Valley Polarization in Janus Single-Layer MoSSe via Magnetic Doping

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Surfaces, Interfaces, and Catalysis; Physical Properties of Nanomaterials and Materials

Valley Polarization in Janus Single-Layer MoSSe via Magnetic Doping Rui Peng, Yandong Ma, Shuai Zhang, Baibiao Huang, and Ying Dai J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.8b01625 • Publication Date (Web): 16 Jun 2018 Downloaded from http://pubs.acs.org on June 16, 2018

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The Journal of Physical Chemistry Letters

Valley Polarization in Janus Single-Layer MoSSe via Magnetic Doping Rui Peng, Yandong Ma,* Shuai Zhang, Baibiao Huang, and Ying Dai* School of Physics, State Key Laboratory of Crystal Materials, Shandong University, Shandanan Str.27, Jinan 250100, China

ABSTRACT Two-dimensional valleytronic systems can provide information storage and processing advantages that complement or surpass conventional charge- and spin-based semiconductor technologies. The major challenge currently is to realize valley polarization for manipulating the valley degree of freedom. Here, we propose that valley polarization can be readily achieved in Janus single-layer MoSSe through magnetic doping, which is highly feasible in experiment. Due to the inversion symmetry breaking combined with strong spin-orbit coupling (SOC), the pure single-layer MoSSe harbors an intriguing multivalleyed band structure and strong coupled spin and valley physics. After doping Cr/V, the long-sought valley polarization is successfully achieved with a remarkable energy difference of ~0.06 eV upon switching on SOC. Furthermore, the valley polarization in Cr/V-doped single-layer MoSSe is tunable via strain engineering. Our work thus provides a promising platform for experimental studies and applications of the valleytronics. TOC Graphic

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Two-dimensional (2D) valleytronic materials on the basis of the valley degree of freedom of carriers have attracted tremendous attention due to their novel physics such as spin/valley Hall effects and potential applications in information storage. Examples mainly include graphene [1-5] and 2D transition metal dichalcogenides (TMDs) MX2 (M= Mo, W; X= S, Se) [6-20]. As the first 2D valleytronic material, graphene has been demonstrated with many interesting valleytronic properties. However, its inversion symmetry has to be broken to control the valley index [2-3], which is challenging in experiment, thus limiting its valleytronic applications. Different from graphene, 2D MX2 displays inversion symmetry breaking and a direct band gap at the Κ points. Strong spin-orbit coupling (SOC) lifts its spin degeneracy at the valleys. Moreover, time-reversal symmetry requires the spin splitting at Κ and Κ’ valley to be opposite, leading to coupled spin and valley physics in 2D MX2, which makes 2D MX2 a promising platform for studies on spintronics and valleytronics. Even though extensive researches have been made on graphene and 2D TMDs to design valleytronic devices, other 2D valleytronic materials are rarely reported [21-23]. Recently, Janus single-layer (SL) MoSSe was synthesized in experiment [24-25] and has generated a surge of interests [26-34]. Similar to 2D MX2, SL MoSSe harbors a multivalleyed band structure [35-36], holding great potential to be a promising 2D valleytronic material. Nevertheless, a detailed investigation on the valleytronic properties of 2D MoSSe has not been reported to date. Since the valley separation is large in momentum space, the valley degree of freedom of carriers is typically robust against scattering by smooth deformations and long wavelength phonons. Therefore, the valley index is expected to be used as a potential information carrier. For the efficient use of the valley degree of freedom, the major challenge currently is to break the degeneracy between Κ and Κ’ valleys to generate and manipulate the valley polarization. At present, many effects have been made to realize the valley polarization in 2D MX2 through few approaches such as optical pumping with circularly polarized light [7-9], external magnetic field [10] and spin injection via a diluted ferromagnetic semiconductor [11]. The magnetic substrate proximity effect which can introduce the Zeeman field to create a large valley splitting is also proposed recently [12-14]. Therefore, to take MoSSe monolayer into applications in valleytronics, the search for an effective approach to realize valley polarization in SL MoSSe is of fundamentally interest and importance. In this work, we systematically investigate the valleytronic properties of 2D MoSSe. We find that pristine single-layer (SL) MoSSe has a direct band gap locating at Κ points of Brillouin zone, and harbors coupled spin and valley physics arising from strong SOC together with inversion symmetry breaking. Most remarkably, we propose an effective method to induce the valley polarization in SL MoSSe by magnetic doping. We find that spin splittings are clearly visible in Cr-doped SL MoSSe, however, valleys at Κ and Κ’ points are still degenerate without taking into ACS Paragon Plus Environment

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account the SOC. When the SOC is switched on, excitingly, valley degeneracy is lifted and valley polarization is achieved successfully. Similar situation is also observed in V-doped SL MoSSe. Moreover, we demonstrate that the valleytronic properties of doped system are sensitive to strain. Our results provide a promising way to induce valley polarization in SL MoSSe. All calculation is performed using the Vienna ab initio simulation package (VASP) [37] based on density functional theory. We employ a projector augmented-wave method for ion-electron interaction and the generalized gradient approximation of exchange-correlation functional [38]. For including strong correlation effects, we perform PBE + U [39] calculation with a moderately effective Ueff = (U − J) = 3.0 eV for dopant atoms [20,40]. Cut-off energy is set to 450 eV and the vacuum space along the z direction is set to 15 Å. A 4 × 4 MoSSe supercell with one substituted dopant atom is used. Brillouin zone integration is sampled with a Monkhorst-Pack grid of 5 × 5 × 1. The structure, including the lattice constant and the positions of all atoms, is relaxed until the force is less than 0.01 eV/Å. The electronic iterations convergence criterion is set as 1 × 10−5 eV. Spin-orbit coupling (SOC) is incorporated in electronic structure calculations. To obtain a comprehensive understanding of SL MoSSe, we first study its structural and electronic properties. The optimized crystal structure of SL MoSSe for a 4 × 4 supercell is shown in Fig. 1. Similar to SL MoS2, SL MoSSe can be described as strongly bound S-Mo-Se sandwiches.

The Mo and S/Se atoms form 2D hexagonal lattices with C3v crystal symmetry, indicating an inversion asymmetric characteristic. The optimized lattice constant is a = 3.25 Å, with S-Se distance d = 3.23 Å. The S-Mo bond length is 2.42 Å, while Se-Mo bond length is 2.53 Å, larger than the S-Mo bond length due to the larger atomic radius.

Fig. 1 (a) Crystal structure of pristine SL MoSSe for a 4 × 4 × 1 supercell. (b) Coordination

environment of the Mo atom. (c) 2D Brillouin zone labeling the Γ point and the two inequivalent Κ ACS Paragon Plus Environment


and Κ’ points. As shown in Fig. 2(a), SL MoSSe is a direct band gap semiconductor with a band gap of 1.56 eV locating at the Κ points, implying a great potential in optoelectronics. Interestingly, both the conduction and valence bands have two energy-degenerate valleys at Κ and Κ’ points. It can be seen from the fatband [Fig. 2(b)] that the valence band edge is dominated mainly by the hybridization between Mo-dx2-y2 and dxy orbitals, whereas the conduction band edge consists mainly of the dz2 orbital. We also plot the partial density of states (DOS) projected onto the S/Se-p and Mo-d state to investigate the component in the conduction and valence band edges, as shown in Fig. 2(c). It reveals clearly that both the spin-down bands and spin-up bands are symmetrically occupied, resulting in 0 µB magnetic moment. The valence and conduction band edges are mainly contributed by the Mo-d orbital, agreeing well with the analysis above. When switching on SOC, as Fig. 2(d) illustrates, the spin degeneracy is lifted, reducing the band gap from 1.56 eV to 1.47 eV. More importantly, a large valley spin splitting (169 meV) is produced at the valence band edge, arising from the strong SOC effect. Compared to the valence band, the conduction band edges exhibit a neglectable valley spin splitting (14 meV), attributing to the fact that the valence and conduction band edges are dominated by different orbitals. The time-reversal symmetry dictates the spin splitting to have opposite signs at the Κ and Κ’ valleys, giving rise to the coupled spin and valley physics. All the data above are well consistent with the previous studies [24]. Similar to the application of the spin degree of freedom in spin-based information storage and processing applications, the valley degree of freedom can be used to store and process binary information. The generation of the valley polarization is the key step for the efficient use of the valley degree of freedom. Since SL MoSSe has conduction and valence band edges characterized by energetically degenerate valleys, we regard it as a valleytronic material of great potential. And the spin and valley degrees of freedom are interdependent in SL MoSSe, suggesting that the valley polarization could be generated through spin polarization. In view of this fact, we propose that magnetic doping could be employed to control the valley polarization in SL MoSSe. Here, we select Cr and V as the dopants as they are conventional magnetic dopants. Moreover, their atomic radii are close to that of Mo, which will not significantly damage the crystal structure of SL MoSSe.


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Fig. 2 (a) The band structure of SL MoSSe without taking SOC into account. (b) The fatband of SL MoSSe monolayer corresponding to (a). The orange curves denote Mo-dxy and dx2-y2 orbitals, and the green curves denote Mo-dz2. (c) The density of states for SL MoSSe monolayer. (d) Band structure of SL MoSSe monolayer with SOC. The red and blue arrows denote spin-up and spin-down electrons, respectively. The horizontal dashed line indicates the Fermi level. The crystal structures of Cr/V-doped SL MoSSe are shown in Fig. 3(a). One Cr/V atom replaces one Mo atom in a 4 × 4 × 1 supercell. So similar to Mo, each Cr/V coordinates to three S and three Se atoms. The Cr-S and Cr-Se bond length are 2.34 Å and 2.45 Å, respectively, while the V-S and V-Se bond length are 2.37 Å and 2.51 Å, indicating a strong interaction between the doped atom and host atoms. Clearly, the V-S and V-Se bond length are respectively a little longer than that of Cr-S and Cr-Se bond but shorter than that of Mo-S and Mo-Se bond. That is because the atomic radius of V is larger than that of Cr but shorter than that of Mo. The binding energy, Eb, is given by the expression: Eb = Ev-MoSSe +Ed - Ed-MoSSe where Ev-MoSSe is the energy of the SL MoSSe with one Mo vacancy, Ed is the energy of the doped atom, and Ed-MoSSe is the energy of the Cr/V-doped SL MoSSe. The calculated binding energies for Cr and V doped cases are 2.204 eV and 2.773 eV, respectively, indicating strong stability of the doped systems. Since MoSSe has been successfully realized in experiment [24,25], the doping can readily be realized by the post-synthesis techniques like low-energy ion irradiation [41-43]. So we believe the Cr/V-doped MoSSe exhibit high experimental feasibility.



Fig. 3 (a) Crystal structure of Cr/V-doped SL MoSSe where a Cr/V atom replaces a Mo atom in a 4 × 4 × 1 supercell. The yellow ball denotes Cr/V atom. (b) The spin charge density of Cr-doped SL MoSSe. (c) The spin charge density of V-doped SL MoSSe. The orange and green isosurfaces correspond to the spin-up and spin-down states, respectively. The isovalue of 0.02 spins per bohr3 for both dopants is used. The spin charge density of the SL MoSSe with different dopants is calculated, see Fig. 3(b,c). In the pristine SL MoSSe, the spin density is distributed symmetrically, leading to no spin polarization. The total magnetic moment is 0.0 µB in the Cr-doped system because the Cr atom is isoelectronic to the Mo atom. Interestingly, the Cr atom has a local magnetic moment of 2.0 µB, which agrees well with the fact that it has more localized 3d orbitals than 4d orbitals in the Mo atom. The magnetic moments on the neighboring S/Se and Mo atoms are attributed to strong interaction with Cr, aligning antiferromagnetically to the Cr atom. Different from the case of Cr, the V atom has one less valence electron than the Mo atom, leading to the total magnetic moment of 1.0 µB. The V atom has a local magnetic moment of 1.0 µB, while relatively small magnetic moment with opposite sign appears in the neighboring S/Se atoms and interstitial regions, reflecting a weak antiferromagnetic coupling and strong interaction between V and MoSSe. The band structure of Cr-doped SL MoSSe without taking SOC into account is shown in Fig. 4(a). Interestingly, the valleys observed in SL MoSSe are preserved, though several defect states emerge in the band gap. Due to the existence of magnetic properties, the spin degeneracy in the bands of SL MoSSe is lifted. Correspondingly, the large valley spin splitting is induced. And different from the pure case, the degenerated bands at Κ and Κ’ valleys exhibit the same sign. This difference arises from the introduction of magnetic dopants. As we mentioned above, for the pure case, the time-reversal symmetry requires the spin splitting at Κ and Κ’ valleys to be opposite. While for the Cr-doped SL MoSSe, the magnetic dopant breaks the time reversal symmetry, leading to same signs at the Κ and Κ' valleys. From Fig. 4(a), we can see that the defect states in the band ACS Paragon Plus Environment

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gap are three spin-up bands and one spin-down band, among which the spin-up bands are unoccupied and the spin-down band is just located below the Fermi level. Furthermore, we can learn from the fatband in Fig. 4(b) that the three spin-up bands are mainly composed of d states of the Mo and Cr atoms, revealing strong orbital hybridization between the Cr dopant and host atoms. However, the valleys are still degenerate. The DOS of the Cr-doped system is shown in Fig. 4(c). The states of Cr spread a large energy scale as it has a strong hybridization with the host SL MoSSe. The spin-up channel locates at different energy from the spin-down channel, indicating magnetic characteristic in the system. The unoccupied states above the Fermi level contain a large component of Cr, which are highly localized as the bands are almost flat. The band structure of the Cr-doped SL MoSSe with SOC is shown in Fig. 4(d). Interestingly, the degeneracy of the valence band maximum in Κ and Κ’ valleys is lifted, confirming the long-sought valley polarization. Here we denote the valley polarization as ∆KK’ = EK’ - EK, indicating the energy difference between the top valence band at K and K’ valleys. As shown in Fig. 4(d), the spin splitting at Κ’ valley is larger than that at Κ valley, and the sign of the top valence bands at the two valleys are the same. To further explain this phenomenon, we define ∆ul = Eu - El, indicating the energy difference between the upper and lower bands of the top valence band at K points. In pure system without SOC, ∆ul(K) = ∆ul(K’) = 0. Magnetic dopant induces a spin splitting ∆m at two valleys, so ∆ul(K) = ∆ul(K’) = ∆m. As we mentioned above, SOC can induce spin splittings

with opposite signs at two valleys, i.e. ∆λ(K) and -∆λ(K’). Therefore, we obtain ∆ul(K) = ∆m + ∆λ at K point and ∆ul(K’) = ∆m - ∆λ at K’ point. We can refer to it as the enhancement/reduction of the spin splitting at K/K’ valley because of the strong SOC effect. The valley polarization is 10 meV. Unfortunately, the doping state originating from strong hybridization between Cr and MoSSe is still located between the valleys and the Fermi level, prohibiting the Cr-doped SL MoSSe monolayer from being a suitable valleytronic material. Nevertheless, we will propose a simple and practicable approach to solve this problem later.



Fig. 4 The band structures of (a) Cr-doped and (e) V-doped SL MoSSe without SOC. The orange and green curves denote spin-up and spin-down states, respectively. The fatbands of (b) Cr-doped and (f) V-doped SL MoSSe. The orange, green and yellow balls denote contribution from Mo atoms, S/Se atoms and Cr (V) atom, respectively. The density of states of (c) Cr-doped and (g) V-doped SL MoSSe. The band structures of (d) Cr-doped and (h) V-doped SL MoSSe with SOC. The orange curve denotes the highest valence bands of the host MoSSe. The insets offer a zoom on the valley polarization. The horizontal dashed line indicates the Fermi level. Similar to Cr-doped case, the valleys’ characteristic is preserved and a large spin splitting in band structure is observed in V-doped SL MoSSe, see Fig. 4(e). And there are only one spin-up band and one spin-down band appearing in the band gap. Both impurity bands are unoccupied as V is one valence electron less than Cr. One important point is that the impurity states lie far away from the Fermi level, leading to the valleys are right below the Fermi level without any bands separating them. In this sense, we expect that the valleys are still located at the Fermi level after taking SOC into consideration. As illustrated in Fig. 4(f), strong hybridization between the V atom and SL MoSSe is reflected in the spin-up band above the Fermi level which is mainly dominated by d states of the V and Mo atoms. The DOS calculation confirm our analysis about the band structure, see Fig.


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4(g). The spin-down state above the Fermi level shows a sharp peak as the corresponding band is rather flat. Upon including SOC, similar situation in observed in V-doped SL MoSSe, where the spin splitting at Κ valley is smaller than that at Κ’ valley because the strong SOC enhance/reduce the spin splitting at Κ’/Κ valley, as we explained in the Cr-doped system. Excitingly, the valleys are located at the Fermi level, and the value of valley polarization is up to 59 meV, see Fig. 4(h), larger than that of WSe2 (0.1-0.2 meV caused by external magnetic field) [10], which is sizeable enough for observing the valley Hall effect at room-temperature. It is also important to mention that as expected, the impurity bands still locate far away from the Fermi level, which will not affect the valleytronic performance. Having one valence electron less than the Cr atom, the V dopant makes the V-doped MoSSe monolayer an ideal valleytronic material. As we mentioned above, the valence band edges in SL MoSSe have large spin splittings with opposite signs at Κ and Κ’ valleys, see Fig. 5(a). What’s more, the valence band edges at the two inequivalent valleys have opposite berry curvatures due to inversion symmetry breaking. Consequently, when holes are injected and an in-plane electric field is applied, the carriers at inequivalent valleys will obtain opposite velocities, giving rise to the spin/valley Hall effect, as shown in Fig. 5(b). The spin/valley Hall effect can be demonstrated by optoelectronic measurements. Under the excitation of a circularly polarized laser, valley-polarized electrons and holes can be injected due to optical selection rules, forming a charge Hall current. The charge Hall current can be measured as a transverse voltage and changes sign with the helicity of the optical polarization. More charming phenomenon, namely anomalous valley Hall effect, exists in Cr/V-doped SL MoSSe due to valley polarization. When the Fermi level is set between two valleys, an additional charge Hall current will be produced under an in-plane electric field, which can be easily detected as a transverse voltage, see Fig. 5(c). The inequivalent valleys can store binary information, enabling doped SL MoSSe for application in valleytronic devices.



Fig. 5 (a) Spin splitting in the highest valence band and the lowest conduction band at two inequivalent valleys. The red and blue curves correspond to spin-up and spin-down states, respectively. (b) Diagram of the spin/valley Hall effect in hole-doped SL MoSSe. (c) Diagram of the anomalous valley Hall effect in Cr/V-doped MoSSe. Orange and green balls correspond to the carriers in Κ and Κ’ valleys, respectively, and the + symbol indicates a hole. For 2D materials, strain engineering is a powerful approach to tuning the electronic properties. What’s more, we can easily implement strain by utilizing a specific substrate in the fabrication of the Janus SL MoSSe. It should be noted that considering compressive strain is only for academic interest, as it can lead to wrinkle [44]. The biaxial strain is defined as ε = (a-a0) / a0, where a0/a is the lattice constant of the unstrained/strained system. The related band structures under strain from -4% to 4% are shown in Fig. S1 and S2. We can see that valleytronic properties of the doped systems are sensitive to strain. In the case of Cr-doped system, the three spin-down bands above the Fermi level move to lower energy as the strain increasing from -4% to 4%, further reducing the band gap. When tensile strain is applied, the valleys are mixed with other bands and become indistinguishable. However, when compressed strain is applied, we are glad to see that valley are preserved and appear right below the Fermi level. This suggests that Cr-doped system under strain of -4% or -2% is an ideal valleytronic material. In the V-doped system, similar situation is observed. In conclusion, we demonstrate that valley polarization can be realized in Janus SL MoSSe by magnetic doping. We find that pure SL MoSSe has a direct band gap and harbors strong coupled spin and valley physics. The promising valley polarization is achieved successfully in Cr/V-doped SL MoSSe. Both systems are perfect 2D valleytronic systems. Moreover, we discuss the strain effects and demonstrate that the valleytronic properties of doped system are sensitive to strain. As the charge Hall current is easily measured, the anomalous valley Hall effect observed in these ACS Paragon Plus Environment

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systems is expected to be utilized in data storage and reading.

ASSOCIATED CONTENT Supporting Information Available: The band structures of doped systems under strain from -4% to 4%.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] (Y.M.). *E-mail: [email protected] (Y.D.). ORCID Ying Dai: 0000-0002-8587-6874 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work is supported by the National Natural Science foundation of China (11604213, 11374190, and 21333006), 111 Project (B13029). We also thank the Taishan Scholar Program of Shandong Province and Qilu Young Scholar Program of Shandong University.

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Valley Polarization in Janus Single-Layer MoSSe via Magnetic Doping

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