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Dynamical conductivity of gated AA-stacking multilayer graphene with spin-orbital coupling

机译：自旋轨道耦合的门禁AA堆叠多层石墨烯的动态电导率

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摘要

An efficient method, without the numerical diagonalization of a huge Hamiltonian matrix and calculation of a tedious Green's function, is proposed to calculate the exact energy spectrum and dynamical conductivity in gated AA-stacking N-layer graphene (AANLG) with intrinsic spin-orbital coupling (SOC). The 2N x 2N tight-binding Hamiltonian matrix, velocity operator and Green's function representation of AANLG are simultaneously reduced to N 2 x 2 diagonal block matrices through a proper transformation matrix. Gated AANLG with intrinsic SOC is reduced to N graphene-like layers. The energy spectrum of a graphene-like layer is E = epsilon(perpendicular to) +/- epsilon(parallel to), and epsilon(perpendicular to) depends on the interlayer interaction, gated voltage and layer number. epsilon(parallel to) = root E-MG(2) vertical bar Delta(2) , where E-MG is the energy spectrum of a graphene monolayer and Delta is the magnitude of the intrinsic SOC. More importantly, by inserting the diagonal block velocity operator and Green's function representation in the Kubo formula, the exact dynamical conductivity of AANLG is shown to be sigma = Sigma(N)(j=i) sigma(j), the sum of the dynamical conductivity of N graphene-like layers. The analytical form of sigma(j) is presented and the dependence of sigma(j) on epsilon(perpendicular to), Delta, and chemical potential is clearly demonstrated. Moreover, the effect of the Rashba SOC on the electronic properties of AANLG is explored with the exact energy spectrum presented.
机译：提出了一种有效的方法，该方法不需要巨大的哈密顿矩阵的数值对角线化和繁琐的格林函数的计算，即可计算出具有内在自旋轨道耦合的门禁AA堆叠N层石墨烯（AANLG）的精确能谱和动态电导率（SOC）。 AANLG的2N x 2N紧束缚哈密顿矩阵，速度算符和格林函数表示通过适当的变换矩阵同时缩减为N 2 x 2对角线块矩阵。具有固有SOC的门控AANLG被还原为N个类石墨烯层。石墨烯样层的能谱为E = epsilon（垂直于）+/- epsilon（平行于），epsilon（垂直于）取决于层间相互作用，栅极电压和层数。 epsilon（平行于）=根E-MG（2）竖线Delta（2），其中E-MG是石墨烯单层的能谱，而Delta是本征SOC的大小。更重要的是，通过在Kubo公式中插入对角线块速度算子和格林函数表示，AANLG的精确动态电导率显示为sigma = Sigma（N）（j = i）sigma（j） N类石墨烯层的电导率。给出了σ（j）的解析形式，并清楚地证明了σ（j）对ε（垂直于），Δ和化学势的依赖性。此外，利用给出的精确能谱，探索了Rashba SOC对AANLG电子性能的影响。

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