An anisotropic van der Waals dielectric for symmetry engineering in functionalized heterointerfaces

Li, Zeya; Huang, Junwei; Zhou, Ling; Xu, Zian; Qin, Feng; Chen, Peng; Sun, Xiaojun; Liu, Gan; Sui, Chengqi; Qiu, Caiyu; Lu, Yangfan; Gou, Huiyang; Xi, Xiaoxiang; Ideue, Toshiya; Tang, Peizhe; Iwasa, Yoshihiro; Yuan, Hongtao

doi:10.1038/s41467-023-41295-6

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Published: 09 September 2023

An anisotropic van der Waals dielectric for symmetry engineering in functionalized heterointerfaces

Nature Communications volume 14, Article number: 5568 (2023) Cite this article

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Abstract

Van der Waals dielectrics are fundamental materials for condensed matter physics and advanced electronic applications. Most dielectrics host isotropic structures in crystalline or amorphous forms, and only a few studies have considered the role of anisotropic crystal symmetry in dielectrics as a delicate way to tune electronic properties of channel materials. Here, we demonstrate a layered anisotropic dielectric, SiP₂, with non-symmorphic twofold-rotational C₂ symmetry as a gate medium which can break the original threefold-rotational C₃ symmetry of MoS₂ to achieve unexpected linearly-polarized photoluminescence and anisotropic second harmonic generation at SiP₂/MoS₂ interfaces. In contrast to the isotropic behavior of pristine MoS₂, a large conductance anisotropy with an anisotropy index up to 1000 can be achieved and modulated in SiP₂-gated MoS₂ transistors. Theoretical calculations reveal that the anisotropic moiré potential at such interfaces is responsible for the giant anisotropic conductance and optical response. Our results provide a strategy for generating exotic functionalities at dielectric/semiconductor interfaces via symmetry engineering.

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Introduction

Symmetry breaking in low dimensional heterostructures can provide unprecedented possibilities to generate emergent quantum phenomena in condensed matter physics^{1,2,3,4,5,6,7,8}. In general, van der Waals (vdW) dielectric at atomically-sharp semiconductor/dielectric interfaces can break the symmetry of the target materials and form moiré patterns with specific lattice mismatch^2,9,10, exhibiting remarkable capabilities to control electronic states and further realize exotic quantum phenomena therein. Examples of these interfacial phenomena such as Chern insulating states^11,12, charge density wave states^13,14 and topological valley currents¹⁵ have been demonstrated in the heterointerfaces based on h-BN dielectric^{2,9,11,12,13,14,15,16,17}, in which both h-BN dielectric and channel materials (graphene or transition metal dichalcogenides, TMDCs) show threefold-rotational symmetry (C₃) along the out-of-plane axis at their interface. In contrast, a low-symmetric dielectric material without C₃ symmetry (for example, with C₂ symmetry) can in principle break the C₃ symmetry in monolayer semiconductors by forming anisotropic moiré potentials at the interface⁵ and result in exotic optical response and anisotropic electronic transport, while retaining the gating capability as a dielectric medium. Therefore, the vdW dielectrics with lower lattice symmetry can generate unique moiré physics and additional device functionalities at the symmetry-mismatched interfaces. However, an experimental confirmation of such a strategy remains elusive.

Herein, we demonstrate a unique anisotropic layered dielectric material SiP₂ and reveal its capability to generate giant anisotropy in optical response and electronic transport in isotropic TMDC semiconductors via symmetry engineering. We realize a high-performance SiP₂-gating MoS₂ transistor with large on/off ratios >10⁵ and low leakage currents (far below the low power limit) and further observe an insulator-to-metal transition in SiP₂-gated 1L-MoS₂, indicating a great dielectric capability of SiP₂ material. Surprisingly, a linearly-polarized photoluminescence and an anisotropic second harmonic generation signals are observed in 1L-MoS₂/SiP₂ heterostructure, which are in sharp contrast to the isotropic features of pristine 1L-MoS₂. Remarkably, we find a large anisotropic conductance in the 1L-MoS₂/SiP₂ heterostructure and the tunable anisotropy index reaches a considerable value of 1000 with SiP₂ gating, which is among the largest values reported so far, including intrinsically anisotropic materials¹⁸. Our first-principles calculations reveal that such giant anisotropy in optical response and electronic transport result from the generated anisotropic moiré potential in 1L-MoS₂/SiP₂ heterostructure that strongly renormalizes the structural and electronic properties of 1L-MoS₂ at the heterointerface. Note that the interfacial symmetry engineering by breaking the C₃ symmetry of 1L-MoS₂ using SiP₂ dielectric with C₂ symmetry can be regarded as a strategy to tune electronic properties of channel semiconductors and realize moiré physics at the heterointerfaces.

Results

MoS₂ transistors gated with SiP₂ dielectric

To evaluate the performance of the SiP₂ dielectric, we measured the transfer characteristics of MoS₂ transistors with dual-gate geometry in which 20-nm-thick SiP₂ and 300-nm-thick SiO₂ are used as top and bottom gate media (Fig. 1a, b and Supplementary Fig. 1). As shown in Fig. 1c, when sweeping the top gate voltage ${V}_{{{{{{\rm{t}}}}}}{{{{{\rm{g}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ up to 5 V, the 5-nm-thick MoS₂ transistor shows an on/off ratio as high as 10⁵, which is comparable to those values in h-BN-gated MoS₂ transistors (Supplementary Table 2) and meets the well-known criterion for practical logic circuit applications¹⁹. In contrast, when sweeping the bottom gate voltage ${V}_{{{{{{\rm{bg}}}}}}{-{{{{{\rm{SiO}}}}}}}_{2}}$ to ~5 V, the transistor generates an on/off ratio as small as 10, and requires a large ${V}_{{{{{{\rm{bg}}}}}}{-{{{{{\rm{SiO}}}}}}}_{2}}$ over 80 V to achieve an on/off ratio of 10⁵ (inset of Fig. 1c). This comparison directly demonstrates that, compared to SiO₂, the SiP₂ gate dielectric with larger dielectric constant and smaller thickness can achieve great capacitive capability. The measured leakage current of SiP₂-gated MoS₂ transistor is as small as approximately 10^–5 A cm^–2 at an external electric field strength of 1.5 MV cm^–1 (Fig. 1d). Such a low leakage current is comparable to those of transistors gated by high-κ dielectrics^19,20,21 such as Al₂O₃, HfO₂ or Bi₂SeO₅, and better than the criteria of the low-power limit and the standard complementary metal–oxide–semiconductor gate limit¹⁹. With increasing ${V}_{{{{{{\rm{t}}}}}}{{{{{\rm{g}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$, the field-effect mobility $\mu$ at 2 K can reach ~600 cm² V^–1 s^–1 when ${V}_{{{{{{\rm{bg}}}}}}{-{{{{{\rm{SiO}}}}}}}_{2}}$ is fixed at 35 V (Fig. 1e). Even for SiP₂-gated 1L-MoS₂ transistors with the same device geometry (Supplementary Fig. 2), the mobility of 330 cm² V^–1 s^–1 at 2 K is better than those reported values in HfO₂-gated 1L-MoS₂ devices²² (174 cm² V^–1 s^–1 at 4 K), indicating that the vdW SiP₂ material with a large dielectric constant can effectively reduce the charge scattering and increase the mobility of MoS₂ transistors. Such excellent performance with high on/off ratio, low leakage current, and high mobility in MoS₂/SiP₂ devices suggests that layered SiP₂ can be a high-performance dielectric in switching devices.

**Fig. 1: High-performance MoS₂ transistors gated with a SiP₂ dielectric with non-symmorphic C₂ rotational symmetry.**

To demonstrate the great gate tunability of SiP₂ dielectric, we measured the temperature-dependent sheet resistance (${R}_{{{{{{\rm{s}}}}}}}$–$T$) and observed a gating-induced insulator–metal transition in the 1L-MoS₂/SiP₂ transistor. As shown in Fig. 1f, the ${R}_{{{{{{\rm{s}}}}}}}$–$T$ curves show typical insulating behavior with negative temperature coefficients ${{{{{\rm{d}}}}}}{R}_{{{{{{\rm{s}}}}}}}/{{{{{\rm{d}}}}}}T$ and follow a thermal activation dependence²³ when ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ < 3.8 V and ${V}_{{{{{{\rm{bg}}}}}}{-{{{{{\rm{SiO}}}}}}}_{2}}$ = 0 V (Supplementary Fig. 3a). The extracted activation energy decreases monotonically from ~7 meV to near zero as ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ increases from 2.5 V to 3.8 V (Supplementary Fig. 3b). As a result, ${R}_{{{{{{\rm{s}}}}}}}$ starts to decrease with cooling temperature and the positive ${{{{{\rm{d}}}}}}{R}_{{{{{{\rm{s}}}}}}}/{{{{{\rm{d}}}}}}T$ shows the typical metallic behavior when ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ $ > $ 3.8 V, directly indicating an insulator–metal transition²³ in SiP₂-gated 1L-MoS₂. Such a transition in SiP₂-gated 1L-MoS₂ transistor directly manifests the excellent dielectric property of layered SiP₂ as a gate medium to modulate the electronic states of ultrathin semiconductors.

To experimentally evaluate the dielectric constant of SiP₂, we measured the sheet carrier density (${n}_{2{{{{{\rm{D}}}}}}}$) of MoS₂ (5 nm) as a function of ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ based on Hall effect measurements. The ${n}_{2{{{{{\rm{D}}}}}}}$ values of top-gated MoS₂ remain nearly unchanged below the threshold voltage of 1.7 V and can be continually modulated to 8 × 10¹²cm^–2 by increasing ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ to 5 V (Supplementary Fig. 4a). Note that the dual-gate-modulated ${n}_{2{{{{{\rm{D}}}}}}}$ can reach a maximum value close to 10¹³cm^–2 (Supplementary Fig. 4b). The relative dielectric constant ${\varepsilon }_{{{{{{\rm{r}}}}}}}$ is evaluated to be 8.1 for SiP₂ by fitting the linear part of the ${n}_{2{{{{{\rm{D}}}}}}}$–${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ data using ${n}_{2{{{{{\rm{D}}}}}}}={\varepsilon }_{0}{\varepsilon }_{{{{{{\rm{r}}}}}}}{V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}/(e{t}_{{{{{{{\rm{SiP}}}}}}}_{2}})$, where $e$ is the electron charge, ${\varepsilon }_{0}$ is the vacuum permittivity, and ${t}_{{{{{{{\rm{SiP}}}}}}}_{2}}$ = 20 nm is the thickness of SiP₂ (more details in “Methods”). Such a dielectric constant of 8.1 in layered SiP₂ is larger than those of SiO₂ and h-BN dielectrics^24,25 and comparable to that of Al₂O₃ dielectric²⁴ (Fig. 1g, a detailed comparison is given in Supplementary Tables 3 and 4), well consistent with the theoretical estimation from first-principles calculations²⁶.

As a typical vdW dielectric with excellent performance, another distinctive nature of SiP₂ is the anisotropic lattice structure with non-symmorphic C₂ symmetry. In sharp contrast to the highly symmetric crystal structure of those widely used dielectrics (oxides and h-BN), such an anisotropic in-plane lattice structure of SiP₂ leads to a highly anisotropic ratio of electron effective masses (~16, Fig. 1g) for the band edge states in its electronic band structure²⁶, and provides an opportunity to engineer the interfacial symmetry of vdW heterostructure combined monolayer TMDCs with SiP₂. For example, the 1L-MoS₂/SiP₂ heterostructure shows no rotational symmetry and can exhibit in-plane anisotropic optical and electronic properties (details discussed below). In particular, if the zigzag direction of MoS₂ and the P_B–P_B chain of SiP₂ (the direction parallel to the P_B–P_B chain of SiP₂ is defined as the y direction, while the perpendicular direction is defined as the x direction) are aligned in parallel (Fig. 2a, b), the mirror symmetry along the x direction can remain in the 1L-MoS₂/SiP₂ heterostructure; otherwise, all crystal symmetries in MoS₂ are broken. The perturbation for the electronic structures of stacked heterostructures can be used to generate in-plane polarization and Berry curvature dipole at the interface²⁷, realizing emergent interfacial phenomena such as directional quantum shift current⁵, nonlinear Hall effect¹ and circular photo-galvanic effect (Supplementary Fig. 5).

**Fig. 2: Anisotropic optical response at the TMDC/SiP₂ interface.**

SiP₂-induced anisotropic optical response in 1L-MoS₂

To understand the engineered symmetry of heterointerfaces, we performed second harmonic generation (SHG) measurements on 1L-MoS₂/SiP₂ heterostructures under a parallel measurement geometry (Fig. 2c). The SHG signal in pristine 1L-MoS₂ shows a sixfold-rotational symmetric pattern with maxima of SHG intensity along its armchair direction and can be well fitted with Eq. (1), implying the C₃-rotational symmetry of 1L-MoS₂ samples²⁸. While in 1L-MoS₂/SiP₂ heterostructure, the SHG signal presents an additional twofold component imposed to the six symmetric petals (detailed analysis in “Methods”). Such a twofold component does not originate from the C₃-symmetric lattice of 1L-MoS₂ itself, but results from the reduced symmetry at the 1L-MoS₂/SiP₂ heterointerface. The SHG intensities can be well fitted with Eq. (2) in the “Methods”, similar to those distorted SHG scenarios in uniaxially-strained 1L-MoS₂ samples^29,30. Note that SiP₂ itself has no SHG signal due to the existing inversion symmetry in its crystal lattice (Supplementary Fig. 9c), ensuring that the observed SHG signal of 1L-MoS₂/SiP₂ heterostructure mainly originates from 1L-MoS₂ whose band structure is effectively modified by the potential on the heterointerface created by the bottom C₂ symmetric SiP₂. More importantly, the anisotropic SHG response at 1L-MoS₂/SiP₂ changes little with increasing SiP₂ thickness (Supplementary Fig. 11), further confirming that this is an interfacial phenomenon induced by symmetry breaking at the 1L-MoS₂/SiP₂ heterointerface between the 1L-MoS₂ and the topmost SiP₂ layer.

To investigate the effect of symmetry engineering on the optical properties of such an interface, we performed polarization-dependent photoluminescence (PL) measurements in the 1L-MoS₂/SiP₂ heterostructure at 77 K (Fig. 2d, e and Supplementary Fig. 6). For SiP₂, the PL signal with an excitonic emission energy of 2.06 eV at 77 K shows a linear polarization along the x direction of the lattice²⁶. In contrast, for 1L-MoS₂ without SiP₂ stacking layer, the excitonic emission of 1L-MoS₂ at 1.91 eV at 77 K remains unchanged with the detection polarization angle and shows no linear polarization. While, for the 1L-MoS₂/SiP₂ heterostructure, the excitonic state of 1L-MoS₂ with an emission energy of 1.91 eV becomes linearly polarized along the x direction of SiP₂ (Fig. 2f and Supplementary Fig. 7). The similar results can be observed at 77 K and 300 K in 1L-WS₂/SiP₂ heterostructure (Supplementary Fig. 8), indicating the anisotropic PL response in TMDC/SiP₂ is robust with temperatures. Similar anisotropic SHG responses are also observed in 1L-WS₂/SiP₂ heterostructure (details in Supplementary Fig. 9), indicating that SiP₂ dielectric can effectively engineer the symmetry of its neighboring monolayer TMDC through tunable interlayer interactions. More interestingly, the anisotropic PL and SHG responses strongly depended on the twist angle between MoS₂ and SiP₂, and the corresponding anisotropy dramatically decreased when the mirror symmetry of moiré superlattice varnishes with changing the twist angle (Supplementary Figs. 12 and 13). This result indicates that the mirror symmetry of MoS₂/SiP₂ moiré superlattice plays an important role in controlling the magnitude of anisotropic optical responses at the heterointerface. The symmetry breaking induced anisotropic behavior can exist at those interfaces stacked with the C₃-symmetric monolayer TMDCs and C₂-symmetric dielectrics, enabling a strategy to explore applications such as polarization-sensitive photodetectors³¹.

Giant anisotropic conductance in SiP₂-gated MoS₂ transistors

To investigate the interfacial symmetry modulation on the electronic transport properties of MoS₂, we measured the conductance ${G}_{x}$ (${G}_{y}$) along the x (y) directions of SiP₂-gated 1L-MoS₂ transistors (Fig. 3a, Supplementary Figs. 14 and 15). Figure 3b shows a comparison between ${G}_{x}$ and ${G}_{y}$ under different ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$. One can see that the anisotropy index ${G}_{y}$/${G}_{x}$ can be as high as 10³ at the off-state with ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$ < 1 V (Fig. 3c), implying that the symmetry engineering using SiP₂ dielectric can drive the isotropic conductivity of C₃-symmetric 1L-MoS₂ into highly-anisotropic electronic states. With further increasing ${V}_{{{{{{\rm{tg}}}}}}{-{{{{{\rm{SiP}}}}}}}_{2}}$, the anisotropy index gradually approaches the value of 1, suggesting that 1L-MoS₂ recovers back to isotopically conducting states at the on-state. Such continuous modulation of ${G}_{x}$, ${G}_{y}$, and ${G}_{y}$/${G}_{x}$ index can also be achieved at a wide range of ${V}_{{{{{{\rm{bg}}}}}}{-{{{{{\rm{SiO}}}}}}}_{2}}$ (Fig. 3d–f). The tunable conductance from anisotropic to isotropic characteristics suggests that SiP₂ with in-plane anisotropy is anticipated to stimulate device functionality exploration for anisotropic digital inverters³², anisotropic memorizers³³, or artificial synaptic devices³⁴.

**Fig. 3: Gate tunable anisotropic transfer characteristics of MoS₂/SiP₂ heterointerfaces.**

To confirm that such anisotropic conductance originates from the MoS₂/SiP₂ heterointerface, we compared the ${G}_{x}$ and ${G}_{y}$ values of SiP₂-gated MoS₂ transistors by increasing the thickness of MoS₂ from monolayer to 20 nm. As a result, the observed anisotropy index ${G}_{y}$/${G}_{x}$ at the off-state decreases rapidly to ~1 when the thickness of MoS₂ is increased to 20 nm (Fig. 3g, Supplementary Figs. 16 and 17), suggesting a nearly isotropic conductance in thicker samples. Such a thickness-dependent behavior is proposed to be attributed to the competition between the surface and bulk conductance, as qualitatively described in Supplementary Fig. 18. Specifically, the anisotropy index of MoS₂ can be written as $\frac{{G}_{y}}{{G}_{x}}=\frac{{G}_{y}^{{{{{{\rm{surface}}}}}}}+{G}_{y}^{{{{{{\rm{bulk}}}}}}}}{{G}_{x}^{{{{{{\rm{surface}}}}}}}+{G}_{x}^{{{{{{\rm{bulk}}}}}}}}$, where bulk conductance (proportional to the sample thickness) is isotropic ${G}_{y}^{{{{{{\rm{bulk}}}}}}}$ ≈ ${G}_{x}^{{{{{{\rm{bulk}}}}}}}$ while surface conductance is anisotropic since only the surface layer of MoS₂ with certain thickness (within the Thomas-Fermi screening length) can be tuned for carrier accumulation with SiP₂ dielectric based on our numerical Poisson-Schrödinger calculations (Supplementary Figs. 19 and 20). For SiP₂-gated 1L-MoS₂ case, ${G}_{y}^{{{{{{\rm{bulk}}}}}}}$ = ${G}_{x}^{{{{{{\rm{bulk}}}}}}}$ = 0 and only the MoS₂ layer on the interface (namely the whole monolayer) contributes to the conductance, so the anisotropy index can be written as $\frac{{G}_{y}}{{G}_{x}}=\frac{{G}_{y}^{{{{{{\rm{surface}}}}}}}}{{G}_{x}^{{{{{{\rm{surface}}}}}}}}$, whose value can be as high as 1000. When increasing the thickness of MoS₂, ${G}_{y}^{{{{{{\rm{bulk}}}}}}}$ and ${G}_{x}^{{{{{{\rm{bulk}}}}}}}$ begin to increase and gradually dominate the total conductance with ${G}^{{{{{{\rm{surface}}}}}}}$ ≪ ${G}^{{{{{{\rm{bulk}}}}}}}$ at the thick limit. As a result, the anisotropy index is reduced to $\frac{{G}_{y}}{{G}_{x}}=\frac{{G}_{y}^{{{{{{\rm{bulk}}}}}}}}{{G}_{x}^{{{{{{\rm{bulk}}}}}}}}=1$, which is consistent with our experimental observation of less anisotropy in SiP₂-gated MoS₂ with a thickness of 20 nm. This result indicates that the anisotropic conductance behavior is contributed exactly from the interface of the MoS₂/SiP₂ heterostructures (details in Supplementary Figs. 18–20). Compared to those vdW materials with in-plane anisotropic crystal lattices and electronic structures^18,35, our SiP₂-gated 1L-MoS₂ not only has the largest anisotropy index but also hosts the greatest capability to tune such an anisotropy index (Fig. 3h).

Anisotropic moiré potential at 1L-MoS₂/SiP₂ interface

To further understand the influence of interface structures on the anisotropic optical and transport behavior, we explore the structural and electronic properties of the 1L-MoS₂/SiP₂ heterostructure by using density functional theory (DFT) calculations. Note that the mirror symmetry of the constructed MoS₂/SiP₂ heterointerface originates from the parallel or antiparallel alignment of the zigzag chain in MoS₂ along the y direction of SiP₂ (see details in Supplementary Fig. 21). Thus, two kinds of moiré patterns can be obtained (labeled as case-I and case-II, details in Section 13 in Supplementary Information). Taking the moiré pattern of case-I as an example (Fig. 4a, b), due to the lattice mismatch between MoS₂ and SiP₂, there are three typical stacking structures, labeled as I-AA, I-AB, and I-BA, as indicated by the colored rectangular areas in Fig. 4a. The details about atomic stacked configurations and stacked structures with II-AA, II-AB, and II-BA in the moiré pattern of case-II are shown in Supplementary Fig. 21d.

**Fig. 4: Structural and electronic properties of the MoS₂/SiP₂ heterointerface.**

The structural corrugations in 1L-MoS₂/SiP₂ heterostructure with two kinds of moiré patterns are simulated via DFT calculations (Fig. 4c and Supplementary Fig. 27b, e). After being placed on the SiP₂ lattice, the atomic flat structure of 1L-MoS₂ will be deformed due to the interface coupling, resulting in the formation of moiré potential on 1L-MoS₂ that effectively breaks C₃-rotational symmetry of the pristine MoS₂. In contrast, the structural corrugations in 1L-SiP₂ are much smaller compared with that in 1L-MoS₂ (Supplementary Fig. 25). Furthermore, we plot the distribution of the interlayer distance (marked in Fig. 4b) for the moiré pattern of case-I in Fig. 4c to demonstrate the moiré potential in this heterostructure. In the moiré pattern of case-I, the stacked region of I-BA hosts the smallest interlayer distance between MoS₂ and SiP₂, indicating the largest structural deformation on 1L-MoS₂ and interlayer coupling. However, in the moiré pattern of case-II such region with the largest moiré potential and lattice deformation becomes II-AA (Supplementary Fig. 27e). On the other hand, the mirror symmetry parallel to the armchair direction of 1L-MoS₂ (also the x direction of the heterostructure) is always observed in both moiré patterns of 1L-MoS₂/SiP₂ heterostructures that is determined by the specific stacked regulations in the fabrication of experimental devices. Such characters with reduced symmetry in corrugated 1L-MoS₂ are consistent with the symmetry analysis to stacking structures with moiré patterns. Our simulated structural deformation of corrugated 1L-MoS₂ with moiré patterns gives a consistent interpretation on the change of the symmetric shape of the experimental SHG spectra from sixfold (1L-MoS₂) to twofold (1L-MoS₂/SiP₂).

The out-of-plane structural corrugations of 1L-MoS₂ with moiré patterns can strongly modulate its electronic structures and thus influence the optical properties. Since the direct simulation of the large-size moiré lattice by using DFT are too expensive to afford, to overcome this issue, we use a strained MoS₂ and SiP₂ to construct a heterostructure guaranteeing the conduction band offset between MoS₂ and SiP₂ same with that in the moiré heterostructure, then simulate the influence of the moiré potential on the electronic states of 1L-MoS₂ (details in Sections 14–17 in Supplementary Information). The exemplified results are presented in the heterostructure model with stacking regions of I-AB and I-BA (named as case-I-ABBA). Figure 4g and h demonstrates the charge density distribution for conduction band edge in case-I-ABBA, and Fig. 4e and f shows the plane-averaged charge density along the z and y directions (Section 17 in Supplementary Information). In the heterostructure model with fully relaxation, out-of-plane corrugation can be clearly observed with the retaining of the mirror symmetry in the moiré pattern. The conduction band edge in 1L-MoS₂/SiP₂ heterostructure is dominated by the state from the MoS₂ layer, while its charge density distribution has been strongly modified by the lattice deformation. The calculated results for other heterostructure models containing different stacked regions are shown in Section 17 in Supplementary Information. The conduction band edge in 1L-MoS₂/SiP₂ heterostructure is always strongly modified by the moiré potential. For the case-II moiré pattern, we build similar models and obtain the same conclusions (details in Sections 16 and 17 in Supplementary Information). Compared with pristine 1L-MoS₂ with C₃-rotational symmetry, the symmetry engineering on the conduction band edge can be clearly observed in 1L-MoS₂/SiP₂ heterostructure. With breaking C₃-rotational symmetry by SiP₂, the conduction band edge on deformed 1L-MoS₂ only keeps the mirror symmetry (Fig. 4f). Therefore, when one electron is excited on conduction band edge and couples with hole states, the optical matrix elements in formed exciton should be strongly modified by the moiré potential with lower symmetry and the lowest bright exciton absorption becomes highly anisotropic, which is consistent with the observation from our PL experiments.

The formation of moiré potential with symmetry engineering can also explain the experimentally observed giant anisotropic conductance in SiP₂-gated MoS₂ transistors. At the off-state with low carrier density (~5 × 10⁹cm^–2) and low temperature (2 K), the charge carriers in 1L-MoS₂/SiP₂ heterostructure are mainly trapped by charged impurities^22,36,37,38 and the moiré potentials, thus the giant anisotropic conductance of 1L-MoS₂ is mainly contributed by the effective hopping between trapped charge states in the moiré potentials^22,36,37,38. Since the charged defects in 1L-MoS₂ are distributed randomly without anisotropy, the anisotropic moiré potential should be a critical factor for the anisotropic conductance in the SiP₂-gated MoS₂ transistor. Similar to previous discussions, we also take the moiré pattern of case-I as an example (the discussion of the moiré pattern of case-II draws the same conclusion), the distribution of interlayer distance between SiP₂ and MoS₂ in real space (Fig. 4c) shows that the smallest interlayer distance is located in the I-BA stacking region, which corresponds to the largest interlayer potential and can effectively trap the charge carriers inside. On the other hand, the anisotropic moiré potential results in highly anisotropic hopping between trapped states. For example, the effective hopping along the parallel direction (||) to the mirror plane is naturally smaller than that along the perpendicular direction (⊥), indicating that, at the off state, the effective mass of these trapped states is highly anisotropic (${m}_{\parallel }\gg {m}_{\perp }$). The large ratio of effective mass (${m}_{\parallel }$/${m}_{\perp }$) leads to the highly-anisotropic conductance in 1L-MoS₂/SiP₂ heterostructure. With increasing the electron density to reach the on-state, the moiré potential cannot fully trap these charge carriers and its influence on transport becomes unimportant, delocalizing the 2D electron gas formed on the 1L-MoS₂ layer. Thus, the conductance turns out to be isotropic at the on-state.

Discussion

In conclusion, we demonstrate an anisotropic van der Waals dielectric SiP₂ that can simultaneously tune the electronic states of channel semiconductors and induce symmetry engineering at TMDC/SiP₂ interfaces. Our first-principles calculations reveal that these anisotropic characteristics originate from the formation of the anisotropic-symmetric moiré potential in the MoS₂/SiP₂ heterostructure, which strongly modulates structural and electronic properties of 1L-MoS₂ with tunable anisotropic symmetry. The tunable interfacial symmetry in the TMDC/SiP₂ heterostructure can provide a unique platform for investigating symmetry-related interfacial physics and corresponding phenomena, including the generation of the in-plane polarization⁵ (bulk photovoltaic effect and quantum shift current) and the Berry curvature dipole^39,40,41 (circular photo-galvanic effect and nonlinear Hall effect). The giant anisotropy generated in the TMDC/SiP₂ heterostructure, which is absent in the pristine TMDC material, sheds light on the moiré physics of the engineered interface with reduced symmetry, and provides an effective way to control the degree of freedom of electrons in condensed matter systems.

Methods

Crystal symmetry analyses of TMDC/SiP₂ heterostructures

The orthorhombic SiP₂ crystal exhibits an anisotropic layered structure (space group $P{nma}$) with an embedded quasi-one-dimensional P_B–P_B chains along the y direction of the crystal lattice. Specifically, three important spatial symmetry operations should be addressed in this atomic structure of the SiP₂ crystal when stacking SiP₂ with monolayer TMDCs. First, there is a non-symmorphic C₂ symmetry about the z direction (the screw symmetry S₂ that combines a twofold rotational symmetry with a translation along the z direction in the half-unit-cell, S₂ = C₂ + z/2) in the SiP₂ crystal. This non-symmorphic C₂ symmetry of bulk SiP₂ is incompatible with C₃ symmetry of TMDCs and will result in highly anisotropic nature (C₁ symmetry) of the TMDC/SiP₂ heterostructures. Second, the atomic structure of SiP₂ is inversion symmetric, which means there is no SHG signal of SiP₂ flakes, ensuring that the distorted SHG signals at the TMDC/SiP₂ heterostructure mainly come from the symmetry breaking at the heterointerface. Third, there is a mirror symmetry perpendicular to the P_B–P_B chains (y direction) of the SiP₂ crystal. This vertical mirror can remain in the TMDC/SiP₂ heterostructures when stacking the TMDCs and SiP₂ by aligning their mirror planes (the zigzag direction of TMDCs is parallel to the P_B–P_B chains of SiP₂), generating a mirror symmetric anisotropic moiré potential at the heterointerface.

Optical measurements of TMDC/SiP₂ heterointerfaces

SiP₂ flakes and TMDC flakes were prepared by mechanical exfoliation onto polydimethylsiloxane (PDMS) stamps and SiO₂/Si wafers (300-nm-thick SiO₂ layer). TMDC/SiP₂ heterointerfaces were fabricated using a dry-transfer method and stacked by parallelly aligning the zigzag direction of MoS₂ and y direction of SiP₂. The crystal axes of the 1L-MoS₂ samples are confirmed by their polarized-SHG results. And the crystal axes of SiP₂ are first identified by their optical image and then confirmed by their polarized PL results. The whole sample fabrication was processed in a glove box to avoid any degradation. Room temperature PL measurements were performed using a confocal Raman system (WITec Alpha 300) using a 50× objective lens with an incident laser (laser power of 1 mW) focused to a 1 μm spot size. Nitrogen-filled environments were established by protecting samples with continuous nitrogen gas flow. Low-temperature PL measurements were performed under vacuum conditions in cryostats (Cryo Instrument of America RC102–CFM Microscopy Cryostat). For polarized PL measurements, the excitation polarization is fixed along the x direction, and the detection polarization is changed from θ = 0° to 180° (θ is the angle between the detection polarization and the x direction).

The SHG measurements were performed using a Ti:sapphire oscillator with an excitation wavelength of 810 nm, pulse width of 70 fs, and repetition rate of 80 MHz. The laser pulse was focused to an ~1 μm spot size by a 40× objective lens. The SHG signals are obtained under a configuration with the detection polarization parallel to the excitation polarization. For the SHG signal of 1L-TMDCs on the SiO₂ substrate, the sixfold symmetric SHG intensities are fitted by Eq. (1):

$${I}_{{{{{{\rm{SHG}}}}}}}^{\parallel }\propto {\cos }^{2}3\theta$$

(1)

Normally, for those uniaxially-strained TMDCs, the SHG intensities ${I}_{{{{{{\rm{SHG}}}}}}}^{\parallel }$ parallel to the incident laser polarization can be written as:

$${I}_{{{{{{\rm{SHG}}}}}}}^{\parallel }\propto {\left[\cos 3\theta+{\varepsilon }_{y}\left({k}_{1}{\cos }^{3}\theta -{k}_{2}{\sin }^{2}\theta \cos \theta \right)\right]}^{2}$$

(2)

where ${\varepsilon }_{y}$ is the strain along the y direction, ${k}_{1}$ and ${k}_{2}$ are parameters related to TMDCs. In our case of the 1L-MoS₂/SiP₂, the C₃ symmetry of 1L-MoS₂ is also reduced to low symmetry such as C₁. Therefore, we fit our data by Eq. (2) to describe the anisotropic SHG response in our 1L-MoS₂/SiP₂.

Electrical transport measurements

The 1L-MoS₂ (or few-layer MoS₂) and SiP₂ flakes for electronic transport measurements were exfoliated onto a PDMS stamp and transferred onto a silicon substrate with prepatterned electrodes (Ti/Au with a thickness of 3/9 nm) in sequence. A top gate on the SiP₂ flake (Ti/Au with a thickness of 5/45 nm) was then made using electron-beam lithography and electron-beam evaporation. Electrical transport measurements were performed in a cryo-free superconducting magnet system (Oxford Instruments Teslatron^PT). Four-terminal resistance ${R}_{{xx}}$ was acquired using a Keithley 2182 voltmeter with a DC current supplied by a Keithley 2400 sourcemeter. The gate voltage is supplied by a Keithley 2400 sourcemeter. The sheet carrier density (${n}_{2{{{{{\rm{D}}}}}}}$) is obtained based on Hall effect measurements on Au/SiP₂/MoS₂ sandwiched devices²². The Au/SiP₂/MoS₂ device can be considered as a parallel plate capacitor, and the amount of charge per unit area can be written as:

$$e{n}_{2{{{{{\rm{D}}}}}}}=\frac{{\varepsilon }_{0}{\varepsilon }_{{{{{{\rm{r}}}}}}-{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}}{{t}_{{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}}{V}_{{{{{{\rm{tg}}}}}}-{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}$$

(3)

where $e$ is the electron charge, ${\varepsilon }_{0}$ is the vacuum permittivity, ${t}_{{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}$ = 20 nm is the thickness of SiP₂, and ${\varepsilon }_{{{{{{\rm{r}}}}}}-{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}$ is the relative dielectric constant of SiP₂ within the Au/SiP₂/MoS₂ sandwiched structure. The ${\varepsilon }_{{{{{{\rm{r}}}}}}-{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}$ is obtained by linear fitting of Eq. (3).

DFT calculations

The Vienna Ab initio Simulation package (VASP)⁴² was used for the first-principles calculations. The generalized-gradient approximation (GGA) of the Perdew-Burke-Ernzerhof-type functional⁴³ was used with the projected-augmented-wave method^44,45 and an energy cutoff of 500 eV. For the electronic self-consistent calculations, the convergence criterion was set as 10^–6 eV. Considering the van der Waals interaction, the DFT-D3 method⁴⁶ was applied as the correction. The force criterion was chosen to be 0.01 eV Å^–1. After fully relaxing the 2H-MoS₂ bulk structure, we obtained the lattice constants of 3.16 Å for a (and b) and 12.39 Å for c, which were consistent with previous studies^47,48. The k-point mesh of 15 × 15 × 3 was used to sample the Brillouin zone (BZ). After the full relaxation of the SiP₂ bulk structure, the lattice constants were 10.11 Å for a, 3.44 Å for b, and 14.18 Å for c, which were consistent with the experimental results⁴⁹. The k-point mesh of 5 × 15 × 4 was used to sample the BZ of bulk SiP₂. Moreover, except for the structural relaxation, the spin-orbit coupling was considered in all DFT calculations. For all slab models used in this work, a vacuum layer with 20 Å was added along the z direction. Moreover, the calculations with the HSE06 functional^50,51 were performed to obtain the accurate values of the work function and bandgap of the unstrained and strained MoS₂ and SiP₂ monolayers.

For these heterostructure models with strained MoS₂ and SiP₂ which were used to simulate the electronic properties of 1L-MoS₂/SiP₂ heterostructure directly, the $2\sqrt{3}\times 1$ rectangle supercell for monolayer MoS₂ was used and its lattice was tensed to 3.25 Å for a, and was compressed to 10.69 Å for b. Correspondingly, the lattice of monolayer SiP₂ was enlarged to 3.50 Å for a and 10.69 Å for b. In each strained heterostructure model, it contains 13 × 1 monolayer SiP₂ unitcells and 14 × 1 rectangle supercells for monolayer MoS₂. The k-point mesh of 5 × 1 × 1 was used to sample the BZ of heterostructure model. For strained case-I-ABBA and case-II-AABA lattices, we fully relaxed the whole structures. While, for strained case-I-AA and case-II-AB lattices, we fixed the x and y coordinates of the two central S atoms in MoS₂ layer and one central P atom in SiP₂ layer in the AA/AB stacking region. Then we fully relaxed other atoms in the strained heterostructure model.

Data availability

The Source Data underlying the figures of this study are available at https://doi.org/10.6084/m9.figshare.23623722. All raw data generated during the current study are available from the corresponding authors upon request.

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Acknowledgements

This work was supported by the A3 Foresight Program—Emerging Materials Innovation. The authors would like to acknowledge the support by the National Natural Science Foundation of China (grant nos. 51861145201 (H.T.Y.), 52072168 (H.T.Y.), 21733001 (H.T.Y.), 12204232 (F.Q.), 12234011 (P.T.)), the National Key Research and Development Program of China (grant nos. 2018YFA0306200 (H.T.Y.), 2021YFA1202901 (J.H.)), the Natural Science Foundation of Jiangsu Province (grant no. BK20220758 (F.Q.)), KAKENHI grant JP19H05602 (Y.I.) and JP23H00088 (T.I.) from Japan Society for the Promotion of Science (JSPS) and JST FOREST (grant no. JPMJFR213A (T.I.)).

Author information

These authors contributed equally: Zeya Li, Junwei Huang, Ling Zhou, Zian Xu.

Authors and Affiliations

National Laboratory of Solid State Microstructures, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China
Zeya Li, Junwei Huang, Ling Zhou, Feng Qin, Peng Chen, Xiaojun Sun, Gan Liu, Chengqi Sui, Caiyu Qiu, Xiaoxiang Xi & Hongtao Yuan
College of Engineering and Applied Sciences, and Jiangsu Key Laboratory of Artificial Functional Materials, Nanjing University, Nanjing, 210023, China
Zeya Li, Junwei Huang, Ling Zhou, Feng Qin, Peng Chen, Xiaojun Sun, Chengqi Sui, Caiyu Qiu & Hongtao Yuan
School of Materials Science and Engineering, Beihang University, Beijing, 100191, China
Zian Xu & Peizhe Tang
School of Physics, Nanjing University, Nanjing, 210093, China
Gan Liu & Xiaoxiang Xi
College of Materials Sciences and Engineering, National Engineering Research Center for Magnesium Alloys, Chongqing University, Chongqing, 400030, China
Yangfan Lu
Center for High Pressure Science and Technology Advanced Research, Beijing, 100094, China
Huiyang Gou
Quantum Phase Electronic Center and Department of Applied Physics, The University of Tokyo, Tokyo, 113-8656, Japan
Toshiya Ideue & Yoshihiro Iwasa
Institute for Solid State Physics, The University of Tokyo, Chiba, 277-8581, Japan
Toshiya Ideue
Max Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Hamburg, 22761, Germany
Peizhe Tang
RIKEN Center for Emergent Matter Science, Hirosawa 2-1, Wako, 351-0198, Japan
Yoshihiro Iwasa

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Zeya Li
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Contributions

Z.L., J.H., L.Z., and Z.X. equally contributed to this work. H.T.Y., P.T., and Y.I. conceived the project and designed the experiments. Z.L., X.S., and C.Q. fabricated samples for optical measurements and carried out PL measurements. L.Z., Z.L., P.C., and C.S. fabricated transport devices. J.H. and L.Z. carried out electrical resistance measurements. G.L. and X.X. carried out SHG measurements. Y.L. and H.G. synthesized the SiP₂ crystals. L.Z. and Z.L. performed Poisson-Schrödinger equation calculations. Z.X. and P.T. performed ab initio calculations and model simulations. Z.L., F.Q., T.I., and Y.I. analyzed the data. Z.L. and H.T.Y. wrote the manuscript with all the authors’ input.

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Correspondence to Toshiya Ideue, Peizhe Tang or Hongtao Yuan.

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Li, Z., Huang, J., Zhou, L. et al. An anisotropic van der Waals dielectric for symmetry engineering in functionalized heterointerfaces. Nat Commun 14, 5568 (2023). https://doi.org/10.1038/s41467-023-41295-6

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Received: 23 March 2023
Accepted: 29 August 2023
Published: 09 September 2023
DOI: https://doi.org/10.1038/s41467-023-41295-6

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