The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essenc...The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.展开更多
Monolayer transition metal dichalcogenides(TMDCs) with the 1 T0 structure are a new class of large-gap two-dimensional(2 D) topological insulators, hosting topologically protected conduction channels on the edges. How...Monolayer transition metal dichalcogenides(TMDCs) with the 1 T0 structure are a new class of large-gap two-dimensional(2 D) topological insulators, hosting topologically protected conduction channels on the edges. However, the 1 T0 phase is metastable compared to the 2 H phase for most of 2 D TMDCs, among which the 1 T0 phase is least favored in monolayer MoS2. Here we report a clean and controllable technique to locally induce nanometer-sized 1 T0 phase in monolayer 2 H-MoS2 via a weak Argon-plasma treatment,resulting in topological phase boundaries of high density. We found that the stabilization of 1 T0 phase arises from the concerted effects of S vacancies and the tensile strain. Scanning tunneling spectroscopy(STS) clearly reveals a spin-orbit band gap(~60 meV) and topologically protected in-gap states residing at the 1 T0-2 H phase boundary, which are corroborated by density-functional theory(DFT) calculations.The strategy developed in this work can be generalized to a large variety of TMDCs materials, with potentials to realize scalable electronics and spintronics with low dissipation.展开更多
基金Majeed Ur Rehman acknowledges the support from the Chinese Academy of Sciences(CAS)and TWAS for his Ph.D.studies at the University of Science and Technology,China in the category of 2016 CAS-TWAS President’s Fellowship Awardee(Grant No.2016-156)
文摘The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number Cs for energy-bands of trilayer graphene having the essence of intrinsic spin-orbit coupling is analytically calculated. We find that for each valley and spin, Cs is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states, consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin-orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin-orbit （RSO） interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin-orbit coupling, while the other two layers have zero intrinsic spin-orbit coupling. Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.
基金supported by National Key Projects for Research and Development of China with Grant No. 2021YFA1400400the National Natural Science Foundation of China with Grants No. 12225407 and 12074174+2 种基金China Postdoctoral Science Foundation with Grants No. 2022M711569 and 2022T150315Jiangsu Province Excellent Postdoctoral Program with Grant No. 20220ZB5Fundamental Research Funds for the Central Universities
基金financially supported by the National Natural Science Foundation of China (11888101, 11634001, 11834017 and 61888102)the National Key R&D Program (2016YFA0300901 and 2017YFA0205003)+3 种基金the Strategic Priority Research Program of Chinese Academy of Sciences (XDB28000000 and XDB30000000)Beijing Municipal Science & Technology Commissionsupport from National Science Fund for Distinguished Young Scholars (21725302)Cheung Kong Young Scholar Program
文摘Monolayer transition metal dichalcogenides(TMDCs) with the 1 T0 structure are a new class of large-gap two-dimensional(2 D) topological insulators, hosting topologically protected conduction channels on the edges. However, the 1 T0 phase is metastable compared to the 2 H phase for most of 2 D TMDCs, among which the 1 T0 phase is least favored in monolayer MoS2. Here we report a clean and controllable technique to locally induce nanometer-sized 1 T0 phase in monolayer 2 H-MoS2 via a weak Argon-plasma treatment,resulting in topological phase boundaries of high density. We found that the stabilization of 1 T0 phase arises from the concerted effects of S vacancies and the tensile strain. Scanning tunneling spectroscopy(STS) clearly reveals a spin-orbit band gap(~60 meV) and topologically protected in-gap states residing at the 1 T0-2 H phase boundary, which are corroborated by density-functional theory(DFT) calculations.The strategy developed in this work can be generalized to a large variety of TMDCs materials, with potentials to realize scalable electronics and spintronics with low dissipation.
