Proximity effects resulting from depositing a graphene layer on a TMD substrate layer change the dynamics of the electronic states in graphene, inducing spin orbit coupling (SOC) and staggered potential effects. An effective Hamiltonian that describes different symmetry breaking terms in graphene, while preserving time reversal invariance, shows that an inverted mass band gap regime is possible. The competition of different perturbation terms causes a transition from an inverted mass phase to a staggered gap in the bilayer heterostructure, as seen in its phase diagram. A tight-binding calculation of the bilayer validates the effective model parameters. A relative gate voltage between the layers may produce such phase transition in experimentally accessible systems. The phases are characterized in terms of Berry curvature and valley Chern numbers, demonstrating that the system may exhibit quantum spin Hall and valley Hall effects.Comment: 5 pages, 4 figure

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...

Electron optics exploits the analogies between rays in geometrical optics and electron trajectories, leading to interesting insights and potential applications. Graphene, with its two-dimensionality and photon-like behavior of its charge carriers, is the perfect candidate for the exploitation of electron optics. We show that a circular gate-or doping-controlled region in the presence of Rashba spinorbit interaction in graphene may indeed behave as a Veselago electronic lens but with two different indices of refraction. We demonstrate that this birefringence results in complex caustics patterns for a circular gate, selective focusing of different spins, and the possible direct measurement of the Rashba coupling strength in scanning probe experiments.PACS numbers: 71.70. Ej, 75.76.+j, 72.10.Fk, 42.25.Lc The analogies between geometrical optics and electron trajectories have resulted in a number of interesting proposals for device applications [1], where interfaces play a similar role to that played by transparent interfaces in physical optics. This leads to the manipulation and control of electron trajectories, where the major factor determining the electron dynamics is the change in group velocity through these interfaces, mimicking refringent physical optics and lenses. Such change in group velocity is typically achieved by local gating, which modulates carrier densities and fixes the corresponding index of refraction.Optical birefringence in materials results from crystal anisotropies which are manifested as different group velocities for different polarizations of the propagating light in the material. In this paper, we show that an equivalent phenomenon to optical birefringence in electron optics is feasible in two dimensional graphene, which in essence reflects the intrinsic crystal structure even at large electronic wavelengths. The effect requires the presence of Rashba spin-orbit interaction, where the different group velocities depend on the chirality of the electronic states, mimicking the light polarization dependence of the group velocities in optical birefringent materials.The low energy dispersion of electrons in graphene is centered near two inequivalent points in the Brillouin zone, the K and K or Dirac points [2][3][4]. The "massless" nature of electrons results in novel phenomena such as the Klein paradox [3,5,6], which leads to full transparency of a sharp gated interface for normal incident electrons, and a high probability of transmission for incoming electrons with finite angles. The linear dispersion of electrons is also evocative of photons, prompting a number of proposals and experiments to probe optical analogs with charge carriers [7], aided in great measure by the high electron mobility in this unique material. In fact, the transparency of barriers and ability to gate regions of the system to change the sign of carriers can lead to the use of graphene gate-controlled interfaces as electronic lenses that follow Snell's law with negative index of refraction and allow the implementatio...

The perfect transmission of charge carriers through potential barriers in graphene (Klein tunneling) is a direct consequence of the Dirac equation that governs the low-energy carrier dynamics. As a result, localized states do not exist in unpatterned graphene, but quasibound states can occur for potentials with closed integrable dynamics. Here, we report the observation of resonance states in photoswitchable self-assembled molecular(SAM)-graphene hybrid. Conductive AFM measurements performed at room temperature reveal strong current resonances, the strength of which can be reversibly gated on- and off- by optically switching the molecular conformation of the mSAM. Comparisons of the voltage separation between current resonances (∼ 70-120 mV) with solutions of the Dirac equation indicate that the radius of the gating potential is ∼ 7 ± 2 nm with a strength ≥ 0.5 eV. Our results and methods might provide a route toward optically programmable carrier dynamics and transport in graphene nanomaterials.

The decoration of graphene samples with adatoms or nanoparticles leads to the enhancement of spin-orbit interactions as well as to the introduction of symmetry breaking effects that could have drastic effects on spin and electronic transport phenomena. We present an analysis based on symmetry considerations and examine the impact on the scattering matrix for graphene systems containing defects that enhance spin-orbit interactions, while conserving the electronic total angular momentum. We show that the appearance and dominance of skew scattering, and the related observation of valley and/or spin Hall effect in decorated graphene samples, suggests the set of symmetries that adatom perturbations should satisfy. We further show that detailed measurements of the transport and elastic times as function of carrier concentration make it possible to not only extract the strength of the spin-orbit interaction, as suggested before, but also obtain the amplitude of the symmetry breaking terms introduced. To examine how different terms would affect measurements, we also present calculations for typical random distributions of impurities with different perturbations, illustrating the detailed energy dependence of different observables.

We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as function of both the film thickness and the momentum in the plane of the film for Bi2Se3 and Bi2Te3. As a result, while the magnitude of the matrix element at the center of the surface Brillouin Zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and non-topological phases, separated by semimetallic states, as the film thickness varies. In the topological phase the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi2Se3, making Bi2Te3, where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators. arXiv:1801.02084v1 [cond-mat.mes-hall]

Depositing monolayer graphene on a transition metal dichalcogenide (TMD) semiconductor substrate has been shown to change the dynamics of the electronic states in graphene, inducing spin orbit coupling (SOC) and staggered potential effects. Theoretical studies on commensurate supercells have demonstrated the appearance of interesting phases, as different materials and relative gate voltages are applied. Here we address the effects of the real incommensurability between lattices by implementing a continuum model approach that does not require small-period supercells. The approach allows us to study the role of possible relative twists of the layers, and verify that the SOC transfer is robust to twists, in agreement with observations. We characterize the nature of the different phases by studying an effective Hamiltonian that fully describes the graphene-TMD heterostructure. We find the system supports topologically non-trivial phases over a wide range of parameter ranges, which require the dominance of the intrinsic SOC over the staggered and Rashba potentials. This tantalizing result suggests the possible experimental realization of a tunable quantum spin Hall phase under suitable conditions. We estimate that most TMDs used to date likely result in weak intrinsic SOC that would not drive the heterostructure into topologically non-trivial phases. Additional means to induce a larger intrinsic SOC, such as strain fields or heavy metal intercalation may be required.

We demonstrate that the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction in graphene can be strongly modified by a time-periodic driving field even in the weak drive regime. This effect is due to the opening of a dynamical band gap at the Dirac points when graphene is exposed to circularly polarized light. Using Keldysh-Floquet Green's functions, we develop a theoretical framework to calculate the time-averaged RKKY coupling under weak periodic drives, and we show that its magnitude in undoped graphene can be decreased controllably by increasing the driving strength, while mostly maintaining its ferromagnetic or antiferromagnetic character. In doped graphene, we find RKKY oscillations with a period that is tunable by the driving field. When a sufficiently strong drive is turned on that brings the Fermi level completely within the dynamically opened gap, the behavior of the RKKY coupling changes qualitatively from that of doped to undoped irradiated graphene.