TeOx nanowires, revealing a very low oxygen concentration in the Te nanowires (Supplementary Fig. 28 and Note 13). Through a series of measurements using PFM and resistive switching performances (Supplementary Figs. 29 and 30), no signs of ferroelectricity or resistive switching were observed in TeOx nanowires, effectively ruling out the impact of oxidation reactions on the observed phenomena. Moreover, given that the region where Te nanowires can sustain ferroelectricity is able to be as small as ~22.5 nm, the storage density of SF-FETs prepared based on this ferroelectric property can reach ~1.92 TB/cm2. The device, featuring continuous-variable resistive states and ultrahigh data density can be integrated with silicon circuits to achieve CMOS-compatible neuromorphic devices through 3D heterogeneous integration. This approach provides a foundational building block for broad-edge intelligence applications.

Fig. 4: Switching characteristics exhibiting nonvolatile memory of a Te nanowire self-gated ferroelectric field-effect transistor (SF-FET).
figure 4

a Schematic showing the device structure. b Rds–Vg characteristics for the Te nanowire and nanosheet SF-FETs (upper) and gm–Vg hysteresis loop of Te nanowire SF-FET (lower). c Nonvolatile switching of Rds measured after applying multiple Vp square pulses with the pulse width of 25 s, exhibiting multilevel resistive states. d Schematic showing polarization bound charge distribution with an external electric field applied and band structures for LRS and HRS at zero field. e Rds–Vp hysteresis loops at Vds = 0.5 V. Measurement of each data point is performed at Vg = 0 V after waiting for 1 min following applying each Vp pulse width of 20 ns, 100 ns, 1 μs, and 10 μs. f Nonvolatile resistive states switched by different Vp. Resistive states are measured after applying Vp pulses (from −100 V to 100 V then back to −100 V in steps of 10 V) of 100-ms width. The inset is the linear Ids–Vds characteristics after applying different Vp pulses labeled.

Full size image

Discussion

To summarize, we have discovered a room-temperature vertical ferroelectricity in Te nanowire, a single-element material Te. A polar structure was detected through the STEM, resulting from a non-centrosymmetric lattice. PFM is used to probe the piezoelectric characteristics, hysteresis behaviors, and field-driven ___domain reversal. Based on the DFT simulations, the observed ferroelectric polarization can be attributed to off-center ion displacements along the inclined edge surface of Te. Moreover, as a ferroelectric semiconductor, Te nanowires possess high mobility along the Te chains and vertical ferroelectricity, which can be employed to realize a SF-FET device. Such device with fewer interfaces, demonstrate nonvolatile resistive switching, continuous-variable resistive states, ultrafast switching speed, and high-density storage, making them appropriate building blocks for in-memory computing. Our work expands the scope of ferroelectric materials and establishes a platform for ultrahigh-density memories and edge computing.

Methods

Materials synthesis

Te nanowires and nanosheets were synthesized using a substrate-free solution method (Supplementary Fig. 1). At first, Na2TeO3 (46 mg) and polyvinylpyrrolidone (PVP) (0.2 g) were mixed with double-distilled water (16 mL) at room temperature. To get a better mix, this solution was stirred with a magnetic stirrer for 20 min. Second, the solution was added with 1.66 mL of ammonia solution (25%, wt/wt %) and 0.84 mL of hydrazine hydrate (80%, wt/wt %). Finally, the above solution was transferred into a Teflon-lined stainless-steel autoclave and heated to a constant reaction temperature of 160 °C. After a set period of heating, the autoclave was naturally cooled down to room temperature. The silver–gray products of Te crystal can be precipitated by centrifugation at 4000 r/min for 15 min. To obtain a suspension of the Te nanowires or nanosheets, the solution was washed by centrifugation with distilled water three times.

The controls of PVP concentration and reaction time play an important role in obtaining different morphology of Te crystal (e.g., nanowires vs nanosheets). For all PVP concentrations, the initial growth products are dominantly 1D nanostructures. After a certain period of reaction, Te nanosheet tend to emerge. Therefore, different Te structures can be formed by adjusting the experimental procedure. When different heating time was set to get different morphology, the time of 10 and 83 h is taken for Te nanowires and nanosheets, respectively.

Characterizations

Raman measurements were performed using a LabRAM HR Evolution Raman system with a green excitation laser of 532 nm. The TEM and Cs-corrected STEM images were obtained on a JEM-200CX and a FEI Titan3 G2 Cube (60–300 kV) with double Cs correctors in the TEM and STEM modes. The cross-sectional STEM samples were fabricated using the FEI Helios 600i dual-beam focused ion beam (FIB) system. Samples are generally transferred onto small copper grids covered with a thin carbon film. AFM and PFM measurements were carried out at the same time in a Bruker Multimode VIII instrument.

Piezoresponse force microscopy measurements

The samples for vertical PFM measurements were fabricated by transferring the Te nanowire and nanosheet onto Au-coated SiO2 (285 nm)/Si substrates and N-doped conductive silicon (Si) substrates. The vertical PFM measurements were performed in the contact mode with Multimode VIII and ICON instruments (Bruker) and Asylum Research MFP-3D (Oxford) at room temperature. A PFM tip (SCM-PIT-V2) with force constant of around 2.8 N m−1 and contact resonance frequency of around 370 kHz was used in the PFM measurements by Bruker instruments. The contact strength was set to be lower than 10 nN to avoid unintentional damage. PFM tip (EFM-50, Nanoworld) was also used for the measurements of ___domain and polarization switching by Asylum Research MFP-3D. The tip has the same force constant (~2.8 N m−1) and contact resonance frequency (~370 kHz) as the one of SCM-PIT-V2.

An AC bias voltage (VAC) was used to drive the PFM tip, whose response (both amplitude and phase lag from the drive) were recorded. And then, the PFM tip needs to carry a constant DC voltage (VDC) while being moved in contact mode across the Te surface. This applied external electric field generated by VDC will cause the switching (or “poling”) of ferroelectric domains. By changing VDC at different locations, ferroelectric ___domain patterns can be formed. This ___domain pattern can be observed by PFM in its amplitude and phase mapping images. Therefore, these images can be used to detect the movement and reversal of ferroelectric ___domain in Te nanowire and nanosheet.

PFM hysteresis measurements were used to verify the ferroelectrcity. We changed the above constant VDC into alternating “on” (during which VDC was held constant) and “off” (VDC = 0 V) periods (each period has a duration of 20 ms), where the consecutive “on” values of step is through a (discretized) triangular waveform (Supplementary Fig. 2b). Therefore, ON- and OFF-field PFM mode can be realized in the on- and off-periods of VDC-sweeping, respectively. The piezoresponse data collected in the on-period (or off-period) are used to plot ON-field (or OFF-field) phase and amplitude hysteresis loops.

Device fabrication and electrical measurements

The as-prepared Te nanowire and nanosheet can be easily transferred onto (90 nm) SiO2/Si substrates. We transferred h-BN as a gate dielectric using poly(bisphenol A carbonate) film on polydimethylsiloxane. The h-BN flake was picked up at 70 °C and released at 170 °C. This stacking of heterostructure (h-BN/Te) was followed by the evaporation of the top gates of Au/Ti onto h-BN, the edge contact to h-BN/Te with Au/Ti with e-beam lithographic techniques and magnetron sputtering (Fig. 4a for a device schematic; some of our devices have two top gates slightly offset to the side away from the Te nanowire and not directly on top to reduce gate leakage, in this case the two top gates are shorted together and connected to the same gate voltage thus acting as one gate).

Our devices for electrical measurements were wire-bonded with aluminum wire for transport measurement. Two-probe DC measurements were used because of the high resistance (>1 MΩ) of few-layer Te nanowires. The transport measurements between drain/source electrodes were conducted along the c-axis of Te nanowire or nanosheet. The carriers in the channel can be induced and modulated by the top gate. The electrical transport measurements were performed with source meters (Keithley: Model 6517B). Top gate voltage pulses were applied with source meters (Keithley: Model 2400). For channel resistance (Rds) vs gate voltage (Vg) curves (e.g., Fig. 4b), each Rds was measured by waiting for 1 s after changing the gate voltage value (Vg) to exclude the hysteresis originating from the measurement lag. The nonvolatile resistive memory effects with multiple high and low resistive states were performed with a constant voltage of 0.5 V between drain and source electrodes. For Rds vs Vp hysteresis loops (Fig. 4e), these resistive states were measured by waiting for 1 min after different voltage pulses (Vp) with pulse duration of 100 ms, which can exclude effects due to the measurement lag and the leakage current. Pulsed voltages with different amplitudes were carried out to produce multilevel resistive states. Multilevel Rds can be switched reproducibly between high and low resistive states (Vds = 0.5 V). Such continuous-variable resistive states can be fundamentally attributed to the nature of multidomain switching dynamics in the single-element ferroelectric Te nanowire. The degree of polarization can be increased with the increasing amplitude of pulsed voltage in a certain direction, which leads to the continuous-variable resistive states.

First-principles calculations

Our first-principles calculations were performed using the projected augmented wave (PAW)46 formalism based on DFT, as implemented in the Vienna ab-initio simulation package (VASP)47. The structural optimizations for α-state bulk Te are performed using SCAN48, PBE49, and various kinds of vdW functionals50,51,52 (DFT-D2, vdW-DF, optPBE-vdW, optB88-vdW, optB86b-vdW, and vdW-DF2). The SCAN functional is in the best agreement with experiments, as listed in Supplementary Table S1. Therefore, the SCAN functional is adopted in all calculations for geometric optimization. The cutoff energy of the plane-wave and the convergence criterion for the total energy were set to be 550 eV and 10–6 eV, respectively. The vacuum space of 20 Å was used to avoid the interaction between adjacent slabs. Atomic structures are fully relaxed until the Hellmann–Feynman force on each atom was smaller than 0.01 eV/Å. The Monkhorst–Pack k-point grids of 15 × 15 × 11 and 1 × 15 × 11 were employed to sample the first Brillouin zone of the α-state bulk and layered until cell, respectively. The band structures of the α-state bulk and layered Te were calculated using the HSE06 functional53 and the SOC was taken into consideration. The climbing image nudged elastic method54 was used to calculate the energy barrier and the ferroelectric switching pathway of the layered Te from state α to state α′. The electric polarization of the α-state layered Te was calculated using the Berry phase method55, as implemented in VASP.