Spin Hall and spin Nernst effects in graphene with intrinsic and Rashba spin-orbit interactions

The spin Hall and spin Nernst effects in graphene are studied based on Green＇s function formalism. We calculate intrinsic contributions to spin Hall and spin Nernst conductivities in the Kane-Mele model with various structures. When both intrinsic and Rashba spin-orbit interactions are present, their interplay leads to some characteristics of the dependence of spin Hall and spin Nernst conductivities on the Fermi level. When the Rashba spin--orbit interaction is smaller than intrinsic spin-orbit coupling, a weak kink in the conductance appears. The kink disappears and a divergence appears when the Rashba spin-orbit interaction enhances. When the Rashba spin-orbit interaction approaches and is stronger than intrinsic spin-orbit coupling, the divergence becomes more obvious.

RKKY Interaction in Gapped or Doped Graphene

In our previous work [1] we calculated RKKY interaction between two magnetic impurities in pristine graphene using the Green’s functions (GF) in the coordinate-imaginary time representation. Now we show that the calculations of the GF in this representation can be simplified by using the Feynman’s trick, which allows to easily calculate RKKY interaction in gapped graphene. We also present calculations of the RKKY interaction in gapped or doped graphene using the coordinate-imaginary frequency representation. Both representations, corresponding to calculation of the bubble diagram in Euclidean space, have an important advantage over those corresponding to calculation in Minkowskii space, which are very briefly reviewed in the Appendix to the present work. The former, in distinction to the latter, operate only with the convergent integrals from the start to the end of the calculation.

Different noncollinear magnetizations on two edges of zigzag graphene nanoribbons

Based on density functional theory and non-equilibrium Green’s function method,we studied noncollinear magnetism and spin transport in a 180°domain wall made of zigzag graphene nanoribbon(ZGNR)with different noncollinear magnetic profiles on the top and bottom edges.Our results show that a helical domain wall on the top(bottom)edge and an abrupt domain wall on the bottom(top)edge can survive in the ZGNR.This indicates that such characteristic magnetization distribution can be obtained by some means,e.g.,the introduction of impurity on one edge.Compared to a wide ZGNR,a narrow ZGNR presents obvious coupling between the two edges which changes the magnetization and transmission greatly.As for the above-mentioned distinct magnetic profile,the spin transport is blocked in the abrupt domain wall due to strong spin flip scattering while remains unaffected in the helical domain wall due to the spin mixing effect.We deduce a formula of the transmission for various magnetic profiles of the ZGNRs.A new result based on this formula is that the transmission at the Fermi level can be zero,one,and two by tuning the edge magnetization.Our results provide insights into the noncollinear spin transport of the ZGNR-based devices.

Optical Conductivity of Graphene Sheet Including Electron-Phonon Interaction

Using an expression of optical conductivity,based on the linear response theory,the Green's function technique and within the Holstein Hamiltonian model,the effect of electron-phonon interaction on the optical conductivity of graphene plane is studied.It is found that the electron-phonon coupling increases the optical conductivity of graphene sheet in the low frequency region due to decreasing quasiparticle weight of electron excitation while the optical conductivity reduces in the high frequency region.The latter is due to role of electrical field's frequency.

Controllable Spin-Polarized Transport in a Three-Terminal Model

By means of the Keldysh Green's function method,we investigate the spin-polarized electron transport in a three-terminal device,which is composed of three normal metal leads and two serially-coupled quantum dots(QDs).The Rashba spin-orbit interaction(RSOI) is also considered in one of the QDs.We show that the spin-polarized charge current with arbitrary spin polarization can be obtained because of the quantum spin interference effect arising from the Rashba spin precession phase,and it can be modulated by the system parameters such as the applied external voltages,the RSOI strength,the QD levels,as well as the dot-lead coupling strengths.Moreover,a fully spin-polarized current or a pure spin current without any accompanying charge current can also be controlled to flow in the system.Our findings indicate that the proposed model can serve as an all-electrical spin device in spintronics field.