Effects of V-shaped edge defect and H-saturation on spin-dependent electronic transport of zigzag MoS2 nanoribbons

Physics Letters A 378 (2014) 2701–2707

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Physics Letters A www.elsevier.com/locate/pla

Effects of V-shaped edge defect and H-saturation on spin-dependent electronic transport of zigzag MoS2 nanoribbons Xin-Mei Li a , Meng-Qiu Long a,b,∗ , Li-Ling Cui a,c , Jin Xiao a , Xiao-Jiao Zhang a , Dan Zhang a , Hui Xu a,∗ a Institute of Super-microstructure and Ultrafast Process in Advanced Materials & Hunan Key Laboratory for Super-microstructure and Ultrafast Process, School of Physics and Electronics, Central South University, Changsha 410083, China b Department of Physics and Materials Science, City University of Hong Kong, Hong Kong, China c School of Science, Hunan University of Technology, Zhuzhou 412007, China

a r t i c l e

i n f o

Article history: Received 24 March 2014 Received in revised form 23 June 2014 Accepted 18 July 2014 Available online 22 July 2014 Communicated by R. Wu Keywords: Zigzag MoS2 nanoribbons V-shaped edge defect H-saturation Spin-dependent transport property Negative differential resistance

a b s t r a c t Based on nonequilibrium Green’s function in combination with density functional theory calculations, the spin-dependent electronic transport properties of one-dimensional zigzag molybdenum disulfide (MoS2 ) nanoribbons with V-shaped defect and H-saturation on the edges have been studied. Our results show that the spin-polarized transport properties can be found in all the considered zigzag MoS2 nanoribbons systems. The edge defects, especially the V-shaped defect on the Mo edge, and H-saturation on the edges can suppress the electronic transport of the systems. Also, the spin-filtering and negative differential resistance behaviors can be observed obviously. The mechanisms are proposed for these phenomena. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Due to the unique electronic transport properties, recently, the layered structure material molybdenum disulfide (MoS2 ) emerged as a promising candidate for the ultimate utilization of next generation nanodevice and has drawn the attention of many research areas [1–4]. Unlike graphite [5] and hexagonal BN [6], the layers of MoS2 are made of hexagons with Mo and S atoms situated at alternating corners. Bulk MoS2 is a semiconductor with an indirect band gap of about 1.3 eV, whereas, monolayer MoS2 is a direct band gap (about 1.9 eV) semiconductor [7,8]. MoS2 nanostructures are receiving considerable attention because of their potential application in catalysts [9], transistor [10], small-signal amplifier [11], lubrication [12], hydrogen evolution [13], as well as promising materials for spin electronic applications [14,15]. Now, the MoS2 nanoribbons (MNRs) have been successfully synthesized [16,17]. Like graphene nanoribbons (GNRs), according to different edge types, the MNRs can be classified as armchair MoS2 nanorib-

*

Corresponding authors at: Institute of Super-microstructure and Ultrafast Process in Advanced Materials & Hunan Key Laboratory for Super-microstructure and Ultrafast Process, School of Physics and Electronics, Central South University, Changsha 410083, China. E-mail addresses: [email protected] (M.-Q. Long), [email protected] (H. Xu). http://dx.doi.org/10.1016/j.physleta.2014.07.024 0375-9601/© 2014 Elsevier B.V. All rights reserved.

bons (AMNRs) and zigzag MoS2 nanoribbons (ZMNRs). Lots of theoretical and experimental studies have shown that ZMNRs are ferromagnetic and metallic, while AMNRs are non-magnetic and semiconducting [18–21]. In practice, it is difficult to fabricate MoS2 nanostructures without defects [22]. Similar to the modification of properties for graphene and its nanoribbons [23–25], as a kind of graphene-like nanomaterial, vacancy defect will affect the properties of MoS2 nanostructures greatly. There are five different types of vacancy defects (namely, single Mo or S vacancy, S-S or Mo-S vacancy, and S-Mo-S vacancy) which have been used to modify the electronic and magnetic states of single-layer MoS2 honeycomb structures [26]. Using density functional theory (DFT) calculations, R. Shidpour showed that a vacancy on the S-edge with 50% coverage can intensify the edge magnetization of MNRs, but the magnetic property will disappear when with 100% coverage [27]. C. Ataca et al. found that net magnetic moment can be achieved through the creation of MoS2 triple vacancy to the non-magnetic AMNRs [28]. Recently, more and more researches have shown some significant properties of the edge-terminated nanoribbons [19,29,30]. And hydrogen (H) is the widely used element for saturating the edges of kinds of materials. By first-principles study, Pan et al. presented a detail investigation about the edge-dependent electronic structure and magnetic properties of MNRs [19]. They found the

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AMNRs, with and without H-saturation, are semiconducting and non-magnetic; and ZMNRs are ferromagnetic and metallic, but Hsaturation at the edges can change their electronic structures and magnetic properties. C. Ataca et al. have demonstrated that the energy band gaps of AMNRs and the magnetic properties of ZMNRs can be modulated by the edge hydrogenation [31]. All the studies above make great sense to the industrial technology application and experimental research guidance of MoS2 . But they focus mainly on the electronic structure and magnetic properties of MNRs. In order to get a systematic and comprehensive understanding of electronic properties for MNRs, especially their application in spin-valve devices, studies about the spin-dependent electronic transport properties of MNRs are very necessary. And since the spin-dependent electronic transport properties of magnetic ZMNRs are more attractive for study than non-magnetic AMNRs [18–21]. So, in this work, we present a unique and intrinsic spin-dependent electronic transport property of ZMNR under finite bias voltage based on first-principles calculations. Edge defects and H-saturation are considered to modulate the spin-dependent electronic transport properties of N-ZMNR (N is the number of the zigzag chains across the ribbon width). Considering the fact that there is σ mirror plane or different parity of π and π ∗ bands for c 2 symmetry operation, zigzag graphene nanoribbon (ZGNR) [32] and zigzag silicone nanoribbon (ZSiNR) [33] can show symmetry-dependent transport properties, and the current–voltage (I–V ) curves of even-N and odd-N ZGNRs (ZSiNRs) are very different from one another. Since the geometry structure of ZMNR is very similar to ZGNR and ZSiNR, we also discuss the symmetry-dependent transport properties of ZMNR in this paper. 2. Computational details In the calculations, we obtain the MNRs by cutting an ideal MoS2 triple layer, and the spin-dependent transport properties of H-saturated ZMNRs with V-shaped edge defect on one edge, and the other edge is pristine, are studied. The model structures are labeled as N-Z-H (pristine H-saturated ZMNR), N-VZ-Mo-H (H-saturated ZMNR with V-shaped defect on the Mo edge) and N-VZ-S-H (H-saturated ZMNR with V-shaped defect on the S edge), respectively. And for each system, the z-direction is parallel to the transport direction. In these models, each edge S (Mo) is passivated by one (two) hydrogen atoms to saturate the edge dangling bonds. As a comparison, transport properties of the according unsaturated perfect ZMNR (N-Z) have also been investigated. The spin-dependent electronic transport properties are calculated based on ATK (Atomistix Toolkit) package [34–36], which is based on real-space, nonequilibrium Green’s function (NEGF) formalism and DFT. The two-probe systems, shown in Figs. 1(a–c), contain three regions: left electrode, right electrode and central region, in which the electrodes are two semi-infinite pristine ZMNRs. In the spin-dependent electronic transport properties calculations, the local spin density approximation (LSDA) is adopted as the exchange-correlation function and the single-zeta plus polarized (SZP) basis set is used. The parameters set as follows: k-point grid is 1 × 1 × 500, cutoff energy of all atoms is 150Ry, each ZMNR is separated by 10 Å in vacuum. And all the configurations are relaxed until their force tolerance being less than 0.05 eV/Å. Under external bias voltage (V b ), the corresponding spin-dependent current I σ ( V b ) through the central region is manifested using the Landauer–Büttiker formula [37]

Iσ (V b ) =

e

μr ( V b )





T σ ( E , V b ) f ( E − μl ) − f ( E − μr ) dE ,

h

(1)

μl ( V b )

where e is the electron charge, h is the Planck constant, σ represents spin-up (↑) or spin-down (↓), μl ( V b ) = μl (0) − eV b /2 and

Fig. 1. (Color online.) The models of two probes systems: (a) 5-Z-H, (b) 5-VZ-Mo-H, (c) 5-VZ-S-H, and (d) side view of the ZMNR.

μr ( V b ) = μr (0) + eV b /2 are the chemical potential of the left and right electrodes, f ( E − μl/r ) is the Fermi–Dirac distribution function of the left(l)/right(r) electrode, and T σ ( E , V b ) is the quantum mechanical transmission probability of electrons, defined as

 T σ ( E , V b ) = Tr I m

 R 

 × Im

 ( E , V b ) G σR ( E , V b )

lσ

  R  A (E, V b) Gσ (E, V b) ,

(2)

rσ

where

R l/r

is the retarded self-energy matrix which takes into

account the left/right electrode, G R / A is the retarded/advanced Green’s function of the central region. 3. Results and discussions Firstly, we discuss the transport properties of non-magnetic ZMNRs (4-Z, 5-Z, 4-Z-H and 5-Z-H) to test the symmetry-dependent properties. From Fig. 2, we can find that 4-Z and 5-Z present almost the same I–V curves, and 4-Z-H exhibits the similar transport properties as 5-Z-H. These phenomena are much different from what shown in ZGNRs [32] and ZSiNRs [33], in which with the applied bias range, the odd-N system (asymmetric) behaves like conductor, but the current in even-N system (symmetric) is close to zero. The similar I–V curves of asymmetric and symmetric systems suggest that there are no apparent symmetrydependent phenomena on the electronic transport of ZMNRs. This result might come from the structure of N-ZMNRs, even if in the

X.-M. Li et al. / Physics Letters A 378 (2014) 2701–2707

Fig. 2. (Color online.) The currents as function of applied bias voltage for 4-Z, 5-Z, 4-Z-H and 5-Z-H.

symmetric N-ZMNR (N is even), there are two different kinds of elements (Mo and S) on the different edges of the ribbon. Then, the asymmetry of elements would offset the influence of structure symmetry. Meanwhile, our result agrees well with the energy band calculations of Pan et al., they found that the symmetric and asymmetric ZMNRs have very similar band structures [19]. So, in the following calculations, the symmetry of the ribbon widths will not be considered any more. In Figs. 3(a–c), we plot the calculated spin-dependent transmission spectra T ( E , V b ) at zero bias voltage for 5-Z-H, 5-VZMo-H and 5-VZ-S-H systems, respectively. And, as a comparison, the T ( E , V b ) of edge-unterminated 5-Z system is also shown in Fig. 3(d). It can be seen that in some energy regions, the transmission is larger than G 0 (G 0 = e 2 /h), which means that there is more than one electron transport channel existing in these energy regions [38]. And we find that all the spin-up and spin-down states are non-degenerate in the four systems. Comparing the

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curves shown in Fig. 3(a) with Fig. 3(d), the average transmission spectra of 5-Z-H is lower than that of 5-Z, which indicates that the electronic transfer ability of the device will be weaken when the edges of ZMNR are terminated by H. And we can find from Figs. 3(b) and 3(c), when the vacancy defects are introduced on the edges, especially on the Mo edge of pristine H-saturated ZMNR, the transmission spectra is decreased greatly, resulting in the suppressed transport properties of 5-VZ-Mo-H and 5-VZ-S-H. To explore the effects of defect on transport properties, in Figs. 3(e–j), we give the electron transmission pathways in central region at the Fermi level. The transmission pathway is an analysis option which splits the transmission coefficient into local bond contributions, T i j . The pathways have the property that if the system is divided into 2 parts ( A , B ), then the pathways across the boundary between  A and B sum up to the total transmission coefficient T ( E ) = i ∈ A , j ∈ B T i j ( E ) [39]. It is shown that similar to GNR-based devices [40,41], there are also two different kinds of transmission channels in MNR-based ones: electron transmission via a chemical bond (such as Mo-S bond) and through hopping between atoms (such as Mo and Mo atoms, Mo and H atoms). From Figs. 3(e) and 3(f), we can see that both the spin-up and spin-down electrons of 5-Z-H can flow through the edges of ribbons and reach the other electrode. And for the 5-VZ-Mo-H system, only the delocalized pathways of spin-down state can be found in Fig. 3(h), and the spin-up ones are almost localized on the left side (Fig. 3(g)), so the spin-up electrons cannot reach the right electrode, leading to the obvious suppressed electron transmissions. Figs. 3(i) and 3(j) depict that the delocalized pathways of spin-up and spin-down states can also be found, but the electronic transport performances of 5-VZ-S-H are weaker than that of 5-Z-H. Interestingly, in Figs. 3(a–c), there are some zero transmission spectra at some higher energy regions. It is well known, the transmission spectra are related to the wave function overlap between the central region and electrodes. The peaks correspond to the resonant transmission through the states of central region, whereas the zero value corresponds to the resonant backscattering states [42]. Here, because of the H saturation on the edges, the effect of resonant backscattering causes a full suppression of the single

Fig. 3. (Color online.) The spin-dependent transmission spectra T ( E ) at zero bias voltage for (a) 5-Z-H, (b) 5-VZ-Mo-H, (c) 5-VZ-S-H, and (d) 5-Z, respectively; the transmission pathways at 0 eV for (e) 5-Z-H↑, (f) 5-Z-H↓, (g) 5-VZ-Mo-H↑, (h) 5-VZ-Mo-H↓, (i) 5-VZ-S-H↑, and (j) 5-VZ-S-H↓, respectively. The ↑ and ↓ refer to spin-up state and spin-down state, respectively. The zero of energy is set to Fermi level (blue dotted line).

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Fig. 4. (Color online.) The spin-up band structure (left panel), spin-dependent transmission spectra (middle panel), and spin-down band structure (right panel) for 5-Z-H under zero bias voltage. The black and red lines refer to spin-up and spindown states, respectively. The energy region between two green dotted lines is [−0.56, 0.28 eV]. The zero of energy is set to Fermi level.

available conduction channel at some certain resonant energy regions. In addition, we can find from Fig. 3(a) that at the energy range of −0.56 to −0.28 eV, the transmission spectra of spindown state are almost zero, and they are obviously lower than that of the spin-up state (about 1G 0 ). Therefore, perfect spin-filtering effects can also be observed. Meanwhile, we also can find the spinfiltering effects for the defected systems in Figs. 3(b) and 3(c). To understand the spin-filtering behavior in Fig. 3, take 5-Z-H as an example, we plot the transmission spectra and band structure of electrode under bias of zero in Fig. 4. We note that 5-Z-H is semiconducting, and in the energy region of [−0.56, −0.28 eV], there is a band gap about 0.28 eV for spin-down state, but there is a band for spin-up state in the same energy. So, we can find the spin-up transmission peek and spin-down transmission gap appear in the energy region. As a result, the spin-filtering behavior can be observed clearly here. Fig. 5(a) shows the spin-dependent I–V curves for 5-Z-H, 5-VZMo-H and 5-VZ-S-H. It can be seen that both the currents of spin-up (I ↑) and spin-down (I ↓) are split in all the systems. And for each spin state, the current intensity of 5-Z-H is the largest one in the three systems under the same bias voltage, confirming the decreasing electronic transport ability of the defected systems. All these phenomena are in good agreement with what shown in Fig. 3. Interestingly, for 5-Z-H, the current of spin-up state is almost larger than that of the spin-down state under the whole

considered bias region, but for 5-VZ-Mo-H and 5-VZ-S-H, the value of I ↑ − I ↓ is greater than 0 under some bias voltages and less than 0 under the others. Thus, the current polarization of the defected systems can be controlled by the bias voltage. To quantify the spin-polarization behavior, we define the spinI ↑− I ↓ polarized effect (SPE) η by the following formula, η = I ↑+ I ↓ × 100%. The calculated SPEs of the three systems are shown in Fig. 5(b). We can see that the absolute maximum SPEs are 33% at 0.9 V, 80% at 0.6 V, and 36% at 0.8 V for 5-Z-H, 5-VZ-Mo-H and 5-VZ-S-H, respectively. And sign-switching of SPEs are obtained in 5-VZ-Mo-H and 5-VZ-S-H. Such reversal has already been found experimentally in the Fe/GaAs (001) interface [43] and predicted theoretically in ZSiNRs [44]. Furthermore, this reversal of spin-polarization caused by bias voltage could have potential application in logic spintronics devices. To obtain the origin of the reversal of SPEs, we study the transmission spectra, local density of states (LDOS) at Fermi level of 5-VZ-Mo-H at 0.2 V (Fig. 6(a)) and 0.6 V (Fig. 6(b)). From Eq. (1), we know that [μl ( V b ), μr ( V b )] is called bias window or integration window, refers to the energy region which contributes to the current integration. If the Fermi Level is set to zero and bias window is [− V b /2, V b /2], the current is determined by T ( E , V b ) in the bias window, which is displayed by shade areas in Fig. 6. We can see from Fig. 6(a) that in the bias window, the integration area of the spin-down is larger than that of the spin-up state. And the corresponding LDOS of spin-up electron is connected mainly in the electrode areas, while that of the spin-down electron is more delocalized and assigns over the edges of ribbon. All the contrasts mentioned above indicate that the spin-down electron dominates over the spin-up electron for 5-VZ-Mo-H at V b = 0.2 V, in accord with a negative SPE about −70% (shown in Fig. 5(b)). However, the dominance between the spin-up and spin-down electrons of it is overturned at V = 0.6 V (Fig. 6(b)), where the comparison of transmission spectra, LDOSs all indicate a dominance of the spin-up electron over the spin-down electron, in agreement with a positive SPE of 80%. This changing dominance of spin-up and spin-down from V b = 0.2 to 0.6 V can explain the sign-changing of the SPEs in 5-VZ-Mo-H. Furthermore, as shown in Fig. 5(a), the obvious negative differential resistance (NDR) behaviors can also be seen for both the spin-up and spin-down states of the systems. NDR suggests a wide range of potential applications in electronic devices such as memory, amplifier and fast switch. However, the origin of the mechanism for NDR is still under debate [45–47]. To get a more in-depth explanation of NDR phenomenon, take spin-up state of 5-Z-H as an example, we have plotted the transmission spectra, partial den-

Fig. 5. (Color online.) (a) The spin-dependent current, and (b) the SPEs as function of the applied bias voltage for 5-Z-H, 5-VZ-Mo-H and 5-VZ-S-H. The ↑ and ↓ refer to spin-up state and spin-down state, respectively.

X.-M. Li et al. / Physics Letters A 378 (2014) 2701–2707

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Fig. 6. (Color online.) The transmission spectra and LDOSs for 5-VZ-Mo-H at (a) V b = 0.2 V, (b) V b = 0.6 V. The regions between the red solid lines are the bias windows and the shaded areas denote the integration areas. The ↑ and ↓ refer to spin-up state and spin-down state, respectively. The zero of energy is set to Fermi level.

Fig. 7. (Color online.) (a–b) The transmission spectra, band structure of left electrode, PDOS of central region, and band structure of right electrode for the spin-up state of 5-Z-H under bias voltage of 0.5 V and 1.0 V, respectively. The regions between the red solid lines are the bias windows and the shaded areas denote the integration areas. The zero of energy is set to Fermi level. (c–d) The electron density distribution of 5-Z-H in the bias windows under the bias of 0.5 V and 1.0 V.

sity of states (PDOS) of the central region in whole energy range, and band structures of both left and right electrodes under bias of 0.5 and 1.0 V in Figs. 7(a–b). When the positive bias is applied, the energy band shifted downward/upward for the left/right elec-

trode. Under the lower bias (0.5 V), the bands of left electrode always keep overlapping with that of the right electrode in the bias windows, leading to the enhanced transmission peeks in the bias window. However, when the bias is 1.0 V, the band gap of left

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Fig. 8. (Color online.) (a–d) The spin-dependent transmission spectra under zero bias voltage for 6-Z-H, 6-VZ-Mo-H, 6-VZ-S-H, and 6-Z, respectively. (e–h) The two different sizes of V-shaped defects on the Mo or S edges for ZMNR with ribbon width of 5. The insert panels are the central regions of the according models. The black and red lines refer to spin-up state and spin-down state, respectively. The zero of energy is set to Fermi level.

electrode enters into the bias window, and the transmission gap appears in the same energy. On the other hand, it is clearly seen from the figures that both the transmission and PDOS spectra are strongly correlated. Under the bias of 0.5 V, we can find there are stronger PDOS and transmission peeks location in the bias window. Nevertheless, under the bias of 1.0 V, the PDOS is suppressed and the corresponding transmission peeks are very small in the bias window. We also plot the electron density distribution of 5-Z-H in the bias windows. As shown in Figs. 7(c–d), when the bias is 0.5 V, we can find the electronic state is almost delocalized over the edges of whole ribbon, however, the electronic state is localized under the bias of 1.0 V. So we can find there are stronger PDOS peeks in Fig. 7(a), but they are suppressed nearly in Fig. 7(b). From the above, we can clearly find the integral area (namely, the shaded areas in Figs. 7(a–b)) of 1.0 V is much smaller than that of 0.5 V in bias window. As a result, the current of 0.5 V is larger than that of 1.0 V markedly and NDR behavior appears. Furthermore, we also study the effects of the size of V-shaped defects and other ribbon width. As shown in Fig. 8, we present the spin-dependent transmission spectra at zero bias voltage for the systems with ribbon width of 6, and two different sizes of V-shaped defects for ZMNRs with ribbon width of 5. Comparing the results of Figs. 8(a–d) with Figs. 3(a–d), we can find that under the same size of V-shaped defect, except the transport ability being strengthen slightly with the ribbon width increasing, the Hsaturation and V-shaped defects have the similar affects on the ZMNRs, such as H-saturation and defect on the edges can suppress the transport ability, when the defect on the Mo edge of the ribbon, the transport ability being suppressed greatly. Moreover, from Figs. 8(e–h), we clearly see that when there is a larger size of V-shaped defect, there are narrower transmission peeks near the Fermi energy, and transport ability of the ZMNRs would be reduced. And when the V-shaped defect is on the Mo edge of ZMNR, the transmission peeks are smaller than that of on the S edge obviously.

4. Conclusion We have presented the first-principles theoretical investigations on the spin-dependent electronic transport properties of ZMNRs with V-shaped edge defects and H-saturation on the edges. We find that compared with the edge-unterminated pristine ZMNR, the defects and H-saturated on the edges can suppress the electronic transport properties of the systems. And the larger the defect size, the weaker the electronic transport ability is. In all the H-saturated systems, spin-filtering effect can be observed. Band structure calculations show that the spin-filtering effect results from the different band structures of electrodes for the spin-up and spin-down states of the system. And we can find very good NDR behaviors in these systems, which originate from the shifting of energy band gap of electrodes and the changing of electron density distributions of central region with the increasing of bias. Meanwhile, the location of defect affects the transport properties of the system greatly, and when the defect is localized at the Mo edge, a good SPE can be obtained. All these characters are potentially useful in the fabrication of spin electronic devices based on ZMNRs. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant Nos. 21103232, 61306149 and 11174371), the Natural Science Foundation of Hunan Province (No. 14JJ3026), Hong Kong Scholars Program (No. XJ2013003) and Shenghua Lieying Scholarship (No. 2011-17) by the Central South University. References [1] I. Popov, G. Seifert, D. Tománek, Phys. Rev. Lett. 108 (2012) 156802. [2] A. Ramasubramaniam, Phys. Rev. B 87 (2013) 195201. [3] D. Kim, D.Z. Sun, W.H. Lu, Z.H. Cheng, Y.M. Zhu, D. Le, T.S. Rahman, L. Bartels, Langmuir 27 (2011) 11650. [4] M.M. Perera, M.W. Lin, H.J. Chuang, B.P. Chamlagain, C.Y. Wang, X.b. Tan, M.M.C. Cheng, D. Tománek, Z.X. Zhou, ACS Nano 7 (2013) 4449.

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