We investigate the effects of Rashba spin-orbit (RSO) interactions on the electronic band-structure and corresponding wavefunctions of graphene. By exactly solving a tight-binding model Hamiltonian we obtain the expected splitting of the bands -due to the SU(2) spin symmetry breaking-that is accompanied by the appearance of additional Dirac points. These points are originated by valenceconduction band crossings. By introducing a convenient gauge transformation we study a model for zigzag nanoribbons with RSO interactions. We show that RSO interactions lift the quasi-degeneracy of the edge band while introducing a state-dependent spin separation in real space. Calculation of the average magnetization perpendicular to the ribbon plane suggest that RSO could be used to produce spin-polarized currents. Comparisons with the intrinsic spin-orbit (I-SO) interaction proposed to exist in graphene are also presented.

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One of the intriguing characteristics of honeycomb lattices is the appearance of a pseudomagnetic field as a result of mechanical deformation. In the case of graphene, the Landau quantization resulting from this pseudomagnetic field has been measured using scanning tunneling microscopy. Here we show that a signature of the pseudomagnetic field is a local sublattice symmetry breaking observable as a redistribution of the local density of states. This can be interpreted as a polarization of graphene's pseudospin due to a strain induced pseudomagnetic field, in analogy to the alignment of a real spin in a magnetic field. We reveal this sublattice symmetry breaking by tunably straining graphene using the tip of a scanning tunneling microscope. The tip locally lifts the graphene membrane from a SiO support, as visible by an increased slope of the I(z) curves. The amount of lifting is consistent with molecular dynamics calculations, which reveal a deformed graphene area under the tip in the shape of a Gaussian. The pseudomagnetic field induced by the deformation becomes visible as a sublattice symmetry breaking which scales with the lifting height of the strained deformation and therefore with the pseudomagnetic field strength. Its magnitude is quantitatively reproduced by analytic and tight-binding models, revealing fields of 1000 T. These results might be the starting point for an effective THz valley filter, as a basic element of valleytronics.

The coupling of geometrical and electronic properties is a promising venue to engineer conduction properties in graphene. Confinement added to strain allows for interplay of different transport mechanisms with potential device applications. To investigate strain signatures on transport in confined geometries, we focus on graphene nanoribbons (GNR) with circularly symmetric deformations. In particular, we study GNR with an inhomogeneous, out of plane Gaussian deformation, connected to reservoirs. We observe an enhancement of the density of states in the deformed region, accompanied with a decrease in the conductance, signaling the presence of confined states. The local density of states exhibits a six-fold symmetric structure with an oscillating sub-lattice occupation asymmetry, that persist for a wide range of energy and model parameters.

We study a one-orbital Anderson impurity in a two-dimensional electron bath with Rashba spin-orbit interactions in the Kondo regime. The spin SU(2) symmetry breaking term couples the impurity to a two-band electron gas. A Schrieffer-Wolff transformation shows the existence of the Dzyaloshinsky-Moriya (DM) interaction away from the particle-hole symmetric impurity state. A renormalization group analysis reveals a two-channel Kondo model with ferro-and antiferromagnetic couplings. The parity breaking DM term renormalizes the antiferromagnetic Kondo coupling with an exponential enhancement of the Kondo temperature.