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The RKKY interaction between two impurities on a curved surface is investigated. Practical curved sample parameters are considered for investigating curvatures, similar to those observed experimentally in available samples such as graphene. For this type of two-dimensional curved systems and for two types of Schr\"{o}dinger and Dirac carriers, the RKKY interaction and local density of states (LDOS) are calculated. Results show that the strength of the RKKY interaction on a curved surface depends significantly on the nature of particles embedded on this surface, indicating that the geometry has a different effect on the dynamics of Schr\"{o}dinger and Dirac carriers. While the curved surface increases the RKKY interaction strength for Schr\"{o}dinger-type carriers in comparison with the flat sample, RKKY interaction decreases in the curved surface for Dirac-type particles. This can be understood regrading the effective magnetic field experienced by the Dirac particles as a result of the curved surface. There is also a correlation between LDOS and the RKKY interaction, which could be explained by the effect of conducting electrons density on the exchange interaction mediated by these carriers.

Edelstein and spin Hall effect response functions for a two-dimensional (2D) system of pseudospin-1 particles is investigated. These two response functions denoted by $ \sigma_{SH} $ and $ \sigma_{EE} $ have been analyzed in a pseudospin-1 particle system in the presence of the Rashba-type spin-orbit interaction using the Kubo-Streda technique and vertex corrections with non-magnetic impurities. Then, for a given range of the Rashba coupling, response functions of the spin Hall effect (SHE) and Edelstein effect (EE) have been estimated at various energy gaps and Fermi energies. Results indicate that in this type of the two-dimensional materials, SHE and EE are essentially induced by the vertex corrections and without considering these corrections the amount of these effects are really negligible. It has also been realized that SHE and EE conductivities can be modulated by the Rashba coupling strength at low and intermediate level of this spin-orbit type interaction.

Non-equilibrium spin-polarized transport properties of antiferromagnetic stanene nanoribbons are theoretically studied under the combining effect of a normal electric field and linearly polarized irradiation based on the tight-binding model at room temperature. Due to the existence of spin-orbit coupling in stanene lattice, applying normal electric field leads to splitting of band degeneracy of spin-resolved energy levels in conduction and valence bands. Furthermore, unequivalent absorption of the polarized photons at two valleys which is attributed to an antiferromagnetic exchange field results in unequal spin-polarized photocurrent for spin-up and spin-down components. Interestingly, in the presence of band bending which has been induced by edge potentials, an allowable quantum efficiency occurs over a wider wavelength region of the incident light. It is especially important that the variation of an exchange magnetic field generates spin semi-conducting behavior in the bended band structure. Moreover, it is shown that optical spin-filtering effect is obtained under the simultaneous effect of uniaxial strain and narrow edge potential.

The role of staggered potential on light-induced spin and pseudo-spin polarization has been investigated in silicene. It has been shown that non-equilibrium spin and pseudo-spin polarizations are emerged in silicene sheet by applying an external perpendicular electric field in the presence of circularly polarized light emission. This electric field results in pseudo-spin resolved states very close to the Dirac points therefore could be considered as a pseudomagnetic field. It has been shown that staggered potential induced spin-valley locking and pseudo-spin resolved bands are responsible for enhancement of the spin and pseudo-spin polarizations. Meanwhile, spin-valley locking suggests a coexistence of both spin and valley polarizations with nearly identical population imbalance at low Fermi energies which could be employed for magnetic detection of the valley polarization. It has been shown that spin-valley locking results in protection of the spin polarizations against the relaxations in elastic scattering regime. In addition results indicate that the pseudo-spin current can be generated by the circularly polarized light which could be explained by asymmetric light absorption of the states in k-space.

Spin to pseudo-spin conversion by which spin population imbalance converts to non-equilibrium pseudo-spin density in Dirac systems has been investigated particularly for graphene and insulator phase of silicene. Calculations have been performed within the Kubo approach and by taking into account the vertex correction. Results indicate that spin converts to pseudo-spin in either graphene or silicene that identified to come from the spin-orbit interactions. The response function of spin to pseudo-spin conversion is weakened several orders of magnitude by vertex correction of impurities in graphene, however, this conversion is strengthened in insulator silicene. In addition, in the case of silicene, results are indicative of an obvious change in the mentioned response function as a result of the change in band-topology which can be observed by manipulation of external electric field, vertically applied to the system surface. At the critical electric field in which the topological phase transition for silicene nano-ribbon has been observed, response function changes abruptly. Interconversion between the quantum numbers could provide a field for information and data processing technologies.

Intrinsic and Rashba spin-orbit interactions in strained graphene is studied within the tight-binding (TB) approach. Dependence of Slater-Koster (SK) parameters of graphene on strain are extracted by fitting the \emph{ab initio} band structure to the TB results. A generalized low-energy effective Hamiltonian in the presence of spin-orbit couplings is proposed for strained graphene subjected to an external perpendicular electric field. Dependence of the modified Rashba strength and other parameters of effective Hamiltonian on the strain and electric field are calculated. In order to analyze the influence of the applied strain on the electronic properties of the graphene, one must take into account the lattice deformation, modifications of the hopping amplitudes and shift of the Dirac points. We find that using the strain it is possible to control the strength of Rashba and intrinsic spin-orbit couplings as well as energy gap at the shifted Dirac points. Meanwhile, the strain slightly modifies the topology of low-energy dispersion around the Dirac points. We describe the SOCs induced energy splitting as a function of strain.

In this study, Rashba coupling induced Aharonov-Casher effect in a graphene based nano ring is investigated theoretically. The graphene based nano ring is considered as a central device connected to semi-infinite graphene nano ribbons. In the presence of the Rashba spin-orbit interaction, two armchair shaped edge nano ribbons are considered as semi-infinite leads. The non-equilibrium Green's function approach is utilized to obtain the quantum transport characteristics of the system. The relaxation and dephasing mechanisms within the self-consistent Born approximation is scrutinized. The Lopez-Sancho method is also applied to obtain the self-energy of the leads. We unveil that the non-equilibrium current of the system possesses measurable Aharonov-Casher oscillations with respect to the Rashba coupling strength. In addition, we have observed the same oscillations in dilute impurity regimes in which amplitude of the oscillations is shown to be suppressed as a result of the relaxations., Comment: Journal of Magnetism and Magnetic Materials (In Press)

Real magnetic and lattice deformation gauge fields have been investigated in honeycomb lattice of graphene. The coexistence of these two gauges will induce a gap difference between two valley points ($K$ and $K'$) of system. This gap difference allows us to study the possible topological valley Hall current and valley polarization in the graphene sheet. In the absence of magnetic field, the strain alone could not generate a valley polarization when the Fermi energy coincides exactly with the Dirac points. Since in this case there is not any imbalance between the population of the valley points. In other words each of these gauges alone could not induce any topological valley-polarized current in the system at zero Fermi energy. Meanwhile at non-zero Fermi energies population imbalance can be generated as a result of the external strain even at zero magnetic field. In the context of Berry curvature within the linear response regime the valley polarization (both magnetic free polarization, $\Pi_0$, and field dependent response function, $\chi_\alpha$) in different values of gauge fields of lattice deformation has been obtained.

Friedel oscillations of the graphene-like materials are investigated theoretically beyond the Dirac point-approximation. Numerical calculations have been performed within the random phase approximation (RPA). For intra-valley transitions it was demonstrated that the contribution of the different Dirac points in the wave-number dependent quantities, such as dielectric function $\epsilon(q)$, has been determined by the orientation of the wave-number with respect to the Dirac point position vector in $k$-space. Therefore identical contribution of the different Dirac points is not automatically guaranteed by the degeneracy of the Hamiltonian at these points. Meanwhile it was shown that the contribution of the inter-valley transitions is always anisotropic even when the Dirac points coincide with the Fermi level ($E_F=0$). This means that the Dirac point approximation based studies give the correct physics only at high wave length limit. The anisotropy of the static dielectric function reveals different contribution of the each Dirac point. Additionally, the anisotropic $k$-space dielectric function results in anisotropic Friedel oscillations in graphene-like materials. Calculations have also been performed in the presence of the Rashba interaction. It was shown that increasing the Rashba interaction strength slightly modifies the Friedel oscillations in graphene-like materials. Therefore the anisotropic dielectric function in $k$-space is the clear manifestation of band anisotropy in the graphene-like systems.

The influence of the non-collinear magnetic configuration on Friedel is investigated theoretically. Specifically the influence of the magnetic configuration on the induced electric charge in a N\'{e}el type domain wall (DW) has been obtained. The well-known Levy and Zhang eigenstates for a linear DW have been employed. Then the dielectric function of this magnetic system has been obtained within the random phase approximation. Results of the current work demonstrated that magnetic configuration of the system manifests itself in the electric properties such as induced charge distribution. Meanwhile the anisotropy of the induced charge distribution in the real space provides a measurable way for the determination of the DW orientation. In addition anisotropy of the dielectric function in k-space arises as a result of the anisotropy of the magnetic configuration. Therefore the orientation of the magnetic DW could also be captured by full optical measurements.

Recently it has been recognized that the electromotive force (emf) can be induced just by the spin precession where the generation of the electromotive force has been considered as a real-space topological pumping effect. It has been shown that the amount of the electromotive force is independent of the functionality of the localized moments. It was also demonstrated that the rigid domain wall (DW) motion cannot generate electromotive force in the system. Based on real-space topological pumping approach in the current study we show that the electromotive force can be induced by rigid motion of a deformed DW. We also demonstrate that the generated electromotive force strongly depends on the DW bulging. Meanwhile results show that the DW bulging leads to generation of the electromotive force both along the axis of the DW motion and normal to the direction of motion.

In the present study, the anisotropic resistivity of the monolayer graphene has been obtained in semiclassical regime beyond the Dirac point approximation. In particular, detailed investigations were made on the dependence of conductivity on the Fermi energy. At low energies, in the vicinity of the Dirac points, band energy of the monolayer graphene is isotropic at the Fermi level. Meanwhile, at the intermediate Fermi energies anisotropic effects such as trigonal warping is expected to be the origin of the anisotropic resistivity. However, besides the band anisotropy there also exists an other source of anisotropic resistivity which was introduced by scattering matrix. At high energies it was shown that the band anisotropy is less effective than the anisotropy generated by the scattering matrix. It was also shown that there exist two distinct regimes of anisotropic resistivity corresponding the trigonal warping and connected Fermi curve at intermediate and high energies respectively.

Using the Kubo formalism, the magnetic properties of the system in the linear regime have been investigated. Mainly the effect of non-magnetic substrate on the spin susceptibility is calculated. Results show that the Rashba coupling interaction has a central role in the magnetic response function of the system and it is really remarkable since this type of spin orbit coupling can be effectively controlled by an external gate voltage. Most importantly it was shown that, in the presence of the Rashba interaction a magnetic phase transition could be observed. This magnetic phase corresponds to a magnetic order of conduction electrons that takes place at some especial frequency of external magnetic field.

Low field response function calculations have been performed on a two-dimensional electron gas with well-defined electron-surface roughness scattering. The Lindhard model was employed to compute the response function. In particular, detailed investigations were made on the system searching for an interplay between surface roughness with well-defined correlation function, (characterizes by asperity height and correlation length) spatial confinement and the dielectric function. We analyze to what extent the normal behavior and functionality of dielectric function of two-dimensional devices are modified by random scattering events caused by the contribution from the surface roughness. Results of the current work indicate that contribution of the surface roughness on scattering and absorption process could not be considered as an underestimating effect. We find, however, that functionality of the dielectric function seems to be quite independent of the particular roughness features.

In this study, the Optical conductivity of substitutionary doped graphene is investigated in presence of the Rashba spin orbit coupling (RSOC). Calculations have been performed within the coherent potential approximation (CPA) beyond the Dirac cone approximation. Results of the current study demonstrate that the optical conductivity is increased by increasing the RSOC strength. Meanwhile it was observed that the anisotropy of the band energy results in a considerable anisotropic optical conductivity (AOC) in monolayer graphene. The sign and magnitude of this anisotropic conductivity was shown to be controlled by the external field frequency. It was also shown that the Rashba interaction results in electron-hole asymmetry in monolayer graphene.

In the current work we have investigated the influence of the Rashba spin-orbit coupling on spin-current of a single layer gapped graphene. It was shown that the Rashba coupling has a considerable role in generation of the spin-current of vertical spins in mono-layer graphene. The behavior of the spin-current is determined by density of impurities. It was also shown that the spin-current of the system could increase by increasing the Rashba coupling strength and band-gap of the graphene and the sign of the spin-current could be controlled by the direction of the current-driving electric field.

We have studied spin-depend electron tunnelling through the Rashba barrier in a monolayer graphene lattice. The transfer matrix method, have been employed to obtain the spin dependent transport properties of the chiral particles. It is shown that graphene sheets in presence of Rashba spin-orbit barrier will act as an electron spin- inverter., Comment: 7 pages