Spin-Orbit Interaction and Isotropic Electronic Transport in Graphene

Abstract

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.PACS numbers: 72.10. Fk, 75.76.+j, 72.80.Vp, 03.65.Pm The discovery of graphene has stimulated numerous theoretical and experimental works [1], opening new doors for promising new technology due to its low dimensionality and high carrier mobility. The low energy electron dynamics is described by two inequivalent points at the Brillouin zone (K and K ) known as Dirac points, since the linear dispersion is equivalent to twodimensional massless Dirac fermions [2,3].The importance of graphene on transport devices also motivates the identification and understanding of spin dynamics [4], as an important element in the development of spintronics. In graphene, interface or bulk broken symmetries allow for the existence of two kinds of spin orbit interaction (SOIs) that affect spin dynamics in different ways [5]. The hexagonal arrangement of carbon atoms allows an intrinsic SOI that respects lattice symmetries and can be seen to arise from the atomic SO coupling. This generates a gap in the spectrum, a mass term in the Dirac equation with sign depending on the spin, pseudospin and Dirac valley [6,7]. An inversion asymmetry in graphene could also generate an extrinsic Rashba SOI, resulting from the effect of substrates, impurities generating sp 3 distortions-such as hydrogen, fluorine or gold-perpendicular electric fields, or lattice corrugations [8][9][10][11][12][13]. Intercalation of gold under graphene deposited on nickel substrates results in very large Rashba interactions [13], while a large enhancement was observed in weakly hydrogenated samples [14]. In addition, recent theoretical studies have shown that decoration of graphene with heavy atoms such as indium and thallium will result in the enhancement of an intrinsic-like SOI in graphene and the associated quantum spin Hall state [15].Adsorbed impurities [16,17], as well as lattice vacancies and other local defects in the lattice [18] provide natural short-range scattering centers known as resonant scatterers. Sources of resonant scatterers are also organic groups [19], clusters of impurities [20], or even artificially controlled metallic islands deposited on the surface of graphene [21]. Extensive work has identified the existence of resonant scatterers as the main mechanism limiting carrier mobility in graphene samples [19,22,23]. These conclusions are supported by the insensitivity to screening effe...

Mass inversion in graphene by proximity to dichalcogenide monolayer

“…σ i acts on the pseudospin sublattice space (A,B), τ i on the K, K valley space, and s i on the spin [31]. We use the 'standard' basis…”

“…The proximity of the TMD monolayer to graphene breaks inversion sym-metry, which allows for the presence of Rashba SOC, in addition to sublattice asymmetry terms in the effective Hamiltonian [31]. A minimal low energy model will include terms that respect time reversal symmetry [23,32], and arise due to the symmetries in the TMD states,…”

Quantum Transport in Graphene: Impurity Scattering as a Probe of the Dirac Spectrum

“…However whereas the configuration of diluted atoms has been investigated in detail, the more realistic situation where atoms form clusters or islands on graphene still needs to be investigated theoretically. It was recently suggested [43] that measuring the ratio τ tr /τ e as discussed in section 1 can provide information on the amplitude of the spin orbit coupling. Asmar and Uloa have shown that SOI leads to an important transformation of short range scattering low energy processes in graphene from highly anisotropic (zero back scattering) to more or fully isotropic, depending on the strength of these interactions.…”

“…On can see that an angular dependence is recovered at large spin orbit coupling which indicates that intravalley back scattering is not forbidden anymore. Inset: evolution of the ratio τ tr /τ e , which varies between 2 to 1 (from [43]). …”

Revival resonant scattering, perfect caustics, and isotropic transport of pseudospin-1 particles

“…To address this question in the simplest possible setting while retaining the essential physics, we study ballistic wave scattering against a circularly symmetric potential barrier. We note that for conventional Dirac cone systems with pseudospin or spin-1/2 quasiparticles, there has been extensive work on scattering [51][52][53] with phenomena such as caustics 54 , Mie scattering resonance 55 , birefringent lens 56 , cloaking 57 , spin-orbit interaction induced isotropic transport and skew scattering 58,59 , and electron whispering gallery modes 60 . To our best knowledge, prior to our work there were no corresponding studies for pseudospin-1 Dirac cone systems.…”