Transport properties of MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ vdW junctions tuned by bias and gate voltages

Abstract

The MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ vdW junctions are designed and the transport properties of their four-terminal devices are comparatively investigated based on density functional theory (DFT) and the nonequilibrium Green's function (NEGF) technique. The MoS₂ and graphene nanoribbons act as the source-to-drain channel and the spin-polarized one-dimensional (1D) benzene–V multidecker complex nanowire (V₇(Bz)₈) serves as the gate channel. Gate voltages applied on V₇(Bz)₈ exert different influences of electron transport on MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈. In MoS₂/V₇(Bz)₈, the interplay of source and gate bias potentials could induce promising properties such as negative differential resistance (NDR) behavior, output/input current switching, and spin-polarized currents. In contrast, the gate bias plays an insignificant effect on the transport along graphene in graphene/V₇(Bz)₈. This dissimilarity is attributed to the fact that the conductivity follows the sequence of MoS₂ < V₇(Bz)₈ < graphene. These transport characteristics are examined by analyzing the conductivity, the currents, the local density of states (LDOS), and the transmission spectra. These results are valuable in designing multi-terminal nanoelectronic devices.

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1. Introduction

Two-dimensional (2D) materials have become the up-to-date focal point of research in past decades owing their prominent electronic, optical, and magnetism properties, which are used in wide fields from field effect transistors (FETs),^1–3 optoelectronics,^4–7 to spintronics.^8–10 As the brightest star in the 2D material family, graphene has attracted constant academic and individual research interest and enthusiasm.^11–17 Inspired by these pioneering works, various kinds of 2D materials, for example, 2D transition metal dichalcogenides (TMDs),^18–22 have sprung up and become research hotspots. Among TMDs, MoS₂ nanosheets have drawn special attention due to their high stability, good semi-conductivity, large surface, etc., which are desirable in nano electronic devices.²³ In recent years, numerous efforts have been devoted to fabricate van der Waals (vdW) heterojunctions of 2D materials by stacking alien components using various chemical techniques for engineering expected and improved properties toward practical applications.^24–31 The carrier mobility of 2D materials can be retained from vdW interactions, since it does not destroy the bonding properties in intralayers. The interlayer coupling between the two vdW-stacked 2D layers can result in novel physical properties. Many theoretical works have focused on studying the transport properties of these 2D heterojunctions by constructing two-terminal devices. However, in experiments, electron transport is usually measured using a four-probe apparatus.^32–37 On the other hand, for most practical applications, multi-terminal electronic devices are needed. Therefore, it is highly necessary to theoretically investigate the transport properties of multi-terminal devices, which is still less studied to date.

Simultaneously, with the approaching physical limit of silicon based transistors, seeking emerging device architectures and new electronic materials has become an essential topic to meet the Moore's law. Recently, spintronic devices have received extensive attentions due to the combined merits of the electron transporting, the magnetic moment, and the electron spin. Therefore, introducing spin-polarized component into 2D materials to construct vdW heterojunctions is anticipated to be an effective strategy to explore novel functional materials with desirable properties.^38–41 However, as far as we know, studies on the spin-polarized 2D vdW heterojunctions are still scarce from both experimental and theoretical points of view. The one-dimensional (1D) benzene–V multidecker complexes nanowire, V_n(Bz)_m, not only has been successfully synthesized from reaction of laser-vaporized metal atoms with C₆H₆ in a He atmosphere, but also have been imaged or detected using scanning tunneling microscopy (STM), UV–vis and IR, electron paramagnetic resonance (EPR), time-of-flight mass spectroscopies, and photoionization spectroscopies.^42–45 Experimental works as well as theoretical studies have confirmed that the unpaired electrons on the V atoms are coupled ferromagnetically (FM), and also suggest that the ground state of V_n(Bz)_m exhibits half-metallicity and spin filter effect.^44,46

Further onward, stimulated by the splendor work on MoS₂ transistors using a single-walled carbon nanotube as the gate electrodes to tune the transport properties,⁴⁷ we construct four-terminal devices for MoS₂ and graphene heterojunctions: MoS₂ and graphene are connected to the source and drain leads, while the spin polarized V_n(Bz)_m nanowire serves as gate terminals. Bias voltages and gate voltages are applied on the source lead and gate lead, respectively. The synergistic tuning effects of the bias and gate voltages on transport properties of MoS₂ and graphene are investigated by employing the density functional theory (DFT) with non-equilibrium Green's function (NEGF) methodology.

2. Models and computational methods

Fig. 1 shows the structures of the four-terminal devices for MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ vdW heterojunctions. MoS₂ and graphene offer the source-to-drain scatter region, and V₇(Bz)₈ nanowire provides the gate channel. For the sake of simplicity, the leads are denoted as lead-S, lead-D, and lead-G for the source, drain, and gate leads, respectively. The source-to-drain direction is defined as the z direction, and the gate to gate direction is referred as the x direction. The MoS₂ and graphene are placed in the x × z plane. The MoS₂ scatter region contains 9-layered S and 8-layered Mo in the z direction, as well as 4-layered S and 3-layered Mo in the x direction, which extends a 11.33 Å × 21.90 Å (x × z) plane. A similar size of graphene ribbon in the x and z direction (11.07 Å × 19.89 Å) is tailored as the scatter region, too. Such scatter region is long enough in the z direction to ignore the interaction between lead-S and lead-D. This can be confirmed by the small potential changes near the electrodes (<0.1 eV) calculated for the two devices (Fig. 2). Every dangling bonds at edges are saturated by H atoms to stabilize the system. The V₇(Bz)₈ nanowire overlies the center of MoS₂ and graphene surfaces with a vdW distance from them, and its longitudinal axis is parallel to the x direction and perpendicular to the z direction. Each lead-G in MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ is modeled by a Au(100)-(3 × 3) surface with 8 layers. The Au–C distance is set to be 2.05 Å based on their covalent radius.⁴⁸ MoS₂ is semi-conductor, so we use Au(100)-(6 × 3) surfaces with 5 layers as the lead-S and lead-D for MoS₂/V₇(Bz)₈. As the S atom has good affinity with the gold surface, dithiolate derivatives have been used for the construction of metal/scatter region/metal devices in general.^49–51 Therefore, in the present work, we also use the S atom layer of MoS₂ to link the Au electrodes. The S–Au distance was set as 2.34 Å according to the reported literature.⁵² To ensure that the bonds match well between graphene and leads, we elongate the graphene additionally by 31.26 Å as the lead-S and lead-D. Since graphene nanoribbon is semi-conductor along the armchair direction, we use the N atoms to dope the graphene lead-S and lead-D since the N atoms can introduce additional π electrons to make the two leads become conductor.^53,54 A vacuum of 20 Å in y direction is involved to eliminate the coupling between adjacent images.

Fig. 1 Schematic plots of MoS₂/V₇(Bz)₈ and Graphene/V₇(Bz)₈ four-terminal devices. Where lead-S, lead-D, and lead-G represent the source, drain, and gate leads, respectively. V_S and V_G represent the bias voltage applied on lead-S and the gate voltage applied on lead-G, respectively.

Fig. 2 The calculated potential distribution of the buffers near the leads in the two four-terminal devices, (a) is that in MoS₂/V₇(Bz)₈ device and (b) is that in graphene/V₇(Bz)₈ device.

The DFT method with generalized gradient approximation (GGA) implemented in ATK package is employed to optimize the four-terminal structures. For both MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ four-terminal devices, all the leads are frozen and the scatter regions are optimized. The self-consistent total energies are converged to 10⁻⁴ eV and the forces are converged to 0.05 eV Å⁻¹. The optimized cartesian coordinates of all the models are given in Tables S1 and S2 in the ESI.† The optimized distance is 2.11 Å from MoS₂ to V₇(Bz)₈ and 1.95 Å from graphene to V₇(Bz)₈, a typical vdW interaction. Then, the transport properties of the optimized devices are calculated using DFT with NEGF methodology within Nanodcal software package.^55,56 The linear combination of atomic orbitals (LCAO) is employed to expand physical parameters. The standard nonlocal norm-conserving pseudopotentials is used to describe the atomic core, and the double-zeta polarized (DZP) basis set is for valence electronic orbitals.^57,58 The exchange-correlation function is considered by the local density approximation (LDA).^58,59 The k-point for the central region is meshed as 1 × 1 × 1 (x × y × z), and that is 1 × 1 × 100 for lead-S and lead-D, 100 × 1 × 1 for lead-G. It is worth noting that, in all calculations the spin of V atoms is considered by using LAD + U scheme, and the U–J is set as 3.0 eV.⁶⁰ 160 Rydberg cutoff energy is applied.

The spin-dependent current in leads for multi-terminal system can be obtained using the Landauer–Büttiker formula (1):^57,61,62

where f_α (f_β) describes the Fermi distribution functions of lead-α (lead-β). V_α (V_β) is the bias voltages applied on lead-α (lead-β). σ ≡ ↑, ↓ is the spin index. The transmission coefficient T_αβ between lead-α and lead-β is dependent on E, V_α, and V_β. And the total current is I = I↑ + I↓.

Considering the multi-terminals, the conductance between lead-α and lead-β can be evaluated by formula (2):

3. Results and discussion

In this section, we mainly document on how the bias voltage (V_S) and the gate voltage (V_G) synergistically influence the transport properties of MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ vdW junctions from the aspects of conductance, currents, LDOS, and transmission. The V_S is set as 0.0, 0.2, 0.4 V, respectively. And at each certain V_S, the V_G ranges from 0.0 to 1.0 V by a step of 0.2 V.

3.1 Conductivity

To convenient description, the channels between any two terminals are denoted as channel S–D, channel S–G, channel D–G, and channel G–G.

Fig. 3 shows the calculated conductance of each channel of MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices with the variation of V_S and V_G. For the sake of comparison, the scales of conductance in vertical-axle in Fig. 3 are the same for all the channels, and Fig. S1† with adapted vertical-axis scales is supplied as ESI.† The conductance is bigger than 0.8e²/h, in the range of 0.5–1.0e²/h, and smaller than 0.3e²/h for graphene channel S–D, V₇(Bz)₈ channel G–G, and MoS₂ channel S-D, respectively. That is, the conductivity follows the sequence of MoS₂ < V₇(Bz)₈ < graphene. Therefore, using V₇(Bz)₈ as gate may play different effects on tuning electron transporting through MoS₂ and graphene. Since the V₇(Bz)₈ nanowire attaches to MoS₂ and graphene via vdW interaction, the conductance of channels S–G and D–G are very small (<0.03e²/h). The potentials from gate and from source couple in different degrees in MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ under various V_S and V_G. This integrates the change of resistance from source to drain, which makes the conductance goes up or down.

Fig. 3 Conductance for channel S–D, channel S–G, channel D–G, and channel G–G as a function of V_G at fixed values of V_S = 0.0, 0.2, or 0.4 V of the four-terminal MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices. (a and b) Are for the MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices, respectively.

3.2 Current

To further understand the transport property of the four-terminal devices, we calculated the total currents, I_S, I_D, and I_G, passing through lead-S, lead-D, and lead-G, respectively. Currents from lead to center region are input and defined as positive values, while those from center region to lead are output and appointed as negative values.

Fig. 4 displays the total currents through the leads with the variation of V_S and V_G applied on MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices. Multi-channels in four-terminal devices could cause complicated transport properties aroused from the intricacy of channel couplings. Actually, the magnitude of each lead current comes from the synergistic action of all pathways. For example, though lead-S current is directly related to channels S–D and S–G, channels S–D and S–G are simultaneously influenced by channels D–G and G–G.

Fig. 4 Total currents for lead-S, lead-D, and lead-G as a function of V_G at fixed values of V_S = 0.0, 0.2, or 0.4 V of the four-terminal devices, where (a) shows those in MoS₂/V₇(Bz)₈ devices, and (b) is in graphene/V₇(Bz)₈.

Now we consider the total currents, I_S, I_D, and I_G of MoS₂/V₇(Bz)₈ device (Fig. 4a). With free gate voltage, a small amount of current leaks off lead-G when applied V_S = 0.2 and 0.4 V, while the lead-G current becomes input once V_G imposed, which could exert considerable effect on the source-to-drain transporting. The lead-D currents are always output owing to its low voltage potential compared with other three leads. At V_S = 0.0 V, lead-S and lead-D give output currents with the absolute values of I_S < 1.0 μA and I_D < 0.5 μA, which are induced by the applied gate voltages. Interestingly, regardless of any V_S, the I_S, I_D, and I_G curves present a pattern of up and down oscillation with the changing of V_G, resulting in NDR peaks. Of course, the magnitude, the position, and the numbers of these NDR peaks are different for different leads at various V_S and V_G. In fact, conductivity, as a complicated phenomenon, relates to comprehensive factors such as scatter region structure, scatter region–lead interaction, couplings between channels, changes of resistance induced by voltages, etc. For example, the asymmetric character of MoS₂ structure not only induces different resistance for different channels, but also induces different left and right MoS₂–lead interactions. Therefore, at zero V_S bias, the I_S and I_D curves give different shapes. All these comprehensive factors may also be responsible for the dissimilarity of the NDR behaviors of I_S, I_D, and I_G. When nonzero V_S is applied, as the V_G increases, the input I_S current decreases as a whole and could switches to output at certain V_G, e.g., at V_G = 0.6 V for V_S = 0.2 V and at V_G = 0.4 and 0.8 V for V_S = 0.4 V. Therefore, the currents across lead-S are rather dependent on the interplay of V_S and V_G. At V_S = 0.2 and 0.4 V, the absolute values of I_D rise comparing with V_S = 0.0 V. This is a reasonable result from the higher potential injected into the channel S–D. The magnitude of the output currents of lead-D tends to be balanced around 1.0 μA. All these properties are much desirable for designing functional devices with fascinating characteristics such as NDR behavior and input/output switching.

As to the graphene/V₇(Bz)₈ device, the total currents of I_S, I_D, and I_G display a much different feature from MoS₂/V₇(Bz)₈ as shown from Fig. 4b. Intuitively, the gate V_G plays a small role on the carries transport via the graphene plane. This result can be deduced from two phenomena: one is that the magnitudes of I_S and I_D (10–40 μA) are much higher than I_G (<1.0 μA) under applied V_G; another is that the input values of I_S are almost equal to the output data of I_D at given V_S and V_G, indicating that the injected I_S almost arrives to the lead-D completely. No evident NDR behavior is observed for graphene/V₇(Bz)₈. In addition, unlike in MoS₂/V₇(Bz)₈ which there exists input/output switching of lead-S, the current of lead-S in graphene/V₇(Bz)₈ is always input within the considered gate bias. The reason for these different phenomena between MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ lies in the fact that graphene has higher conductivity than MoS₂.

To investigate how the spin-polarized character of V₇(Bz)₈ influence the transport property of MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈, we computed the spin-up currents, I_S↑, I_D↑, and I_G↑ as well as the spin-down currents, I_S↓, I_D↓, and I_G↓, for lead-S, lead-D, and lead-G, respectively. The results are plotted in Fig. 5 and 6 as a function of V_G at a given V_S.

Fig. 5 Spin currents for lead-S, lead-D, and lead-G as a function of V_G at fixed values of V_S = 0.0, 0.2, or 0.4 V of the four-terminal MoS₂/V₇(Bz)₈ device. (a) Depicts the spin-up states of MoS₂/V₇(Bz)₈, and (b) depicts those for spin-down state, respectively.

Fig. 6 Spin currents for lead-S, lead-D, and lead-G as a function of V_G at fixed values of V_S = 0.0, 0.2, or 0.4 V of the four-terminal graphene/V₇(Bz)₈ device. (a) Depicts the spin-up states, and (b) depicts those for spin-down state, respectively.

As expected, for V₇(Bz)₈ in both two devices, the I_G↑ remains nearly zero, while the I_G↓ possesses the same magnitude to the total I_G. This thoroughly inherits the intrinsic spin-polarized feature of pure V₇(Bz)₈.^60,63 Quite significantly, the spin polarized feature of V₇(Bz)₈ induces different polarized transport property from MoS₂/V₇(Bz)₈ to graphene/V₇(Bz)₈. In the case of MoS₂/V₇(Bz)₈, spin-up and spin-down channels of lead-S and lead-G are split by the polarization property of V₇(Bz)₈. At V_S = 0.0 V, the spin-up paths of both lead-S and lead-D of MoS₂/V₇(Bz)₈ are closed with almost zero current, and the total currents I_S and I_D entirely come from the spin-down I_S↓ and I_D↓. This is mainly due to the fact that the spin-up channel of V₇(Bz)₈ is almost closed and hence cannot cause perturbation on the spin-up pathway of MoS₂. On the contrary, the spin-down state of V₇(Bz)₈ dominates electron transporting, enabling strong coupling with the spin-down channel of MoS₂. Under nonzero V_S, the currents through lead-S and lead-D in MoS₂/V₇(Bz)₈ are polarized by a large extent. For the spin-up state, the currents of I_S↑ are all input and those of I_D↑ are all output. Both I_S↑ and I_D↑ curves of MoS₂/V₇(Bz)₈ change smoothly in a small scale of 0.0–0.5 μA along the variation of V_G. In striking contrast, the spin-down currents of I_S↓ and I_D↓ fluctuate significantly with the changing of V_G, with a large range of from 1.0 to −0.5 μA for I_S↓ and from 0.0 to −1.7 μA for I_D↓. Observed carefully, one can find that the changing trends of I_S↓ and I_D↓ curves are roughly analogous to those of the total I_S and I_D. The NDR behavior and the input/output switch character of MoS₂/V₇(Bz)₈ are mainly dominated by the spin-down state. Now turn to graphene/V₇(Bz)₈, quite different from MoS₂/V₇(Bz)₈, no matter what V_S and V_G applied, the spin-up currents are almost equivalent to spin-down values for both lead-S and lead-D. Though the polarized characteristic of V₇(Bz)₈ is preserved in graphene/V₇(Bz)₈, its conductivity is too much weaker than graphene that can not exert valid influence on channel S–D.

3.3 Local density of states

Table 1 displays the computed local density of states (LDOS) results of two devices under V_S = 0.2 V, where the even LDOS distribution suggests an effective transport channel. The scenario of the polarized transport behavior of MoS₂/V₇(Bz)₈ leads becomes more obvious by analyzing the LDOS distributions. As representative example, it is clear that the LDOS of the spin-down state of V₇(Bz)₈ delocalizes stronger than the spin-up state, which could bring about coupling with the spin-down state of MoS₂, and consequently, lead to the spin-polarized splitting of MoS₂/V₇(Bz)₈. The electronic potential on the whole system changes along with the relative magnitude of V_S and V_G, as can be reflected from the LDOS distributions. Clearly, charge carries in the spin-up state of either channel S–D or channel G–G are blocked more seriously than the spin-down state. As for the graphene/V₇(Bz)₈ device, the spin-down passage of V₇(Bz)₈ is open with uniform LDOS distribution while the spin-up path is closed with almost no LDOS. Despite of the maintained polarized character of V₇(Bz)₈, spin-up and spin-down channels along graphene has nearly identical LDOS spreading. This again demonstrates the unpolarized character of lead-S and lead-D currents.

Table 1 Local density of states (LDOS) of the four-terminal MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices at various V_G exemplified by V_S = 0.2 V

VG (V)	LDOS at VS = 0.2 V
	MoS2/V7(Bz)8 device		Graphene/V7(Bz)8 device
	Spin-up	Spin-down	Spin-up	Spin-down
0.0
0.2
0.4
0.6
0.8
1.0

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3.4 Transmission coefficients and spectra

To further shed light on how the gate bias tune the transport property of MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices, we computed spin polarized transmission coefficients (TC) of each channel at the case of V_S = 0.0 V and V_G from 0.0 to 1.0 V, and the results are shown in Fig. 7.

Fig. 7 Transmission coefficient of all channels in two devices with variational V_G from 0.0 to 1.0 V at V_S = 0 V. (a) Shows spin-up and spin-down state in MoS₂/V₇(Bz)₈ device, and (b) is that for graphene/V₇(Bz)₈ device.

Evidently, in both MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices, spin-down channel G–G composed of V₇(Bz)₈ has much higher TC than other channels, again demonstrating the preserved striking half-metallic character of V₇(Bz)₈. One can find that, in MoS₂/V₇(Bz)₈, the main channel S–D consisting of MoS₂ can not be largely influenced by the spin polarized character of the gate V₇(Bz)₈, as can be clearly seen from the comparable spin-up and spin-down TC. However, the spin polarized V₇(Bz)₈ directly consists of channels S–G and D–G, and thereby, it could induce spin split of channels S–G and D–G and generate larger spin-down TC than spin-up TC. Therefore, the spin polarized transport character of MoS₂/V₇(Bz)₈ mainly derives from the perturbation of the spin-down state of V₇(Bz)₈ upon the channels S–G and D–G. Regarding graphene/V₇(Bz)₈, charge carriers can easily flow from lead-S to lead-D since channel S–D has large TC, while other channels are almost closed with nearly zero TC except the spin-down channel G–G. In addition, spin-up and spin-down states of channel S–D display the same TC curves, illustrating the ignoring polarization influence of V₇(Bz)₈ on graphene.

Furtherly, we calculated the transmission spectra (TS) of the main channel S–D for MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ devices at each V_S and V_G, as plotted in Fig. 8. In the case of MoS₂/V₇(Bz)₈, at V_S = 0.0 V and V_G = 0.0 V, TS peak located above the E_f mainly arises from the native MoS₂. When adding V_G merely, an extra peak appears near the E_f owing to the gate carries injection into the channel S–D of MoS₂/V₇(Bz)₈. Once adding V_S together with V_G, only one peak exists below the E_f due to the suppression effect of the incoming V_G potential upon the V_S. Furthermore, with the increasing of V_G, such suppression effect in MoS₂/V₇(Bz)₈ becomes more significant, as the TS peak moves farer away from the E_f. In contrast, regardless of V_S and V_G, lots of TS peaks of channel S–D appear around the E_f of graphene/V₇(Bz)₈, again indicating the high conductivity of graphene.

Fig. 8 Transmission spectra of channel S–D in MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ device with variational V_G from 0.0 to 1.0 V at a certain V_S, where (a) depicts the case in MoS₂/V₇(Bz)₈, and (b) is that for graphene/V₇(Bz)₈, respectively.

4. Conclusion

The MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈ vdW junctions are designed and the transport properties of their four-terminal devices are comparatively investigated based on the DFT and NEGF techniques. The MoS₂ and graphene nanoribbons act as the source-to-drain channel and the spin-polarized V₇(Bz)₈ nanowire serves as the gate channel. The transport characteristic is explored by investigating the conductance, currents, LDOS, and transmission spectra. Gate voltages applied on V₇(Bz)₈ exert different influences of electron transporting on MoS₂/V₇(Bz)₈ and graphene/V₇(Bz)₈. The interplay of source and gate bias potentials generates a pronounced influence on the transport property of MoS₂/V₇(Bz)₈. Evident NDR behavior, input/output current switches, as well as spin-polarized currents are found for MoS₂/V₇(Bz)₈. In contrast, the gate bias plays insignificant effect on the transporting along graphene. These results are promising in designing multi-terminal nanoelectronic devices.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 51973046). And more, We gratefully acknowledge HZWTECH for providing computation facilities.

References

1. Q. Lv, F. Yan, N. Mori, W. Zhu, C. Hu, Z. R. Kudrynskyi, Z. D. Kovalyuk, A. Patane and K. Wang, Interlayer band-to-band tunneling and negative differential resistance in van der Waals BP/InSe field-effect transistors, Adv. Funct. Mater., 2020, 30, 1910713.
2. B. Jiang, X. Zou, J. Su, J. Liang, J. Wang, H. Liu, L. Feng, C. Jiang, F. Wang, J. He and L. Liao, Impact of thickness on contact issues for pinning effect in black phosphorus field-effect transistors, Adv. Funct. Mater., 2018, 28, 1801398.
3. W. Ahmad, Y. N. Gong, G. Abbas, K. Khan, M. Khan, G. Ali, A. Shuja, A. K. Tareen, Q. Khan and D. L. Li, Evolution of low-dimensional material-based field-effect transistors, Nanoscale, 2021, 13, 5162.
4. J. L. Du, H. H. Yu, B. S. Liu, M. Y. Hong, Q. L. Liao, Z. Zhang and Y. Zhang, Strain engineering in 2d material-based flexible optoelectronics, Small Methods, 2020, 5, 2000919.
5. Z. X. Li, D. Y. Li, H. Y. Wang, P. Chen, L. J. Pi, X. Zhou and T. Y. Zhai, Intercalation strategy in 2D materials for electronics and optoelectronics, Small Methods, 2021, 5, 2100567.
6. Y. K. Liao, Z. F. Zhang, Z. B. Gao, Q. K. Qian and M. Y. Hua, Tunable properties of novel Ga₂O₃ monolayer for electronic and optoelectronic applications, ACS Appl. Mater. Interfaces, 2020, 12, 30659–30669.
7. E. Singh, P. Singh, K. S. Kim, G. Y. Yeom and H. S Nalwa, Flexible molybdenum disulfide (MoS₂) atomic layers for wearable electronics and optoelectronics, ACS Appl. Mater. Interfaces, 2019, 11, 11061–11105.
8. Y. P. Liu, C. Zeng, J. H. Zhong, J. N. Ding, Z. M. Wang and Z. W. Liu, Spintronics in two-dimensional materials, Nano-Micro Lett., 2020, 12, 93.
9. C. K. Safeer, J. Ingla-Aynés, F. Herling, J. H. Garcia, M. Vila, N. Ontoso, M. R. Calvo, S. Roche, L. E. Hueso and F. Casanova, Room temperature spin Hall effect in graphene/MoS₂ van der Waals heterostructures, Nano Lett., 2019, 19, 1074–1082.
10. A. Avsar, H. Ochoa, F. Guinea, B. Ozyilmaz, B. J. Van Wees and I. J. Vera-Marun, Colloquium: spintronics in graphene and other two-dimensional materials, Rev. Mod. Phys., 2020, 92, 021003.
11. A. P. Johnson, C. Sabu, N. K. Swamy, A. Anto, H. V. Gangadharappa and K. Pramod, Graphene nanoribbon: an emerging and efficient flat molecular platform for advanced biosensing, Biosens. Bioelectron., 2021, 184, 113245.
12. Y. J. Gao, J. L. Chen, G. R. Chen, C. H. Fan and X. G. Liu, Recent progress in the transfer of graphene films and nanostructures, Small Methods, 2021, 5, 2100771.
13. S. Achra, T. Akimoto, J. F. de Marneffe, S. Sergeant, X. Y. Wu, T. Nuytten, S. Brems, I. Asselberghs, Z. Tokei and K. Ueno, Enhancing interface doping in graphene-metal hybrid devices using H-2 plasma clean, Appl. Surf. Sci., 2021, 538, 148046.
14. K. M. Wyss, D. X. Luong and J. M. Tour, Large-scale syntheses of 2d materials: flash joule heating and other methods, Adv. Mater., 2022, 34, 2106970.
15. I. Alcón, G. Calogero, N. Papior and M. Brandbyge, Electrochemical control of charge current flow in nanoporous graphene, Adv. Funct. Mater., 2021, 31, 2104031.
16. T. Chen, W. C. Ding, H. L. Li and G. H. Zhou, Length-independent multifunctional device based on penta-tetra-pentagonal molecule: a first-principles study, J. Mater. Chem. C, 2021, 9, 3652.
17. Q. Sun, X. L. Yao, O. Groning, K. Eimre, C. A. Pignedoli, K. Muellen, A. Narita, R. Fasel and P. Ruffieux, Coupled spin states in armchair graphene nanoribbons with asymmetric zigzag edge extensions, Nano Lett., 2020, 20, 6429–6436.
18. P. L. Zhao, J. Yu, H. Zhong, M. Rosner, M. I. Katsnelson and S. J. Yuan, Electronic and optical properties of transition metal dichalcogenides under symmetric and asymmetric field-effect doping, New J. Phys., 2020, 22, 083072.
19. S. Y. Seo, D. H. Yang, G. Moon, O. F. N. Okello, M. K. Park, S. H. Lee, S. Y. Choi and M. H. Jo, Identification of point defects in atomically thin transition-metal dichalcogenide semiconductors as active dopants, Nano Lett., 2021, 21, 3341–3354.
20. T. K. Rao, H. D. Wang, Y. J. Zeng, Z. N. Guo, H. Zhang and W. G. Liao, Phase transitions and water splitting applications of 2D transition metal dichalcogenides and metal phosphorous trichalcogenides, Adv. Sci., 2021, 8, 2002284.
21. S. S. Li, H. Wang, J. Wang, H. J. Chen and L. Shao, Control of light-valley interactions in 2D transition metal dichalcogenides with nanophotonic structures, Nanoscale, 2021, 13, 6357.
22. Y. C. Lin, R. Torsi, D. B. Geohegan, J. A. Robinson and K. Xiao, Controllable thin-film approaches for doping and alloying transition metal dichalcogenides monolayers, Adv. Sci., 2021, 8, 2004249.
23. S. Wang, M. S. Ukhtary and R. Saito, Strain effect on circularly polarized electroluminescence in transition metal dichalcogenides, Phys. Rev. Res., 2020, 2, 033340.
24. Y. F. Zhang, J. B. Pan and S. X. Du, Geometric, electronic, and optical properties of MoS₂/WSSe van der Waals heterojunctions: a first-principles study, Nanotechnology, 2021, 32, 355705.
25. X. T. Yu, X. Wang, F. F. Zhou, J. L. Qu and J. Song, 2D van der Waals heterojunction nanophotonic devices: from fabrication to performance, Adv. Funct. Mater., 2021, 31, 2104260.
26. S. Q. Hu, J. P. Xu, Q. H. Zhao, X. G. Luo, X. T. Zhang, T. Wang, W. Q. Jie, Y. C. Cheng, R. Frisenda, A. Castellanos-Gomez and X. T. Gan, Gate-switchable photovoltaic effect in BP/MoTe₂ van der Waals heterojunctions for self-driven logic optoelectronics, Adv. Opt. Mater., 2020, 9, 2001802.
27. H. D. Wang, S. Gao, F. Zhang, F. X. Meng, Z. N. Guo, R. Cao, Y. H. Zeng, J. L. Zhao, S. Chen, H. G. Hu, Y. J. Zeng, S. J. Kim, D. Y. Fan, H. Zhang and P. N. Prasad, Repression of Interlayer recombination by graphene generates a sensitive nanostructured 2d vdW heterostructure based photodetector, Adv. Sci., 2021, 8, 2100503.
28. R. C. Luo, W. W. Xu, Y. Z. Zhang, Z. Q. Wang, X. D. Wang, Y. Ga, P. Liu and M. W. Chen, Van der Waals interfacial reconstruction in monolayer transition-metal dichalcogenides and gold heterojunctions, Nat. Commun., 2020, 11, 1011.
29. L. Yuan, B. Y. Zheng, J. Kunstmann, T. Brumme, A. B. Kuc, C. Ma, S. B. Deng, D. Blach, A. Pan and L. B. Huang, Twist-angle-dependent interlayer exciton diffusion in WS₂-WSe₂ heterobilayers, Nat. Mater., 2020, 19, 617–623.
30. X. D. Guo, R. N. Liu, D. B. Hu, H. Hu, Z. Wei, R. Wang, Y. Y. Dai, Y. Cheng, K. Chen, K. H. Liu, G. Y. Zhang, X. Zhu, Z. P. Sun, X. X. Yang and Q. Dai, Efficient all-optical plasmonic modulators with atomically thin van der Waals heterostructures, Adv. Mater., 2020, 32, 1907105.
31. C. L. Tang, Z. W. Zhang, S. Lai, Q. H. Tan and W. B. Gao, Magnetic proximity effect in graphene/CrBr₃ van der Waals heterostructures, Adv. Mater., 2020, 32, 1908498.
32. K. S. Kamal, W. C. Lu, J. Bernholc and V. Meunier, Electron transport in multiterminal molecular devices: A density functional theory study, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 81, 125420.
33. M. W. Iqbala, K. Shahzada, H. Ateeqa, I. Aslamb, S. Aftabc, S. Azama, M. A. Kamrand and M. F. Khan, An effectual enhancement to the electrical conductivity of graphene FET by silver nanoparticles, Diamond Relat. Mater., 2020, 106, 107833.
34. Y. B. Hu, J. S. Yoo, H. T. Ji, A. Goodman and X. M. Wu, Probe measurements of electric field and electron density fluctuations at megahertz frequencies using in-shaft miniature circuits, Rev. Sci. Instrum., 2021, 92, 033534.
35. D. V. Gruznev, L. V. Bondarenko, A. Y. Tupchaya, V. G. Kotlyar, O. A. Utas, A. N. Mihalyuk, N. V. Denisov, A. V. Matetskiy, A. V. Zotov and A. A. Saranin, Atomic, electronic and transport properties of In-Au 2D compound on Si(100), J. Phys.: Condens. Matter, 2019, 32, 135003.
36. N. Papadopoulos, E. Flores, K. Watanabe, T. Taniguchi, J. R. Ares, C. Sanchez, I. J. Ferrer, A. Castellanos-Gomez, G. A. Steele and H. S. J. van der Zant, Multi-terminal electronic transport in boron nitride encapsulated TiS₃ nanosheets, 2D Mater., 2019, 7, 015009.
37. N. V. Denisov, A. V. Matetskiy, A. N. Mihalyuk, S. V. Eremeev, S. Hasegawa, A. V. Zotov and A. A. Saranin, Superconductor-insulator transition in an anisotropic two-dimensional electron gas assisted by one-dimensional Friedel oscillations: (Tl, Au)/Si(100)-c(2 × 2), Phys. Rev. B: Condens. Matter Mater. Phys., 2019, 100, 155412.
38. J. Q. Zhou, J. F. Qiao, C. G. Duan, A. Bournel, K. L. Wang and W. S. Zhao, Large tunneling magnetoresistance in VSe₂/MoS₂ magnetic tunnel junction, ACS Appl. Mater. Interfaces, 2019, 11, 17647–17653.
39. H. Y. Zhou, Y. G. Zhang and W. S. Zhao, Tunable tunneling magnetoresistance in van der Waals magnetic tunnel junctions with 1T-CrTe₂ electrodes, ACS Appl. Mater. Interfaces, 2021, 13, 1214–1221.
40. Y. L. Guo, Y. H. Zhang, Z. B. Zhou, X. W. Zhang, B. Wang, S. J. Yuan, S. Dong and J. L. Wang, Spin-constrained optoelectronic functionality in two-dimensional ferromagnetic semiconductor heterojunctions, Mater. Horiz., 2021, 8, 1323.
41. S. K. Behera and P. Deb, Spin-transfer-torque mediated quantum magnetotransport in MoS₂/phosphorene vdW heterostructure based MTJs, Phys. Chem. Chem. Phys., 2020, 22, 19139.
42. K. Miyajima, A. Nakajima, S. Yabushita, M. B. Knickelbein and K. Kaya, Ferromagnetism in one-dimensional vanadium-benzene sandwich clusters, J. Am. Chem. Soc., 2004, 126, 13202–13203.
43. M. Mitsui, S. Nagaoka, T. Matsumoto and A. Nakajima, Soft-landing isolation of Vanadium−Benzene sandwich clusters on a room-temperature substrate using-alkanethiolate self-assembled monolayer matrixes, J. Phys. Chem. B, 2006, 110, 2968–2971.
44. J. Wang, H. P. Acioli and J. Jellinek, Structure and magnetism of V_nBz_n+1 sandwich clusters, J. Am. Chem. Soc., 2005, 127, 2812–2813.
45. S. Nagao, A. Kato and A. Nakajima, Multiple-decker sandwich poly-ferrocene clusters, J. Am. Chem. Soc., 2000, 122, 4221–4222.
46. X. Y. Liang, G. L. Zhang, P. Sun, Y. Shang, Z. D. Yang and X. C. Zeng, The electronic and transport properties of (VBz)_n@CNT and (VBz)_n@BNNT nanocables, J. Mater. Chem. C, 2015, 3, 4039.
47. S. B. Desai, S. R. Madhvapathy, A. B. Sachid, J. P. Llinas, Q. Wang, G. H. Ahn, G. Pitner, M. J. Kim, J. Bokor, C. Hu, H. S. P. Wong and A. Javey, MoS₂ transistors with 1-nanometer gate lengths, Science, 2016, 354, 99–102.
48. A. Antušek, M. Blaško, M. Urban, P. Noga, D. Kisić, M. Nenadović, D. Lončarevićd and Z. Rakočević, Density functional theory modeling of C–Au chemical bond formation in gold implanted polyethylene, Phys. Chem. Chem. Phys., 2017, 19, 28891–28906.
49. S. S. Li, H. Yu, G. L. Zhang and Y. Y. Hu, Four probe electron transport characteristics porphyrin phenylacetylene molecule devices, New J. Chem., 2020, 45, 2520–2528.
50. D. Jariwala, V. K. Sangwan, D. J. Late, J. E. Johns, V. P. Dravid, T. J. Marks, L. J. Lauhon and M. C. Hersam, Band-like transport in high mobility unencapsulated single-layer MoS₂ transistors, Appl. Phys. Lett., 2013, 102, 173107.
51. H. Yu, Y. Shang, L. Pei, G. L. Zhang and H. Yan, Spin-polarized gate tuned transport property of a four-terminal MoS₂ device: a theoretical study, J. Mater. Sci., 2021, 56, 11847–11865.
52. A. Nourbakhsh, A. Zubair, M. S. Dresselhaus and T. Palacios, Transport properties of a MoS₂/WSe₂ heterojunction transistor and its potential for application, Nano Lett., 2016, 16, 1359–1366.
53. L. T. Qu, Y. Liu, J. B. Baek and L. M. Dai, Nitrogen-doped graphene as efficient metal-free electrocatalyst for oxygen reduction in fuel cells, ACS Nano, 2010, 4, 1321–1326.
54. Y. X. Wang, Y. J. Jiang, S. N. Gao, H. Yu, G. L. Zhang and F. M. Zhang, Tuning magnetism and transport property of planar and wrinkled FePP@GNR hybrid materials, AIP Adv., 2020, 10, 045112.
55. J. Taylor, H. Guo and J. Wang, Ab initio modeling of quantum transport properties of molecular electronic devices, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 245407.
56. B. Wang, J. Wang and H. Guo, Ab initio calculation of transverse spin current in graphene nanostructures, Phys. Rev. B, 2009, 79, 165417.
57. H. C. Lü, Y. Zhang, X. J. Liu, Y. Wang, Q. Zhang and H. T. Yin, Theoretical limit of how small we can make MoS₂ transistor channels, J. Phys. D: Appl. Phys., 2022, 55, 105304.
58. J. Junquera, Ó. Paz, D. Sánchez-Portal and E. Artacho, Numerical atomic orbitals for linear-scaling calculations, Phys. Rev. B, 2001, 64, 235111.
59. X. Liu, Y. Z. Tan, Z. Y. Ma and Y. Pei, First-principles study of structural, electronic, and magnetic properties of one-dimensional transition metals incorporated vinylnaphthalene molecular wires on hydrogen-terminated silicon surface, J. Phys. Chem. C, 2016, 120, 27980–27988.
60. I. Solovyev, N. Hamada and K. Terakura, t_2g versus all 3d localization in LaMO₃ perovskites (M = Ti–Cu): First-principles study, Phys. Rev. B: Condens. Matter Mater. Phys., 1996, 53, 7158–7170.
61. M. Büttiker, Y. Imry, R. Landauer and S. Pinhas, Generalized many-channel conductance formula with application to small rings, Phys. Rev. B: Condens. Matter Mater. Phys., 1985, 31, 6207–6215.
62. H. Wang, J. Zhou, X. J. Liu, C. B. Yao, H. Li, L. Niu, Y. Wang and H. T. Yin, Spin transport through a junction entirely consisting of molecules from first principles, Appl. Phys. Lett., 2017, 111, 172408.
63. T. Gan, G. L. Zhang, Y. Shang, X. H. Su, Z. D. Yang and X. J. Sun, Electronic and transport properties of the (VBz)_n@MoS₂NT nanocable, Phys. Chem. Chem. Phys., 2016, 18, 4385–4393.

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Footnote

† Electronic supplementary information (ESI) available. See https://doi.org/10.1039/d2ra02196j

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