Introduction

Ferroelectrics (FE) are a class of materials with the ability to maintain a spontaneous electric polarisation that can be switched by an external electric field. Due to this, ferroelectric materials have become the key element in devices for a broad range of electronic applications including sensors, capacitors, non-volatile memory, electro-optical switching, and many others1. Room temperature FE devices are typically based on conventional bulk ferroelectrics, such as perovskites (e.g. PbTiO3, BaTiO3, SrTiO3), with a minimum thickness of a few nanometres2,3,4,5. While decreasing their thickness is desirable to reduce operating voltages and miniaturize their design, there are major challenges in engineering atomically thin metal-oxide ferroelectrics due to instability caused by depolarisation, interface chemistry, and high contact resistances6.

2D materials are promising candidates for the next generation of (opto-)electronic devices with memory function due to their ultimate thickness limit and the lack of dangling bonds, making them immune to depolarisation7. In previous years, various groups have reported observations of intrinsic 2D in-plane ferroelectricity in materials such as (monolayer) SnTe8, out-of-plane ferroelectricity in (d1T) MoTe29, (1T’) WTe210 few-layer (Td) WTe211 and CuInP2S612,13 and both types in In2Se314,15,16. More recently, engineering the ferroelectric interfaces with broken inversion symmetry has opened a path to achieving interfacial ferroelectricity in twisted homo-bilayers of insulating hBN17,18,19,20, exfoliated21 and twisted semiconducting transition metal dichalcogenides (TMDs) such as bilayer MoS2, MoSe2, WSe2, and WS220,22,23. In these studies, two thin crystals of 2D materials have been mechanically stacked with a small rotational misalignment (twist). This enables atomic reconstruction, resulting in large structural domains of alternating stacking order featuring broken inversion symmetry20. Due to asymmetric hybridisation between the conduction band states in one layer and the valence band states in the other layer, charge transfer occurs between the layers producing a built-in electric field across the van der Waals gap. Such out-of-plane ferroelectric polarisation is bound to the underlying atomic structure of each domain, with switching enabled by the sliding movement of the partial dislocations separating reconstructed domains. While multiple applications of sliding ferroelectricity have been proposed7, an understanding of its switching behaviour in the context of electronic devices is still lacking.

Here, we study the polarisation-dependent tunneling electro-resistance (TER) in ferroelectric tunnel junctions (FTJ) with a composite FE and non-polar dielectric barrier. We design the ferroelectric interface with transition metal dichalcogenides which have recently been shown to display robust sliding ferroelectricity20,22, high crystalline and electronic quality24, as well as outstanding optical properties25 and are considered necessary for next-generation optoelectronic devices. We demonstrate ambipolar switching behaviour in the tunnelling current with ON/OFF ratios > 10. While methods of substantially increasing the ON/OFF ratio have been extensively demonstrated for conventional ferroelectrics1,3,4,5, here we focus on the switching behaviour instead, and show that it is remarkably different. We study multiple devices positioned over various layouts of the complex domain network and reveal a strong dependence on switching behaviour due to the nature of the local domain structure.

Results

To produce the ferroelectric interface, two monolayers of MoS2 have been transferred on top of each other with marginal twist angle using the tear-and-stamp process26 and then placed onto a thick (typically several tens of nanometers) exfoliated graphite crystal. This process results in twist angle disorder (typically ±0.1°27,28,29), a common feature of twisted bilayers assembled from isolated 2D crystals, as a consequence of the random strain produced during the transfer process. Here, the twist angle variation is more pronounced due to the use of a flexible polymer support in order to achieve a diverse domain network in each sample. An example of such a domain network visualised using lateral/friction-mode AFM with a conductive tip can be seen in Fig. 1a. The bright and dark regions correspond to domains with different local stacking order, which we denote as MotSb (Mo atom in the top layer is aligned with S atom in the bottom layer) and StMob (vice versa), Fig. 1b. These structural domains possess opposite out-of-plane/perpendicular electrical polarisation with a ferroelectric potential of ΔVFE = ± 63 mV and can be locally switched by lateral migration of the partial dislocations separating the domains. Furthermore, the expansion and compression of the domains can be controlled by the applied external field20.

Fig. 1: Ferroelectric domains in rhombohedral MoS2 bilayer.
figure 1

a Contact mode friction AFM map of a marginally twisted bilayer sample on graphite with a variety of differently shaped domains present. Oppositely polarised MotSb and StMob domains display clearly differentiated contrast. The black dashed circles highlight the 4 distinct domain geometries studied in this work, illustrated with matching schematics (bottom). b Schematics of the oppositely polarised MotSb and StMob stacking configurations of the marginally twisted bilayer MoS2 (R-MoS2). c Schematic of the ferroelectric tunnelling junction. The graphene source electrode is routed over thick (10-20 nm) hBN onto the region of interest, where the tunnelling junction with few-layer hBN and R-MoS2 bilayer is formed. Schematic of atomic structure across a d partial and e perfect dislocation obtained using multiscale modelling [28] and TEM studies [29]. Note that this configuration is for the case when dislocations are aligned with the underlying crystallographic orientations of the TMDs, while in the sample shown in a these often deviate and therefore may have more complex structure.

Four characteristic domain configurations have been selected for device fabrication as highlighted with dashed circles in Fig. 1a: (1) over a single partial dislocation between two large, roughly equal MotSb / StMob domains; (2) over regular triangular domains with tens of nm period; (3) over three domains separated by domain walls; (4) similar configuration to (3) but with the middle domain fully collapsed into a perfect dislocation. The heterostructure was then covered by a few-layer hBN flake acting as a tunnelling barrier, a top graphene (source) electrode, and a bottom graphite (drain) electrode, as shown in Fig. 1c. The graphene electrode was selectively patterned producing small tunnelling contacts (~500 nm) over the selected domain configurations 1-4, so that both tunnelling current and electric field switching behaviour can be studied locally. The resulting FTJs allow measuring a change in tunnelling current with the reversal of FE polarisation. The hBN tunnelling barrier serves to enhance FTJs performance30 and protects the device by suppressing high tunnelling currents while allowing the application of sufficient electric fields for FE switching.

The band diagram of the resulting system, corresponding to the zero potential difference set between the source and drain electrodes (Vsd = 0) is shown in Fig. 2a. Here, the conduction band of the MoS2 bilayer is UMoS ≈ 0.3 eV above the Fermi level of graphite31, while the valence band of the hBN layer is UBN ≈ −2.66 eV below the Dirac point of graphene as determined from complementary ARPES experiments (see SI Section 2). Due to the equal potentials initially set on the source and the drain, a small carrier density emerges in graphene and graphite to compensate for the contact potential difference (0.26 eV32) between them, and to negate the FE potential from the rhombohedral MoS2 bilayer (ΔFE ≈ 63 meV33,34). This results in a corresponding electric field so that the potential profile across the dielectric stack has an additional linear contribution equalising the electrochemical potentials μ1 and μ2. Depending on the FE polarisation state of the MoS2 bilayer, the combined tunnelling barrier in both MoS2 and hBN can be switched to a lower or a higher state, which applies for both current directions. As the bias voltage is applied across the junction, Fig. 2b, 60 % of the total potential Vsd drops across the hBN (3L) and 40 % in the MoS2 bilayer according to the ratio of dielectric constants and thicknesses of these materials. This holds up to a point where the MoS2 conduction band edge dips into the bias window at Vsb0.8 V and the direct tunnelling into the bilayer becomes significant. Even though the tunnelling behaviour changes, the ferroelectric polarisation persists at finite electron densities up to ~1013 cm−220,23. This behaviour is indeed observed in devices where a single boundary is positioned roughly in the middle of the tunnelling contact (type 1).

Fig. 2: Switching behaviour of FTJ over a MotSb/StMob dislocation (configuration 1) enabling full domain switching within the tunnelling area.
figure 2

a Schematic band diagram with equipotential source and drain, Vsd = 0. A small charge density σ is induced in graphene and graphite to cancel out the contact potential difference and ferroelectric potential from the rhombohedral MoS2 bilayer. Bold and dashed lines illustrate the potential profile created for upward and downward polarisation respectively. b Schematic band diagram when applying a small reverse bias Vsd, before the conduction band states of MoS2 become available for tunnelling. c Tunnelling conductance (dI/dV) as a function of the transverse electric field (Vsd) between the graphene source and the graphite drain. The direction of the Vsd sweeps is indicated by the arrows. Schematic insets show the domain configuration that produces the observed tunnelling behaviour, where the area of the FTJ electrode is indicated in grey (E). In the bottom-right corner, a friction AFM map shows the existing domain configuration prior to the sweeps. For this device, the tunnelling hBN has a thickness of 3 layers. These results were acquired at T = 1.5 K. d Same as c but with the field only applied in one direction showing that no polarisation reversal is occurring within the sample. No hysteresis is observed in these cases.

In Fig. 2c we plot the differential conductance in such a device, which shows clear hysteresis between the upwards and downwards directions of the applied field. It is important to note here that no hysteresis is observed until we increase the bias voltage above ±1.2 V, corresponding to external electric fields ≈ 0.55 V/nm, above which significant domain wall movement is expected20. Therefore, the appearance of the pronounced switching at higher bias voltages can be attributed to the domain wall being fully expelled from the tunnelling area, creating a configuration where all the current flows through one polarised domain only. Once the Vsd drops below -1 V, the opposite configuration is enabled, achieved by the reverse movement of the domain boundary across the tunnelling area and its expulsion on the other side, switching the FE polarisation in the entire device area. This is confirmed by a substantial change in the tunnelling current threshold on the return curve, both for positive and negative currents, ΔV+sd ≈ 170 mV and ΔV-sd ≈ 140 mV, respectively, which indicates a clear change in the tunnelling barrier height for different polarisations. The observed behaviour is consistent with the microscopic observations of the domain wall movement, where a substantial opposite field is required to completely reverse the domain layout20. The gradual movement of the domain wall across the device suggested by the absence of abrupt changes in the dI/dV characteristics is similar to conventional ferroelectric switching, where this phenomenon is attributed to disorder-controlled creep processes35. Consequently, if the voltage is repeatedly applied in one direction only (Fig. 2d), the switching is not observed as the FE polarisation remains in the same state. At higher temperatures, we observe strong activation behaviour, whereby electrons are thermally excited from the metallic graphite drain into the MoS2 since their energy separation is only UMoS ≈ 0.3 eV (see SI Fig. S5).

To understand the observed hysteresis behaviour, we model the FE tunnelling junction as a sequence of tunnel barriers with the profiles set by the band offsets and electric field distribution across the structure36,

$$I \propto {\int }_{\!\!\!0}^{-e{V}_{{{{{{\rm{sd}}}}}}}}{e}^{-2S\left(\varepsilon \right)}d\varepsilon,\; S\left({{{{{\rm{\varepsilon }}}}}}\right)={S}_{{{{{{\rm{MoS}}}}}}}+{S}_{{{{{{\rm{BN}}}}}}},\\ {S}_{X} ={\int }_{\!\!\!0}^{{d}_{{{{{{\rm{X}}}}}}}}\sqrt{\frac{2{m}_{X}}{{{{\hslash }}}^{2}}}\sqrt{{\varepsilon }_{\pm,X}(z)-{{{{{\rm{\varepsilon }}}}}}}{dz},\; X={{{{{\rm{MoS}}}}}},\, {{{{{\rm{BN}}}}}}.$$
(1)

Here, under the barrier action, \(S\left(\varepsilon \right)\) of a current carrier with energy \({{{{{\rm{\varepsilon }}}}}}\) is composed of contributions from hBN and MoS2, characterized by barrier profiles \({\varepsilon }_{\pm,{MoS}}(z)\) and \({\varepsilon }_{\pm,{BN}}\left(z\right)\) (see below), with \(+\) and \(-\) signs distinguishing two polarization states (MotSb and StMob) of MoS2 bilayer, and effective masses \({m}_{{{{{{\rm{MoS}}}}}}}\) and \({m}_{{{{{{\rm{BN}}}}}}}\), respectively. In hBN we take into account that the valence band is much closer to the graphene’s Fermi level than the conduction band, in contrast to MoS2 where the conduction band is closer to the graphite’s Fermi level. We also note that the band offsets relevant for the tunneling process are larger than the actual offsets of the valence band edge in hBN, \({-U}_{{BN}}\), and the conduction band edge in MoS2, \({U}_{{MoS}}\), as those crystals are not aligned/commensurate with the graphitic source and drain, so that tunneling through them involves arbitrary middle areas of their respective Brillouin zones away from band edge points. Because of this, we cannot uniquely quantify the value of the offsets for both materials (\({U}_{{{{{{\rm{BN}}}}}}}\, < \,0\) and \({U}_{{{{{{\rm{MoS}}}}}}}\)), as well as their out-of-plane effective masses for the conduction band states in MoS2 (\({m}_{{{{{{\rm{MoS}}}}}}}\)) and the valence band states in hBN (\({m}_{{{{{{\rm{BN}}}}}}}\, < \,0\)). Moreover, the absolute value of tunnelling transparency would additionally depend on the matching of the conduction/valence band states in MoS2/hBN at their interface and their contact with the graphitic electrodes.

Therefore, instead of attempting a detailed quantitative description of the I(V) characteristics, we focus on the qualitative trends related to the observed hysteresis behavior due to polarization switching. That is, we expand the barriers and their respective contributions towards the tunneling action to the linear order of the bias field, \({{{{{{\mathscr{F}}}}}}}_{{{{{{\rm{MoS}}}}}}/{{{{{\rm{BN}}}}}}}\), in MoS2/BN and double layer potential (\(\pm \triangle\) for the two polarization states -- MotSb and StMob -- of MoS2 bilayer):

$${\varepsilon }_{\pm,{{{{{\rm{MoS}}}}}}}\left(z \, < \, \frac{{d}_{{{{{{\rm{MoS}}}}}}}}{2}\right) ={U}_{{MoS}}+e{{{{{{\mathscr{F}}}}}}}_{{{{{{\rm{MoS}}}}}}}z{{{{{\rm{;}}}}}}\\ {\varepsilon }_{\pm,{{{{{\rm{MoS}}}}}}}\left(z \, > \, \frac{{d}_{{{{{{\rm{MoS}}}}}}}}{2}\right) ={\varepsilon }_{\pm,{{{{{\rm{MoS}}}}}}}^{(c/v)}\left(z \, < \, \frac{{d}_{{{{{{\rm{MoS}}}}}}}}{2}\right)\pm \triangle {{{{{\rm{;}}}}}} \, \\ {\varepsilon }_{\pm,{{{{{\rm{BN}}}}}}}\left(z\right) ={U}_{{{{{{\rm{BN}}}}}}}+e{{{{{{\mathscr{F}}}}}}}_{{{{{{\rm{MoS}}}}}}}{d}_{{{{{{\rm{MoS}}}}}}}+e{{{{{{\mathscr{F}}}}}}}_{{{{{{\rm{BN}}}}}}}\left(z-{d}_{{{{{{\rm{MoS}}}}}}}\right)\pm \triangle,$$
(2)

determining the exponential dependence of I(V) characteristics as

$$\begin{array}{c}{\left.{{{{\mathrm{ln}}}}}\frac{{dI}}{d{V}_{{{{{{\rm{sd}}}}}}}}\right|}_{{V}_{{{{{{\rm{sd}}}}}}} > 0}\propto \left|{{eV}}_{{{{{{\rm{sd}}}}}}}\right|\pm \frac{{\delta }_{ > }}{2},\, {\delta }_{ > }\, \approx \, \frac{2\sigma \left(\theta -1\right)}{\theta -\sigma -2}\Delta \\ {\left.{{{{\mathrm{ln}}}}}\frac{{dI}}{d{V}_{{{{{{\rm{sd}}}}}}}}\right|}_{{V}_{{{{{{\rm{sd}}}}}}} < 0}\propto \left|{{eV}}_{{{{{{\rm{sd}}}}}}}\right|\pm \frac{{\delta }_{ < }}{2},\, {\delta }_{ < }\, \approx \, \frac{2\sigma \left(\theta \, -\, 1\right)}{\theta \,-\, \sigma \,+\, 2\theta \sigma }\Delta \end{array},$$
(3)

Here, \(+\) is used for MotSb bilayer stacking and \(\mbox{--}\) for StMob, showing that MotSb stacking promotes tunneling for both directions of the applied bias, whereas StMob stacking demotes tunneling, which is a result of lack of mirror asymmetry in the device architecture (Fig. 1). The size of the bias offsets, \({\delta }_{ > }/e\) and \({\delta }_{ < }/e\), between the I(V) characteristics for the two FE states of MoS2 bilayer is parametrized using the following characteristics of the two materials:

$$\sigma=\frac{{d}_{{{{{{\rm{BN}}}}}}}}{{d}_{{{{{{\rm{MoS}}}}}}}}\frac{{\epsilon }_{{{{{{\rm{MoS}}}}}}}}{{\epsilon }_{{{{{{\rm{BN}}}}}}}},\, \theta=\frac{{d}_{{MoS}}}{{d}_{{BN}}}\sqrt{\frac{{m}_{{{{{{\rm{MoS}}}}}}}{U}_{{{{{{\rm{BN}}}}}}}^{3}}{{m}_{{{{{{\rm{BN}}}}}}}{U}_{{{{{{\rm{MoS}}}}}}}^{3}}}$$
(4)

Here, \({d}_{{{{{{\rm{MoS}}}}}}}=12.3 \, \text {{\AA}}\) and \({d}_{{{{{{\rm{BN}}}}}}}=3\times 3.33 \, \text {{\AA}}=9.99 \, \text {{\AA}}\) are the thicknesses of the corresponding layers, while \({\epsilon }_{{BN}}\, \approx \, 3\) and \({\epsilon }_{{MoS}}\, \approx \, 6.2\) are their dielectric permittivities37,38,39, hence, \(\sigma \, \approx \, 1.68\). Without knowledge of the precise values of the band offsets and effective masses, we can assess the qualitative features of the I(V) characteristics such as the bias voltage asymmetry. In this regard, eq. (3) shows a systematic difference between the bias offsets (due to the FE polarization of the MoS2 bilayer) for positive and negative voltages. In particular, in the case of \(\theta \, \gg \, 1\), expected for \(|{U}_{{{{{{\rm{BN}}}}}}}|\, \gg \, {U}_{{{{{{\rm{MoS}}}}}}}\) and \({m}_{{{{{{\rm{MoS}}}}}}} \sim -{m}_{{{{{{\rm{BN}}}}}}} \sim {m}_{0}\), we find that \({\delta }_{ > }\, \approx \, 231\) \({{{{{\rm{meV}}}}}}\,{{{{{\boldsymbol{ > }}}}}}\,{\delta }_{ < }\) \(\approx \, 48\) \({{{{{\rm{meV}}}}}}\) which is in general agreement with the experiment (Fig. 2c). Also, we note only a 10-fold ratio between ON current values in the two polarization states of MoS2 interface; to increase this ratio, one may try to vary hBN layer thickness, use monolayer/bilayer or bilayer/bilayer MoS2 structures (SI Fig. S9), employ multiple ferroelectric interfaces or make bilayer devices of narrower-gap TMDs, including MoTe2.

Having understood the effect of polarisation switching in single-domain tunnelling structures, we study devices fabricated of marginally twisted MoS2 bilayers where local lattice reconstruction leads to a periodic triangular domain layout (type 2). Such devices show a much smaller hysteresis, \(\delta /e\, \le \, 50\) mV (regardless of the bias voltage sweep range), Fig. 3a. This indicates that while the domain network does experience some changes due to expansion/contraction of MotSb/StMob areas, complete switching cannot be achieved, since both types of polarisation are present in the tunnelling area at all times. This complies with the earlier observed transformations of domains/domain wall networks in marginally twisted MoS2 bilayers, where it was noted that the networks of domain walls separating areas with opposite FE polarisation have a higher rigidity in bilayers with shorter moiré periods, and nodes of such networks are essentially pinned40,41 due to C3 symmetry of the acting forces. Also, we note that the period of the network of partial dislocations – domain walls is set by the local twist angle, imprinted in the device by the transfer, encapsulation, and contact deposition.

Fig. 3: Polarisation switching in FTJ with different domain layout and various nucleation scenarios.
figure 3

Tunnelling conductance (dI/dV) as a function of the transverse electric field (Vsd) between the graphene source and the graphite drain for: a periodic triangular domain network (L~60−150 nm) b three domains with domain walls pinned at the edges of tunnelling area using RIE and (c) uniform domain area with two perfect dislocations crossing the studied region. Tunnelling hBN thickness is 2 layers (a, b), and 4 layers (c). This hysteresis is only observable for a and b, reaching 17 mV in a and 7 mV in b between the forward and reverse sweeps. For the devices in a and b, the underlying hBN and R-MoS2 were etched as well as the top graphene contact to eliminate the possible interaction between devices and the surrounding unbiased bilayer. All the results were acquired at T = 1.5 K. Insets show the pre-existing domain configuration visualised using friction AFM (left) and its schematic representation (right) with colour indicating domain polarisation (blue and yellow for in and out of plane) and solid lines showing dislocations. d Dependences of critical size of a reversal polarisation domain seed on out-of-plane electric field for five scenarios of nucleation shown in e. In case (v) we estimated η = 0.04 eV as configuration-averaged energy (~0.4 eV/nm [2,28]) of stacking fault with the area of MoS2 monolayer unit cell.

Similar behaviour is observed in a sample where two domain walls are present and connected to an adjacent intersection, Fig. 3b. In this sample, however, the tunnelling junction was defined not only in graphene, but also etched into the MoS2 bilayer, removing the ferroelectric material around the junction. While we can only see the initial domain configuration, we expect the domain configuration to be pinned at the boundary of the tunnelling area due to the etching process, known to introduce substantial damage in the vicinity of the edge42. Therefore, the partial dislocation cannot be fully expelled from the sample. Similar pinning behaviour was recently observed on other structural defects, such as cracks, edges and contamination20,43.

The application of ferroelectric materials in electronic devices depends on one’s ability to switch the polarisation states of ferroelectric layer. The repolarisation can be considered as a two-stage process starting from nucleation of seeds, separated by domain walls from oppositely-polarised surrounding, followed their expansion into mesoscopic domains. Note that these domain walls are nothing but partial dislocations in rhombohedral layered crystals and are examples of topologically stable defects. The above-discussed examples of FE switching/hysteresis behaviour all include tunnel junctions for which domain nucleation did not happen as the areas under the source contained both MotSb and StMob domains, so that the repolarisation of the structure required only motion or elastic deformation of the pre-existing domain walls. Therefore, to test an opportunity of the seed nucleation, we also investigated tunnelling through single polarisation domain areas of MoS2 bilayer, both pristine and pierced by one perfect (full) dislocation, joining domains with the same polarisation (Fig. 3c). In the fabrication of such devices, we used a 7 L hBN tunnelling barrier enabling application of a higher electric bias for a wider range control of the ferroelectric state. However, despite applying stronger out-of-plane electric fields up to 0.85 V/nm, we systematically do not observe any hysteresis in the measurements. This behaviour qualitatively differs from the observations made on conventional FE materials, such as Pb(Zr,Ti)O3 and BaTiO3 where nucleation of domains with inverted FE polarisation was observed44,45 in electric fields as low as 0.01 V/nm.

We attribute this difference in behaviour to the sliding nature of the polarisation switching, specific to van der Waals systems with interfacial ferroelectricity17,18,19,20, which involves high elastic energy costs on domain wall bending to encompass a nanoscale seed with opposite polarisations. Below we consider several scenarios for a seed nucleation, including those tested in experiment, and evaluate for each of them a critical linear size of a seed that satisfies energetical trade-off between costs of extending length of domain wall and its bending as compared to the gain due to polarisation reversal inside the seed.

Below, we compare various options for how repolarisation can develop in the studied devices. First, we consider an isolated circular seed of StMob stacking inside a MotSb domain (case (i) in Fig. 3e). Such seed will have a critical radius when it becomes energetically favourable, \(r={w}_{{avg}}/{EP}\), determined by \({w}_{{avg}}=1.305\) eV/nm, the orientation-averaged domain wall energy per unit length34 and \(E,\) the repolarising field. Such critical nucleation radius would be smaller, \(r=({w}_{{avg}}-{u}_{*}/\pi )/{EP}\), for a seed initiated at a perfect dislocation (case (ii) in Fig. 3e, characterised34 by an energy per unit length of \({u}_{*}=2.24\) eV/nm). Here, we use the experimentally-confirmed32,38 theoretical estimations18 that domain wall energy per unit length is ~1 eV/nm, determined by the energy cost of strain. We also note that such large domain wall energy protects the studied devices against dipolar instability, as for the interfacial FE polarisation studied here, the dipole-dipole interaction for domains with a size L is equivalent to only \(\sim 6\frac{\mu {eV}}{{nm}}{{{{\mathrm{ln}}}}}\left(\frac{L}{{nm}}\right)\) reduction of domain wall energy (see in SI Section 6). Alternatively, one can imagine repolarisation to happen via unzipping a perfect dislocation in a pair of parallel partial dislocations (case (iii) in Fig. 3e): which would have energetically unfavourable orientations with energy per unit length \({w}_{*}=1.13\) eV/nm. This determines the critical width for the repolarised stripe as \(r=\left({2w}_{*}-{u}_{*}\right)/2{EP}\) (stability of an optimally-oriented perfect dislocation at E = 0 against such splitting has been shown in Ref. 18, whereas individual transfer-induced perfect dislocations would be pinned in a narrower part of the flake by simply their shorter geometrical length). The above three scenarios of a critical seed formation are illustrated in Fig. 3d to show that forming a seed with size comparable to twice a typical domain wall width would require a high field, \(E \sim 1\) eV/nm. Together the cases (i), (ii) and (iii) provide relatively high energy cost of the spontaneous domain nucleation, which explains lack of switching in devices where no, or only a perfect dislocation exist, such as in Fig. 3c. We would like to point out that this is not the case when two partial dislocations are pushed together by an external field and have been subsequently shown to split upon the field reversal20,23. This is likely due to incomplete merger of the partial dislocations seen in20 which provides seed for the reverse switching, as opposed to our case where the perfect dislocation is fully formed during the sample fabrication.

Potentially, seeding the inverted polarisation may be promoted at the physical edge of the MoS2 bilayer. One option is that a repolarised domain forms as a stripe (case (iv) in Fig. 3e) with the energy cost determined by a single domain wall energy. This energy cost would be minimised for a domain wall oriented following the armchair direction in the crystal, \(w=0.96\) eV/nm, with the corresponding critical stripe width being \(r=w/2{EP}\). This scenario is slightly less restrictive than the polarisation reversal inside a homogeneous domain. In a flake pierced by a full dislocation the nucleation of reversed polarisation appears to be even easier if it happens at the point where the full dislocation reaches the crystal’s edge. As an estimate we consider an armchair edge with a perfect screw dislocation sticking along zigzag direction (case (v) in Fig. 3e). Then, the repolarisation seed unzips this dislocation, forming a triangular seed with sides oriented along the other two armchair axes (lowest energy direction for MotSb/StMob domain wall). The energy of the triangular seed with a width \(r\) is \(-\frac{2}{\sqrt{3}}{EP}{r}^{2}+2w\frac{2r}{\sqrt{3}}-{u}_{*}r+\eta\), where \(\eta\) characterises energies of stacking faults at the edge termination and merging site of individual dislocations. We note34 that, accidentally, \(\frac{4w}{\sqrt{3}}\, \approx \,{u}_{*}\), so that we arrive at conditions for the critical seed size, \(r=\sqrt{\sqrt{3}\eta /2{EP}}\), which are relaxed when compared to all the other cases, Fig. 3d, over a broad range of energy \(\eta\). Therefore, we conclude that crystal edges would play a major role in polarisation switching. Further investigations of the domain wall textures near the edges are required, as well as their dependence on crystallographic orientation, and functionalization or passivation of dangling bonds. To realise such studies, one would need to design a suitable device architecture that would avoiding direct tunnelling currents near the R-TMD bilayer edge.

In conclusion, we observe drastically different switching behaviour to that of classical ferroelectric materials, which is extremely sensitive to the location of the FTJ. To achieve full switching, a single domain boundary must pre-exist within the device area and the ferroelectric material must extend beyond the source electrode footprint, providing room for the domain boundary to exit from the junction. Other domain layouts enable partial switching, which nevertheless has merit and can be considered for applications where continuous resistive switching can be employed. Finally, the devices with no domain boundaries or those only containing perfect dislocations do not display switching behaviour, however our modelling indicates that a presence of the physical edge of the ferroelectric crystal within the tunnelling can provide a nucleation point and make the switching possible.

Methods

For SPM domain mapping, Electrical AFM techniques such as piezo-responsive force microscopy (PFM) and electrostatic force microscopy (EFM) were used. Here, equally high-domain-contrast was achieved using lateral/friction and tapping mode when conductive (budget sensors Multi-75G) probes were used.

All electrical transport measurements were performed at 1.5 K (see SI for higher temperature data). When measuring the differential tunnelling conductance as a function of the transverse field, a sweeping DC bias with a constant small AC bias (1 mV) were applied to the graphene source electrode and the drain current was measured by a SR860 lock-in amplifier using a SR560 current preamplifier. The tunnelling conductance is defined as the ratio between the AC component of the tunnelling current and the applied AC bias.