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, SiP_{2}, with nonsymmorphic twofoldrotational C_{2} symmetry as a gate medium which can break the original threefoldrotational C_{3} symmetry of MoS_{2} to achieve unexpected linearlypolarized photoluminescence and anisotropic second harmonic generation at SiP_{2}/MoS_{2} interfaces. In contrast to the isotropic behavior of pristine MoS_{2}, a large conductance anisotropy with an anisotropy index up to 1000 can be achieved and modulated in SiP_{2}gated MoS_{2} 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 atomicallysharp 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 currents^{15} have been demonstrated in the heterointerfaces based on hBN dielectric^{2,9,11,12,13,14,15,16,17}, in which both hBN dielectric and channel materials (graphene or transition metal dichalcogenides, TMDCs) show threefoldrotational symmetry (C_{3}) along the outofplane axis at their interface. In contrast, a lowsymmetric dielectric material without C_{3} symmetry (for example, with C_{2} symmetry) can in principle break the C_{3} symmetry in monolayer semiconductors by forming anisotropic moiré potentials at the interface^{5} 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 symmetrymismatched interfaces. However, an experimental confirmation of such a strategy remains elusive.
Herein, we demonstrate a unique anisotropic layered dielectric material SiP_{2} and reveal its capability to generate giant anisotropy in optical response and electronic transport in isotropic TMDC semiconductors via symmetry engineering. We realize a highperformance SiP_{2}gating MoS_{2} transistor with large on/off ratios >10^{5} and low leakage currents (far below the low power limit) and further observe an insulatortometal transition in SiP_{2}gated 1LMoS_{2}, indicating a great dielectric capability of SiP_{2} material. Surprisingly, a linearlypolarized photoluminescence and an anisotropic second harmonic generation signals are observed in 1LMoS_{2}/SiP_{2} heterostructure, which are in sharp contrast to the isotropic features of pristine 1LMoS_{2}. Remarkably, we find a large anisotropic conductance in the 1LMoS_{2}/SiP_{2} heterostructure and the tunable anisotropy index reaches a considerable value of 1000 with SiP_{2} gating, which is among the largest values reported so far, including intrinsically anisotropic materials^{18}. Our firstprinciples calculations reveal that such giant anisotropy in optical response and electronic transport result from the generated anisotropic moiré potential in 1LMoS_{2}/SiP_{2} heterostructure that strongly renormalizes the structural and electronic properties of 1LMoS_{2} at the heterointerface. Note that the interfacial symmetry engineering by breaking the C_{3} symmetry of 1LMoS_{2} using SiP_{2} dielectric with C_{2} symmetry can be regarded as a strategy to tune electronic properties of channel semiconductors and realize moiré physics at the heterointerfaces.
Results
MoS_{2} transistors gated with SiP_{2} dielectric
To evaluate the performance of the SiP_{2} dielectric, we measured the transfer characteristics of MoS_{2} transistors with dualgate geometry in which 20nmthick SiP_{2} and 300nmthick SiO_{2} 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 5nmthick MoS_{2} transistor shows an on/off ratio as high as 10^{5}, which is comparable to those values in hBNgated MoS_{2} transistors (Supplementary Table 2) and meets the wellknown criterion for practical logic circuit applications^{19}. 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 10^{5} (inset of Fig. 1c). This comparison directly demonstrates that, compared to SiO_{2}, the SiP_{2} gate dielectric with larger dielectric constant and smaller thickness can achieve great capacitive capability. The measured leakage current of SiP_{2}gated MoS_{2} 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 highκ dielectrics^{19,20,21} such as Al_{2}O_{3}, HfO_{2} or Bi_{2}SeO_{5}, and better than the criteria of the lowpower limit and the standard complementary metal–oxide–semiconductor gate limit^{19}. With increasing \({V}_{{{{{{\rm{t}}}}}}{{{{{\rm{g}}}}}}{{{{{{\rm{SiP}}}}}}}_{2}}\), the fieldeffect mobility \(\mu\) at 2 K can reach ~600 cm^{2} V^{–1} s^{–1} when \({V}_{{{{{{\rm{bg}}}}}}{{{{{{\rm{SiO}}}}}}}_{2}}\) is fixed at 35 V (Fig. 1e). Even for SiP_{2}gated 1LMoS_{2} transistors with the same device geometry (Supplementary Fig. 2), the mobility of 330 cm^{2} V^{–1} s^{–1} at 2 K is better than those reported values in HfO_{2}gated 1LMoS_{2} devices^{22} (174 cm^{2} V^{–1} s^{–1} at 4 K), indicating that the vdW SiP_{2} material with a large dielectric constant can effectively reduce the charge scattering and increase the mobility of MoS_{2} transistors. Such excellent performance with high on/off ratio, low leakage current, and high mobility in MoS_{2}/SiP_{2} devices suggests that layered SiP_{2} can be a highperformance dielectric in switching devices.
To demonstrate the great gate tunability of SiP_{2} dielectric, we measured the temperaturedependent sheet resistance (\({R}_{{{{{{\rm{s}}}}}}}\)–\(T\)) and observed a gatinginduced insulator–metal transition in the 1LMoS_{2}/SiP_{2} 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 dependence^{23} 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 transition^{23} in SiP_{2}gated 1LMoS_{2}. Such a transition in SiP_{2}gated 1LMoS_{2} transistor directly manifests the excellent dielectric property of layered SiP_{2} as a gate medium to modulate the electronic states of ultrathin semiconductors.
To experimentally evaluate the dielectric constant of SiP_{2}, we measured the sheet carrier density (\({n}_{2{{{{{\rm{D}}}}}}}\)) of MoS_{2} (5 nm) as a function of \({V}_{{{{{{\rm{tg}}}}}}{{{{{{\rm{SiP}}}}}}}_{2}}\) based on Hall effect measurements. The \({n}_{2{{{{{\rm{D}}}}}}}\) values of topgated MoS_{2} remain nearly unchanged below the threshold voltage of 1.7 V and can be continually modulated to 8 × 10^{12 }cm^{–2} by increasing \({V}_{{{{{{\rm{tg}}}}}}{{{{{{\rm{SiP}}}}}}}_{2}}\) to 5 V (Supplementary Fig. 4a). Note that the dualgatemodulated \({n}_{2{{{{{\rm{D}}}}}}}\) can reach a maximum value close to 10^{13 }cm^{–2} (Supplementary Fig. 4b). The relative dielectric constant \({\varepsilon }_{{{{{{\rm{r}}}}}}}\) is evaluated to be 8.1 for SiP_{2} 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 SiP_{2} (more details in “Methods”). Such a dielectric constant of 8.1 in layered SiP_{2} is larger than those of SiO_{2} and hBN dielectrics^{24,25} and comparable to that of Al_{2}O_{3} dielectric^{24} (Fig. 1g, a detailed comparison is given in Supplementary Tables 3 and 4), well consistent with the theoretical estimation from firstprinciples calculations^{26}.
As a typical vdW dielectric with excellent performance, another distinctive nature of SiP_{2} is the anisotropic lattice structure with nonsymmorphic C_{2} symmetry. In sharp contrast to the highly symmetric crystal structure of those widely used dielectrics (oxides and hBN), such an anisotropic inplane lattice structure of SiP_{2} leads to a highly anisotropic ratio of electron effective masses (~16, Fig. 1g) for the band edge states in its electronic band structure^{26}, and provides an opportunity to engineer the interfacial symmetry of vdW heterostructure combined monolayer TMDCs with SiP_{2}. For example, the 1LMoS_{2}/SiP_{2} heterostructure shows no rotational symmetry and can exhibit inplane anisotropic optical and electronic properties (details discussed below). In particular, if the zigzag direction of MoS_{2} and the P_{B}–P_{B} chain of SiP_{2} (the direction parallel to the P_{B}–P_{B} chain of SiP_{2} 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 1LMoS_{2}/SiP_{2} heterostructure; otherwise, all crystal symmetries in MoS_{2} are broken. The perturbation for the electronic structures of stacked heterostructures can be used to generate inplane polarization and Berry curvature dipole at the interface^{27}, realizing emergent interfacial phenomena such as directional quantum shift current^{5}, nonlinear Hall effect^{1} and circular photogalvanic effect (Supplementary Fig. 5).
SiP_{2}induced anisotropic optical response in 1LMoS_{2}
To understand the engineered symmetry of heterointerfaces, we performed second harmonic generation (SHG) measurements on 1LMoS_{2}/SiP_{2} heterostructures under a parallel measurement geometry (Fig. 2c). The SHG signal in pristine 1LMoS_{2} shows a sixfoldrotational symmetric pattern with maxima of SHG intensity along its armchair direction and can be well fitted with Eq. (1), implying the C_{3}rotational symmetry of 1LMoS_{2} samples^{28}. While in 1LMoS_{2}/SiP_{2} 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 C_{3}symmetric lattice of 1LMoS_{2} itself, but results from the reduced symmetry at the 1LMoS_{2}/SiP_{2} heterointerface. The SHG intensities can be well fitted with Eq. (2) in the “Methods”, similar to those distorted SHG scenarios in uniaxiallystrained 1LMoS_{2} samples^{29,30}. Note that SiP_{2} 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 1LMoS_{2}/SiP_{2} heterostructure mainly originates from 1LMoS_{2} whose band structure is effectively modified by the potential on the heterointerface created by the bottom C_{2} symmetric SiP_{2}. More importantly, the anisotropic SHG response at 1LMoS_{2}/SiP_{2} changes little with increasing SiP_{2} thickness (Supplementary Fig. 11), further confirming that this is an interfacial phenomenon induced by symmetry breaking at the 1LMoS_{2}/SiP_{2} heterointerface between the 1LMoS_{2} and the topmost SiP_{2} layer.
To investigate the effect of symmetry engineering on the optical properties of such an interface, we performed polarizationdependent photoluminescence (PL) measurements in the 1LMoS_{2}/SiP_{2} heterostructure at 77 K (Fig. 2d, e and Supplementary Fig. 6). For SiP_{2}, 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 lattice^{26}. In contrast, for 1LMoS_{2} without SiP_{2} stacking layer, the excitonic emission of 1LMoS_{2} at 1.91 eV at 77 K remains unchanged with the detection polarization angle and shows no linear polarization. While, for the 1LMoS_{2}/SiP_{2} heterostructure, the excitonic state of 1LMoS_{2} with an emission energy of 1.91 eV becomes linearly polarized along the x direction of SiP_{2} (Fig. 2f and Supplementary Fig. 7). The similar results can be observed at 77 K and 300 K in 1LWS_{2}/SiP_{2} heterostructure (Supplementary Fig. 8), indicating the anisotropic PL response in TMDC/SiP_{2} is robust with temperatures. Similar anisotropic SHG responses are also observed in 1LWS_{2}/SiP_{2} heterostructure (details in Supplementary Fig. 9), indicating that SiP_{2} 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 MoS_{2} and SiP_{2}, 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 MoS_{2}/SiP_{2} 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 C_{3}symmetric monolayer TMDCs and C_{2}symmetric dielectrics, enabling a strategy to explore applications such as polarizationsensitive photodetectors^{31}.
Giant anisotropic conductance in SiP_{2}gated MoS_{2} transistors
To investigate the interfacial symmetry modulation on the electronic transport properties of MoS_{2}, we measured the conductance \({G}_{x}\) (\({G}_{y}\)) along the x (y) directions of SiP_{2}gated 1LMoS_{2} 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 10^{3} at the offstate with \({V}_{{{{{{\rm{tg}}}}}}{{{{{{\rm{SiP}}}}}}}_{2}}\) < 1 V (Fig. 3c), implying that the symmetry engineering using SiP_{2} dielectric can drive the isotropic conductivity of C_{3}symmetric 1LMoS_{2} into highlyanisotropic electronic states. With further increasing \({V}_{{{{{{\rm{tg}}}}}}{{{{{{\rm{SiP}}}}}}}_{2}}\), the anisotropy index gradually approaches the value of 1, suggesting that 1LMoS_{2} recovers back to isotopically conducting states at the onstate. 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 SiP_{2} with inplane anisotropy is anticipated to stimulate device functionality exploration for anisotropic digital inverters^{32}, anisotropic memorizers^{33}, or artificial synaptic devices^{34}.
To confirm that such anisotropic conductance originates from the MoS_{2}/SiP_{2} heterointerface, we compared the \({G}_{x}\) and \({G}_{y}\) values of SiP_{2}gated MoS_{2} transistors by increasing the thickness of MoS_{2} from monolayer to 20 nm. As a result, the observed anisotropy index \({G}_{y}\)/\({G}_{x}\) at the offstate decreases rapidly to ~1 when the thickness of MoS_{2} is increased to 20 nm (Fig. 3g, Supplementary Figs. 16 and 17), suggesting a nearly isotropic conductance in thicker samples. Such a thicknessdependent 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 MoS_{2} 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 MoS_{2} with certain thickness (within the ThomasFermi screening length) can be tuned for carrier accumulation with SiP_{2} dielectric based on our numerical PoissonSchrödinger calculations (Supplementary Figs. 19 and 20). For SiP_{2}gated 1LMoS_{2} case, \({G}_{y}^{{{{{{\rm{bulk}}}}}}}\) = \({G}_{x}^{{{{{{\rm{bulk}}}}}}}\) = 0 and only the MoS_{2} 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 MoS_{2}, \({G}_{y}^{{{{{{\rm{bulk}}}}}}}\) 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 SiP_{2}gated MoS_{2} with a thickness of 20 nm. This result indicates that the anisotropic conductance behavior is contributed exactly from the interface of the MoS_{2}/SiP_{2} heterostructures (details in Supplementary Figs. 18–20). Compared to those vdW materials with inplane anisotropic crystal lattices and electronic structures^{18,35}, our SiP_{2}gated 1LMoS_{2} 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 1LMoS_{2}/SiP_{2} 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 1LMoS_{2}/SiP_{2} heterostructure by using density functional theory (DFT) calculations. Note that the mirror symmetry of the constructed MoS_{2}/SiP_{2} heterointerface originates from the parallel or antiparallel alignment of the zigzag chain in MoS_{2} along the y direction of SiP_{2} (see details in Supplementary Fig. 21). Thus, two kinds of moiré patterns can be obtained (labeled as caseI and caseII, details in Section 13 in Supplementary Information). Taking the moiré pattern of caseI as an example (Fig. 4a, b), due to the lattice mismatch between MoS_{2} and SiP_{2}, there are three typical stacking structures, labeled as IAA, IAB, and IBA, as indicated by the colored rectangular areas in Fig. 4a. The details about atomic stacked configurations and stacked structures with IIAA, IIAB, and IIBA in the moiré pattern of caseII are shown in Supplementary Fig. 21d.
The structural corrugations in 1LMoS_{2}/SiP_{2} heterostructure with two kinds of moiré patterns are simulated via DFT calculations (Fig. 4c and Supplementary Fig. 27b, e). After being placed on the SiP_{2} lattice, the atomic flat structure of 1LMoS_{2} will be deformed due to the interface coupling, resulting in the formation of moiré potential on 1LMoS_{2} that effectively breaks C_{3}rotational symmetry of the pristine MoS_{2}. In contrast, the structural corrugations in 1LSiP_{2} are much smaller compared with that in 1LMoS_{2} (Supplementary Fig. 25). Furthermore, we plot the distribution of the interlayer distance (marked in Fig. 4b) for the moiré pattern of caseI in Fig. 4c to demonstrate the moiré potential in this heterostructure. In the moiré pattern of caseI, the stacked region of IBA hosts the smallest interlayer distance between MoS_{2} and SiP_{2}, indicating the largest structural deformation on 1LMoS_{2} and interlayer coupling. However, in the moiré pattern of caseII such region with the largest moiré potential and lattice deformation becomes IIAA (Supplementary Fig. 27e). On the other hand, the mirror symmetry parallel to the armchair direction of 1LMoS_{2} (also the x direction of the heterostructure) is always observed in both moiré patterns of 1LMoS_{2}/SiP_{2} heterostructures that is determined by the specific stacked regulations in the fabrication of experimental devices. Such characters with reduced symmetry in corrugated 1LMoS_{2} are consistent with the symmetry analysis to stacking structures with moiré patterns. Our simulated structural deformation of corrugated 1LMoS_{2} with moiré patterns gives a consistent interpretation on the change of the symmetric shape of the experimental SHG spectra from sixfold (1LMoS_{2}) to twofold (1LMoS_{2}/SiP_{2}).
The outofplane structural corrugations of 1LMoS_{2} with moiré patterns can strongly modulate its electronic structures and thus influence the optical properties. Since the direct simulation of the largesize moiré lattice by using DFT are too expensive to afford, to overcome this issue, we use a strained MoS_{2} and SiP_{2} to construct a heterostructure guaranteeing the conduction band offset between MoS_{2} and SiP_{2} same with that in the moiré heterostructure, then simulate the influence of the moiré potential on the electronic states of 1LMoS_{2} (details in Sections 14–17 in Supplementary Information). The exemplified results are presented in the heterostructure model with stacking regions of IAB and IBA (named as caseIABBA). Figure 4g and h demonstrates the charge density distribution for conduction band edge in caseIABBA, and Fig. 4e and f shows the planeaveraged charge density along the z and y directions (Section 17 in Supplementary Information). In the heterostructure model with fully relaxation, outofplane corrugation can be clearly observed with the retaining of the mirror symmetry in the moiré pattern. The conduction band edge in 1LMoS_{2}/SiP_{2} heterostructure is dominated by the state from the MoS_{2} 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 1LMoS_{2}/SiP_{2} heterostructure is always strongly modified by the moiré potential. For the caseII moiré pattern, we build similar models and obtain the same conclusions (details in Sections 16 and 17 in Supplementary Information). Compared with pristine 1LMoS_{2} with C_{3}rotational symmetry, the symmetry engineering on the conduction band edge can be clearly observed in 1LMoS_{2}/SiP_{2} heterostructure. With breaking C_{3}rotational symmetry by SiP_{2}, the conduction band edge on deformed 1LMoS_{2} 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 SiP_{2}gated MoS_{2} transistors. At the offstate with low carrier density (~5 × 10^{9 }cm^{–2}) and low temperature (2 K), the charge carriers in 1LMoS_{2}/SiP_{2} heterostructure are mainly trapped by charged impurities^{22,36,37,38} and the moiré potentials, thus the giant anisotropic conductance of 1LMoS_{2} is mainly contributed by the effective hopping between trapped charge states in the moiré potentials^{22,36,37,38}. Since the charged defects in 1LMoS_{2} are distributed randomly without anisotropy, the anisotropic moiré potential should be a critical factor for the anisotropic conductance in the SiP_{2}gated MoS_{2} transistor. Similar to previous discussions, we also take the moiré pattern of caseI as an example (the discussion of the moiré pattern of caseII draws the same conclusion), the distribution of interlayer distance between SiP_{2} and MoS_{2} in real space (Fig. 4c) shows that the smallest interlayer distance is located in the IBA 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 highlyanisotropic conductance in 1LMoS_{2}/SiP_{2} heterostructure. With increasing the electron density to reach the onstate, the moiré potential cannot fully trap these charge carriers and its influence on transport becomes unimportant, delocalizing the 2D electron gas formed on the 1LMoS_{2} layer. Thus, the conductance turns out to be isotropic at the onstate.
Discussion
In conclusion, we demonstrate an anisotropic van der Waals dielectric SiP_{2} that can simultaneously tune the electronic states of channel semiconductors and induce symmetry engineering at TMDC/SiP_{2} interfaces. Our firstprinciples calculations reveal that these anisotropic characteristics originate from the formation of the anisotropicsymmetric moiré potential in the MoS_{2}/SiP_{2} heterostructure, which strongly modulates structural and electronic properties of 1LMoS_{2} with tunable anisotropic symmetry. The tunable interfacial symmetry in the TMDC/SiP_{2} heterostructure can provide a unique platform for investigating symmetryrelated interfacial physics and corresponding phenomena, including the generation of the inplane polarization^{5} (bulk photovoltaic effect and quantum shift current) and the Berry curvature dipole^{39,40,41} (circular photogalvanic effect and nonlinear Hall effect). The giant anisotropy generated in the TMDC/SiP_{2} 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/SiP_{2} heterostructures
The orthorhombic SiP_{2} crystal exhibits an anisotropic layered structure (space group \(P{nma}\)) with an embedded quasionedimensional 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 SiP_{2} crystal when stacking SiP_{2} with monolayer TMDCs. First, there is a nonsymmorphic C_{2} symmetry about the z direction (the screw symmetry S_{2} that combines a twofold rotational symmetry with a translation along the z direction in the halfunitcell, S_{2} = C_{2} + z/2) in the SiP_{2} crystal. This nonsymmorphic C_{2} symmetry of bulk SiP_{2} is incompatible with C_{3} symmetry of TMDCs and will result in highly anisotropic nature (C_{1} symmetry) of the TMDC/SiP_{2} heterostructures. Second, the atomic structure of SiP_{2} is inversion symmetric, which means there is no SHG signal of SiP_{2} flakes, ensuring that the distorted SHG signals at the TMDC/SiP_{2} 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 SiP_{2} crystal. This vertical mirror can remain in the TMDC/SiP_{2} heterostructures when stacking the TMDCs and SiP_{2} by aligning their mirror planes (the zigzag direction of TMDCs is parallel to the P_{B}–P_{B} chains of SiP_{2}), generating a mirror symmetric anisotropic moiré potential at the heterointerface.
Optical measurements of TMDC/SiP_{2} heterointerfaces
SiP_{2} flakes and TMDC flakes were prepared by mechanical exfoliation onto polydimethylsiloxane (PDMS) stamps and SiO_{2}/Si wafers (300nmthick SiO_{2} layer). TMDC/SiP_{2} heterointerfaces were fabricated using a drytransfer method and stacked by parallelly aligning the zigzag direction of MoS_{2} and y direction of SiP_{2}. The crystal axes of the 1LMoS_{2} samples are confirmed by their polarizedSHG results. And the crystal axes of SiP_{2} 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. Nitrogenfilled environments were established by protecting samples with continuous nitrogen gas flow. Lowtemperature 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 1LTMDCs on the SiO_{2} substrate, the sixfold symmetric SHG intensities are fitted by Eq. (1):
Normally, for those uniaxiallystrained TMDCs, the SHG intensities \({I}_{{{{{{\rm{SHG}}}}}}}^{\parallel }\) parallel to the incident laser polarization can be written as:
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 1LMoS_{2}/SiP_{2}, the C_{3} symmetry of 1LMoS_{2} is also reduced to low symmetry such as C_{1}. Therefore, we fit our data by Eq. (2) to describe the anisotropic SHG response in our 1LMoS_{2}/SiP_{2}.
Electrical transport measurements
The 1LMoS_{2} (or fewlayer MoS_{2}) and SiP_{2} 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 SiP_{2} flake (Ti/Au with a thickness of 5/45 nm) was then made using electronbeam lithography and electronbeam evaporation. Electrical transport measurements were performed in a cryofree superconducting magnet system (Oxford Instruments Teslatron^{PT}). Fourterminal 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/SiP_{2}/MoS_{2} sandwiched devices^{22}. The Au/SiP_{2}/MoS_{2} device can be considered as a parallel plate capacitor, and the amount of charge per unit area can be written as:
where \(e\) is the electron charge, \({\varepsilon }_{0}\) is the vacuum permittivity, \({t}_{{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}\) = 20 nm is the thickness of SiP_{2}, and \({\varepsilon }_{{{{{{\rm{r}}}}}}{{{{{\rm{Si}}}}}}{{{{{{\rm{P}}}}}}}_{2}}\) is the relative dielectric constant of SiP_{2} within the Au/SiP_{2}/MoS_{2} 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 firstprinciples calculations. The generalizedgradient approximation (GGA) of the PerdewBurkeErnzerhoftype functional^{43} was used with the projectedaugmentedwave method^{44,45} and an energy cutoff of 500 eV. For the electronic selfconsistent calculations, the convergence criterion was set as 10^{–6} eV. Considering the van der Waals interaction, the DFTD3 method^{46} was applied as the correction. The force criterion was chosen to be 0.01 eV Å^{–1}. After fully relaxing the 2HMoS_{2} 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 kpoint mesh of 15 × 15 × 3 was used to sample the Brillouin zone (BZ). After the full relaxation of the SiP_{2} 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 results^{49}. The kpoint mesh of 5 × 15 × 4 was used to sample the BZ of bulk SiP_{2}. Moreover, except for the structural relaxation, the spinorbit 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 MoS_{2} and SiP_{2} monolayers.
For these heterostructure models with strained MoS_{2} and SiP_{2} which were used to simulate the electronic properties of 1LMoS_{2}/SiP_{2} heterostructure directly, the \(2\sqrt{3}\times 1\) rectangle supercell for monolayer MoS_{2} 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 SiP_{2} was enlarged to 3.50 Å for a and 10.69 Å for b. In each strained heterostructure model, it contains 13 × 1 monolayer SiP_{2} unitcells and 14 × 1 rectangle supercells for monolayer MoS_{2}. The kpoint mesh of 5 × 1 × 1 was used to sample the BZ of heterostructure model. For strained caseIABBA and caseIIAABA lattices, we fully relaxed the whole structures. While, for strained caseIAA and caseIIAB lattices, we fixed the x and y coordinates of the two central S atoms in MoS_{2} layer and one central P atom in SiP_{2} 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.
References
Du, L. et al. Engineering symmetry breaking in 2D layered materials. Nat. Rev. Phys. 3, 193–206 (2021).
Finney, N. R. et al. Tunable crystal symmetry in graphene–boron nitride heterostructures with coexisting moiré superlattices. Nat. Nanotechnol. 14, 1029–1034 (2019).
Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).
Liu, Y. et al. Van der Waals heterostructures and devices. Nat. Rev. Mater. 1, 16042 (2016).
Akamatsu, T. et al. A van der Waals interface that creates inplane polarization and a spontaneous photovoltaic effect. Science 372, 68–72 (2021).
Xu, Y. et al. Correlated insulating states at fractional fillings of moire superlattices. Nature 587, 214–218 (2020).
Tang, Y. et al. Simulation of Hubbard model physics in WSe_{2}/WS_{2} moiré superlattices. Nature 579, 353–358 (2020).
Bai, Y. et al. Excitons in straininduced onedimensional moire potentials at transition metal dichalcogenide heterojunctions. Nat. Mater. 19, 1068–1073 (2020).
Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).
Yankowitz, M., Ma, Q., JarilloHerrero, P. & LeRoy, B. J. van der Waals heterostructures combining graphene and hexagonal boron nitride. Nat. Rev. Phys. 1, 112–125 (2019).
Spanton, E. M. et al. Observation of fractional Chern insulators in a van der Waals heterostructure. Science 360, 62–66 (2018).
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Chen, G. et al. Emergence of tertiary dirac points in graphene moiré superlattices. Nano Lett. 17, 3576–3581 (2017).
Wang, L. et al. Evidence for a fractional fractal quantum Hall effect in graphene superlattices. Science 350, 1231–1234 (2015).
Gorbachev, R. V. et al. Detecting topological currents in graphene superlattices. Science 346, 448–451 (2014).
Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).
Hunt, B. et al. Massive dirac fermions and hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).
Zhao, S. et al. Inplane anisotropic electronics based on lowsymmetry 2D materials: progress and prospects. Nanoscale Adv. 2, 109–139 (2020).
Li, T. et al. A native oxide highκ gate dielectric for twodimensional electronics. Nat. Electron. 3, 473–478 (2020).
Illarionov, Y. Y. et al. Insulators for 2D nanoelectronics: the gap to bridge. Nat. Commun. 11, 3385 (2020).
Park, J. H. et al. Atomic layer deposition of Al_{2}O_{3} on WSe_{2} functionalized by titanyl phthalocyanine. ACS Nano 10, 6888–6896 (2016).
Radisavljevic, B. & Kis, A. Mobility engineering and a metalinsulator transition in monolayer MoS_{2}. Nat. Mater. 12, 815–820 (2013).
Li, T. et al. Continuous Mott transition in semiconductor moire superlattices. Nature 597, 350–354 (2021).
Wilk, G. D., Wallace, R. M. & Anthony, J. M. Highκ gate dielectrics: current status and materials properties considerations. J. Appl. Phys. 89, 5243–5275 (2001).
Dean, C. R. et al. Boron nitride substrates for highquality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010).
Zhou, L. et al. Unconventional excitonic states with phonon sidebands in layered silicon diphosphide. Nat. Mater. 21, 773–778 (2022).
Duan, S. et al. Berry curvature dipole generation and helicitytospin conversion at symmetrymismatched heterointerfaces. Nat. Nanotechnol. 18, 867–874 (2023).
Jiang, T. et al. Valley and band structure engineering of folded MoS_{2} bilayers. Nat. Nanotechnol. 9, 825–829 (2014).
Liang, J. et al. Monitoring local strain vector in atomiclayered MoSe_{2} by secondharmonic generation. Nano Lett. 17, 7539–7543 (2017).
Mennel, L. et al. Optical imaging of strain in twodimensional crystals. Nat. Commun. 9, 516 (2018).
Yuan, H. et al. Polarizationsensitive broadband photodetector using a black phosphorus vertical pn junction. Nat. Nanotechnol. 10, 707–713 (2015).
Liu, E. et al. Integrated digital inverters based on twodimensional anisotropic ReS_{2} fieldeffect transistors. Nat. Commun. 6, 6991 (2015).
Wang, H. et al. Gate tunable giant anisotropic resistance in ultrathin GaTe. Nat. Commun. 10, 2302 (2019).
Tian, H. et al. Anisotropic black phosphorus synaptic device for neuromorphic applications. Adv. Mater. 28, 4991–4997 (2016).
Sucharitakul, S. et al. V_{2}O_{5}: a 2D van der Waals oxide with strong inplane electrical and optical anisotropy. ACS Appl. Mater. Interfaces 9, 23949–23956 (2017).
Ma, N. & Jena, D. Charge scattering and mobility in atomically thin semiconductors. Phys. Rev. X 4, 011043 (2014).
Kaasbjerg, K., Thygesen, K. S. & Jauho, A.P. Acoustic phonon limited mobility in twodimensional semiconductors: deformation potential and piezoelectric scattering in monolayer MoS_{2} from first principles. Phys. Rev. B 87, 235312 (2013).
Kaasbjerg, K., Thygesen, K. S. & Jacobsen, K. W. Phononlimited mobility in ntype singlelayer MoS_{2} from first principles. Phys. Rev. B 85, 115317 (2012).
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in timereversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).
Ma, Q. et al. Observation of the nonlinear Hall effect under timereversalsymmetric conditions. Nature 565, 337–342 (2019).
Sinha, S. et al. Berry curvature dipole senses topological transition in a moiré superlattice. Nat. Phys. 18, 765–770 (2022).
Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio totalenergy calculations using a planewave basis set. Phys. Rev. B 54, 11169–11186 (1996).
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Blöchl, P. E. Projector augmentedwave method. Phys. Rev. B 50, 17953–17979 (1994).
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev. B 59, 1758–1775 (1999).
Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFTD) for the 94 elements HPu. J. Chem. Phys. 132, 154104 (2010).
Kadantsev, E. S. & Hawrylak, P. Electronic structure of a single MoS_{2} monolayer. Solid State Commun. 152, 909–913 (2012).
Wilson, J. A. & Yoffe, A. D. The transition metal dichalcogenides discussion and interpretation of the observed optical, electrical and structural properties. Adv. Phys. 18, 193–335 (1969).
Zhang, X., Wang, S., Ruan, H., Zhang, G. & Tao, X. Structure and growth of single crystal SiP_{2} using flux method. Solid State Sci. 37, 1–5 (2014).
Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003).
Heyd, J., Scuseria, G. E. & Ernzerhof, M. Erratum: “Hybrid functionals based on a screened Coulomb potential” [J. Chem. Phys. 118, 8207 (2003)]. J. Chem. Phys. 124, 219906 (2006).
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.)).
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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 SiP_{2} crystals. L.Z. and Z.L. performed PoissonSchrödinger 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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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/s41467023412956
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DOI: https://doi.org/10.1038/s41467023412956
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