Dynamical conductivity of gated AA-stacking multilayer graphene with spin-orbital coupling (original) (raw)

Magnetic Field-Controlled Electrical Conductivity in AA Bilayer Graphene

C

We consider the effect of the external magnetic field on the in-plane conductivity in the AA-stacked bilayer graphene system in the strong excitonic condensate regime. We include the effects of the applied inter-layer electric field and the Coulomb interactions. The on-site and inter-layer Coulomb interactions were treated via the bilayer Hubbard model. Using the solutions for the physical parameters in the system, we calculate the in-plane conductivity of the bilayer graphene. By employing the Green-Kubo formalism for the polarization function in the system, we show that the conductivity in the AA bilayer system is fully controlled by the applied magnetic field. For the partial filling in the layers, the electrical conductivity is different for different spin orientations, and, at the high values of the magnetic field, only one component remains with the given spin orientation. Meanwhile, for the half-filling limit, there is no spin-splitting observed in the conductivity function. ...

Study of edge states and conductivity in spin-orbit coupled bilayer graphene

The European Physical Journal B, 2019

We present an elaborate and systematic study of the conductance properties of a zigzag bilayer graphene nanoribbon modeled by a Kane-Mele (KM) Hamiltonian. The interplay of the Rashba and the intrinsic spin-orbit couplings with the edge states, electronic band structures, charge and spin transport are explored in details. We have analytically derived the conditions for the edge states for a bilayer KM nanoribbon and show how these modes decay for lattice sites inside the bulk. It is particularly interesting to note that for a finite-size ribbon an even number of zigzag ribbon hosts a finite energy gap at the Dirac points, while the odd ones do not. This asymmetry is present both in presence and absence of a bias voltage that may exist between the layers. The interlayer Rashba spin-orbit coupling, along with the intralayer intrinsic spin-orbit and intralayer Rashba spin-orbit couplings seem to destroy the quantum spin Hall (QSH) phase where the QSH phase is identified by the presence of a conductance plateau (of magnitude 4e 2 /h) in the vicinity of zero Fermi energy. The plateau is sensitive to the values of the spin-orbit coupling parameters. Further, the spin polarized conductance data reveal that a bilayer KM ribbon is found to be more efficient for spintronic applications compared to a monolayer graphene. Finally, a quick check with experiments is done via computing the effective mass of electrons.

Features due to spin-orbit coupling in the optical conductivity of single-layer graphene

Physical Review B, 2010

We have calculated the optical conductivity of a disorder-free single graphene sheet in the presence of spin-orbit coupling, using the Kubo formalism. Both intrinsic and structural-inversion-asymmetry induced types of spin splitting are considered within a low-energy continuum theory. Analytical results are obtained that allow us to identify distinct features arising from spin-orbit couplings. We point out how optical-conductivity measurements could offer a way to determine the strengths of spin splitting due to various origins in graphene.

Electronic transport and Klein tunneling in gapped AA-stacked bilayer graphene

Journal of Applied Physics

We demonstrate that AA-stacked bilayer graphene (AA-BLG) encapsulated by dielectric materials can possess an energy gap due to the induced mass term. Using the four-band continuum model, we evaluate transmission and reflection probabilities along with the respective conductances. Considering interlayer mass-term difference opens a gap in the energy spectrum and also couples the two Dirac cones. This cone coupling induces an inter-cone transport that is asymmetric with respect to the normal incidence in the presence of asymmetric mass-term. The energy spectrum of the gapped AA-BLG exhibits electron-hole asymmetry that is reflected in the associated intraand inter-cone channels. We also find that even though Klein tunneling exists in gated and biased AA-BLG, it is precluded by the interlayer mass-term difference and instead Febry-Pérot resonances appear.

Charge-spin interconversion in graphene-based systems from density functional theory

Physical Review B

We present a methodology to address, from first principles, charge-spin interconversion in two-dimensional materials with spin-orbit coupling. Our study relies on an implementation of density functional theory based quantum transport formalism adapted to such purpose. We show how an analysis of the k-resolved spin polarization gives the necessary insight to understand the different charge-spin interconversion mechanisms. We have tested it in the simplest scenario of isolated graphene in a perpendicular electric field where effective tight-binding models are available to compare with. Our results show that the flow of an unpolarized current across a single layer of graphene produces, as expected, a spin separation perpendicular to the current for two of the three spin components (out-of-plane and longitudinal), which is the signature of the spin Hall effect. Additionally, it also yields an overall spin accumulation for the third spin component (perpendicular to the current), which is the signature of the Rashba-Edelstein effect. Even in this simple example, our results reveal an unexpected competition between the Rashba and the intrinsic spin-orbit coupling. Remarkably, the sign of the accumulated spin density does not depend on the electron or hole nature of the injected current for realistic values of the Rashba coupling.

Tight-Binding Model Study of Anti-ferromagnetic Order in AA-Stacked Bi-layer Graphene

Journal of Superconductivity and Novel Magnetism, 2017

We address here the anti-ferromagnetic order present in AA-stacked bi-layer graphene in a transversely applied electric field. The system is described by kinetic energy with nearest-neighbor electron hopping with same hopping integral t 1 for both the layers. Besides this, Coulomb interaction exists at A and B sub-lattices with same Coulomb correlation energy. The electron Green's functions are calculated by Zubarev's Green's technique. The temperature-dependent anti-ferromagnetic magnetization is calculated from the Green's function and is computed numerically and self-consistently. The strong on-site Coulomb interaction stabilizes the anti-ferromagnetic order in graphene. We assume that the electron spin at A site in the first layer is directed in the opposite direction to that of A site electron in the second layer. Similar spin order is observed for electrons in B site atom in reversed order. It is observed that anti-ferromagnetic (AFM) magnetization in the first layer nearly remains constant up to certain temperature and then increases with temperature, while the AFM magnetization in the second layer remains nearly constant and then rapidly decreases with temperature. The net AFM magnetization in bi-layer graphene remains constant and then rapidly increases with temperature. The evolution G. C.

Comparison between charge and spin transport in few-layer graphene

Physical Review B, 2011

Transport measurements on few layer graphene (FLG) are important because they interpolate between the properties of single layer graphene (SLG) as a true 2-dimensional material and the 3-dimensional bulk properties of graphite. In this article we present 4-probe local charge transport and non-local spin valve and spin precession measurements on lateral spin field-effect transistors (FET) on FLG. We study systematically the charge and spin transport properties depending on the number of layers and the electrical back gating of the device. We explain the charge transport measurements by taking the screening of scattering potentials into account and use the results to understand the spin data. The measured samples are between 3 and 20 layers thick, and we include in our analysis our earlier results of the measurements on SLG for comparison. In our room temperature spin transport measurements we manage to observe spin signals over distances up to 10 µm and measure enhanced spin-relaxation times with an increasing number of layers, reaching τs ∼ 500 ps as a maximum, about 4 times higher than in SLG. The increase of τs can result from the screening of scattering potentials due to additional intrinsic charge carriers in FLG. We calculate the density of states (DOS) of FLG using a zone-folding scheme to determine the charge diffusion coefficient DC from the square resistance RS. The resulting DC and the spin-diffusion coefficient DS show similar values and depend only weakly on the number of layers and gate induced charge carriers. We discuss the implications of this on the identification of the spin-relaxation mechanism.

Spin-Orbit Interaction and Isotropic Electronic Transport in Graphene

Physical Review Letters, 2014

Broken symmetries in graphene affect the massless nature of its charge carriers. We present an analysis of scattering by defects in graphene in the presence of spin-orbit interactions (SOIs). A characteristic constant ratio ( 2) of the transport to elastic times for massless electrons signals the anisotropy of the scattering. We show that SOIs lead to a drastic decrease of this ratio, especially at low carrier concentrations, while the scattering becomes increasingly isotropic. As the strength of the SOI determines the energy (carrier concentration) where this drop is more evident, this effect could help evaluate these interactions through transport measurements.

Intrinsic and Rashba spin-orbit interactions in graphene sheets

Physical Review B, 2006

Starting from a microscopic tight-binding model and using second order perturbation theory, we derive explicit expressions for the intrinsic and Rashba spin-orbit interaction induced gaps in the Dirac-like low-energy band structure of an isolated graphene sheet. The Rashba interaction parameter is first order in the atomic carbon spin-orbit coupling strength ξ and first order in the external electric field E perpendicular to the graphene plane, whereas the intrinsic spin-orbit interaction which survives at E = 0 is second order in ξ. The spin-orbit terms in the low-energy effective Hamiltonian have the form proposed recently by Kane and Mele. Ab initio electronic structure calculations were performed as a partial check on the validity of the tight-binding model.