Manipulation of the large Rashba spin splitting in polar two-dimensional transition metal dichalcogenides

📝 Abstract

Transition metal dichalcogenide (TMD) monolayers MXY (M=Mo, W, X(not equal to)Y=S, Se, Te) are two-dimensional polar semiconductors. Setting WSeTe monolayer as an example and using density functional theory calculations, we investigate the manipulation of Rashba spin orbit coupling (SOC) in the MXY monolayer. It is found that the intrinsic out-of-plane electric field due to the mirror symmetry breaking induces the large Rashba spin splitting around the Gamma point, which, however, can be easily tuned by applying the in-plane biaxial strain. Through a relatively small strain (from -2% to 2%), a large tunability (from around -50% to 50%) of Rashba SOC can be obtained due to the modified orbital overlap, which can in turn modulate the intrinsic electric field. The orbital selective external potential method further confirms the significance of the orbital overlap between W-dz2 and Se-pz in Rashba SOC. In addition, we also explore the influence of the external electric field on Rashba SOC in the WSeTe monolayer, which is less effective than strain. The large Rashba spin splitting, together with the valley spin splitting in MXY monolayers may make a special contribution to semiconductor spintronics and valleytronics.

💡 Analysis

Transition metal dichalcogenide (TMD) monolayers MXY (M=Mo, W, X(not equal to)Y=S, Se, Te) are two-dimensional polar semiconductors. Setting WSeTe monolayer as an example and using density functional theory calculations, we investigate the manipulation of Rashba spin orbit coupling (SOC) in the MXY monolayer. It is found that the intrinsic out-of-plane electric field due to the mirror symmetry breaking induces the large Rashba spin splitting around the Gamma point, which, however, can be easily tuned by applying the in-plane biaxial strain. Through a relatively small strain (from -2% to 2%), a large tunability (from around -50% to 50%) of Rashba SOC can be obtained due to the modified orbital overlap, which can in turn modulate the intrinsic electric field. The orbital selective external potential method further confirms the significance of the orbital overlap between W-dz2 and Se-pz in Rashba SOC. In addition, we also explore the influence of the external electric field on Rashba SOC in the WSeTe monolayer, which is less effective than strain. The large Rashba spin splitting, together with the valley spin splitting in MXY monolayers may make a special contribution to semiconductor spintronics and valleytronics.

📄 Content

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Manipulation of the large Rashba spin splitting in polar two-dimensional transition metal dichalcogenides

Qun-Fang Yao1, Jia Cai1, Wen-Yi Tong1, Shi-Jing Gong1*,
Ji-Qing Wang1, Xiangang Wan2, Chun-Gang Duan1,3, J. H. Chu1,3 1Key Laboratory of Polar Materials and Devices, Ministry of Education, East China Normal University, Shanghai 200062, China 2National Laboratory of Solid State Microstructures and Department of Physics,
Nanjing University, Nanjing, Jiangsu 210093, China 3Collaborative Innovation Center of Extreme Optics, Shanxi University,
Taiyuan, Shanxi 030006, China

ABSTRACT Transition metal dichalcogenide (TMD) monolayers MXY (M = Mo, W; X  Y = S, Se, Te) are two-dimensional polar semiconductors. Setting WSeTe monolayer as an example and using density functional theory calculations, we investigate the manipulation of Rashba spin orbit coupling (SOC) in the MXY monolayer. It is found that the intrinsic out-of-plane electric field due to the mirror symmetry breaking induces the large Rashba spin splitting around the  point, which, however, can be easily tuned by applying the in-plane biaxial strain. Through a relatively small strain (from -2% to 2%), a large tunability (from around -50% to 50%) of Rashba SOC can be obtained due to the modified orbital overlap, which can in turn modulate the intrinsic electric field. The orbital selective external potential method further confirms the significance of the orbital overlap between W- 2 zd and Se- zp in Rashba SOC. In addition, we also explore the influence of the external electric field on Rashba SOC in the WSeTe monolayer, which is less effective than strain. The large Rashba spin splitting, together with the valley spin splitting in MXY monolayers may make a special contribution to semiconductor spintronics and valleytronics.

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I. INTRODUCTION
Since the successful exfoliation of graphene by Novoselov et al. in 2004,1 growing research attention has been focused on the two-dimensional materials, which consequently accelerates the emergence of other two-dimensional materials, such as boron nitride (BN),2 silicene,3 and transition-metal dichalcogenide (TMD) monolayers MX2 (M = Mo, W; X = S, Se, Te),4, 5 etc. Because of the intrinsic band gap about 1.1~1.9 eV, 5, 6 TMD monolayers are considered to be good candidates for the channel materials in field effect transistor (FET), as well as promising materials for optoelectronics.7-9 In addition, the inversion symmetry breaking together with the giant spin orbit coupling (SOC) originated from the d -orbitals of the metal atoms in TMD monolayers induces the large spin splitting from 150 meV to nearly 500 meV at the corners of the two-dimensional hexagonal Brillouin zone.10-13 The strong coupling between spin and valley degrees of freedom makes TMD monolayers the ideal valleytronic materials.14-16
Different from MX2 monolayers, polar MXY (M = Mo, W; X  Y = S, Se, Te) monolayers can show additional Rashba spin splitting17 around the  point, due to the intrinsic out-of-plane electric field induced by the mirror symmetry breaking. According to Cheng et al.’s report, Rashba SOC strength in MXY monolayers is around 0.01 eV Å.10 Rashba SOC was initially investigated in semiconductor heterostructures,18-24 and wins the growing research interest because of its gate tunability25 and its great significance in the spin FET,26 in which the spin precession can be
electrically controlled in a precise and predictable way.27, 28 Great efforts have been made to overcome the several fundamental challenges in the spin FET, such as the low spin-injection efficiency, the spin relaxation, and the control of spin precession.28 Recently, an all-electric and all-semiconductor spin FET has been experimentally realized based on Rashba SOC.29 The polar two-dimensional MXY monolayers with the intrinsic structure inversion asymmetry will surely enrich the family of Rashba SOC and possibly promote the progress of the spin FET, it is therefore necessary to explore the tunability of Rashba SOC in these materials. Since TMD monolayer has three atomic layers in its unit cell, the in-plane strain will certainly result in the change of bonding angles and lengths, which could dramatically influence the electronic structure.30-39 For example in MoS2 monolayer, there exists a direct-to-indirect band gap transition under 2% tensile strain,30, 35-37 and a semiconducting to metal transition under 1015% tensile strain.38, 39 For MXY monolayer, it is expected that the in-plane strain can effectively manipulate Rashba SOC, which is of great significance for both the fundamental physics and the potential application in the spin FET.
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In the present work, we investigate the influence of the biaxial strain on Rashba SOC of MXY monolayers. Since the physics in MXY monolayers is essentially the same,10 we select WSeTe monolayer as an example to demonstrate th

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