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.

Deformations in graphene systems are central elements in the novel field of straintronics. Various strain geometries have been proposed to produce specific properties but their experimental realization has been limited. Because strained folds can be engineered on graphene samples on appropriate substrates, we study their effects on graphene transport properties. We show the existence of an enhanced local density of states (LDOS) along the direction of the strained fold that originates from localization of higher energy states, and provides extra conductance channels at lower energies. In addition to exhibit sublattice symmetry breaking, these states are valley polarized, with quasi-ballistic properties in smooth disorder potentials. We confirmed that these results persist in the presence of strong edge disorder, making these geometries viable electronic waveguides. These findings could be tested in properly engineered experimental settings.

The lack of some spatial symmetries in planar devices with Rashba spin-orbit interactions opens up the possibility of producing spin polarized electrical currents in the absence of external magnetic fields or magnetic impurities. We study how the direction of the spin polarization of the current is related to spatial symmetries of the device. As an example of these relations we study numerically the spin-resolved current in graphene nanoribbons. Different configurations are explored and analyzed to demonstrate that graphene nanoflakes may be used as excellent spintronic devices in an all-electrical setup.

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