Quantum spin Hall effect in graphene
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Cites background from "Quantum spin Hall effect in graphen..."
...The intrin-si and extrinsi spin orbit intera tions an be writtenas (Dresselhaus and Dresselhaus, 1965; Kane and Mele,2005): HSO;int ≡ ∆so ∫ d2rΨ̂†(r)ŝz σ̂z τ̂zΨ̂(r) , HSO;ext ≡ λR ∫ d2rΨ̂†(r)(−ŝxσ̂y+ŝyσ̂xτ̂z)Ψ̂(r) ,(124)where σ̂ and τ̂ are Pauli matri es whi h des ribe the sub-latti e and valley…...
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...The spin orbit intera tion leads to a spin de-pendent shift of the orbitals, whi h is of a di erent signfor the two sublatti es, a ting as an e e tive mass withinea h Dira point (Dresselhaus and Dresselhaus, 1965;Kane and Mele, 2005; Wang and Chakraborty, 2007a)....
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Cites background from "Quantum spin Hall effect in graphen..."
...The edge states have a distinct helical property: two states with opposite spin polarization counterpropagate at a given edge (Kane and Mele, 2005; Wuet al., 2006; Xu and Moore, 2006)....
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...The conceptof spin Hall insulator motivated Kane and Mele in 2005 to investigate the QSH effect in graphene (Kane and Mele, 2005), a material first discovered experimentally that same year....
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...Some important concepts were developed in earlier works (Bernevig and Zhang, 2006; Haldane, 1988; Kane and Mele, 2005; Murakamiet al., 2003, 2004; Sinovaet al., 2004; Zhang and Hu, 2001), culminating in the construction of the topological band theory (TBT) and the 3 TFT of 2D and 3D topological…...
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...More generally, the topological properties of the QSH state are mathematically characterized by aZ2 topological invariant (Kane and Mele, 2005)....
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...The physical picture described above applies only to the case of a single pair of QSH edge states (Kane and Mele, 2005; Wuet al., 2006; Xu and Moore, 2006)....
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