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Conductivity tensor of graphene dominated by spin-orbit coupling scatterers: A comparison between the results from Kubo and Boltzmann transport theories.

Liu Z, Jiang L, Zheng Y - Sci Rep (2016)

Bottom Line: By performing numerical calculations, we find that the Kubo quantum transport result of the diagonal conductivity within the self-consistent Born approximation exhibits an insulating gap around the Dirac point.In contrast, the semi-classical Boltzmann theory fails to predict such a topological insulating phase.The Boltzmann diagonal conductivity is nonzero even in the insulating gap, in which the Boltzmann spin Hall conductivity does not exhibit any quantized plateau.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Physics and Technology for Advanced Batteries, College of Physics, Jilin University, Ministry of Education, Changchun 130012, China.

ABSTRACT
The diagonal and Hall conductivities of graphene arising from the spin-orbit coupling impurity scattering are theoretically studied. Based on the continuous model, i.e. the massless Dirac equation, we derive analytical expressions of the conductivity tensor from both the Kubo and Boltzmann transport theories. By performing numerical calculations, we find that the Kubo quantum transport result of the diagonal conductivity within the self-consistent Born approximation exhibits an insulating gap around the Dirac point. And in this gap a well-defined quantized spin Hall plateau occurs. This indicates the realization of the quantum spin Hall state of graphene driven by the spin-orbit coupling impurities. In contrast, the semi-classical Boltzmann theory fails to predict such a topological insulating phase. The Boltzmann diagonal conductivity is nonzero even in the insulating gap, in which the Boltzmann spin Hall conductivity does not exhibit any quantized plateau.

No MeSH data available.


Feynman diagrams of the correlation function Jαβ (ε, ε′) within SCBA.
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f2: Feynman diagrams of the correlation function Jαβ (ε, ε′) within SCBA.

Mentions: The velocity operator vα can be represented by Heisenberg equation vα = [H, α] = (γ/)σα. In general, Jαβ is a complex function of complex energy arguments ε and ε′. Within SCBA, the correlation function Jαβ (ε, ε′) can be obtained by summing the Feynman diagrams including the vertex corrections, as shown in Fig. 2. The summation turns out to be the sum of a geometrical series, and the results for Jxx and Jxy are


Conductivity tensor of graphene dominated by spin-orbit coupling scatterers: A comparison between the results from Kubo and Boltzmann transport theories.

Liu Z, Jiang L, Zheng Y - Sci Rep (2016)

Feynman diagrams of the correlation function Jαβ (ε, ε′) within SCBA.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4815021&req=5

f2: Feynman diagrams of the correlation function Jαβ (ε, ε′) within SCBA.
Mentions: The velocity operator vα can be represented by Heisenberg equation vα = [H, α] = (γ/)σα. In general, Jαβ is a complex function of complex energy arguments ε and ε′. Within SCBA, the correlation function Jαβ (ε, ε′) can be obtained by summing the Feynman diagrams including the vertex corrections, as shown in Fig. 2. The summation turns out to be the sum of a geometrical series, and the results for Jxx and Jxy are

Bottom Line: By performing numerical calculations, we find that the Kubo quantum transport result of the diagonal conductivity within the self-consistent Born approximation exhibits an insulating gap around the Dirac point.In contrast, the semi-classical Boltzmann theory fails to predict such a topological insulating phase.The Boltzmann diagonal conductivity is nonzero even in the insulating gap, in which the Boltzmann spin Hall conductivity does not exhibit any quantized plateau.

View Article: PubMed Central - PubMed

Affiliation: Key Laboratory of Physics and Technology for Advanced Batteries, College of Physics, Jilin University, Ministry of Education, Changchun 130012, China.

ABSTRACT
The diagonal and Hall conductivities of graphene arising from the spin-orbit coupling impurity scattering are theoretically studied. Based on the continuous model, i.e. the massless Dirac equation, we derive analytical expressions of the conductivity tensor from both the Kubo and Boltzmann transport theories. By performing numerical calculations, we find that the Kubo quantum transport result of the diagonal conductivity within the self-consistent Born approximation exhibits an insulating gap around the Dirac point. And in this gap a well-defined quantized spin Hall plateau occurs. This indicates the realization of the quantum spin Hall state of graphene driven by the spin-orbit coupling impurities. In contrast, the semi-classical Boltzmann theory fails to predict such a topological insulating phase. The Boltzmann diagonal conductivity is nonzero even in the insulating gap, in which the Boltzmann spin Hall conductivity does not exhibit any quantized plateau.

No MeSH data available.