Local versus extended deformed graphene geometries for valley filtering

The existence of two inequivalent valleys in the band structure of graphene has motivated the search of mechanisms that allow their separation and control for potential device applications. Among the several schemes proposed in the literature, strain-induced out-of-plane deformations (occurring naturally or intentionally designed in graphene samples), ranks among the best candidates to produce separation of valley currents. Because the valley filtering properties in these structures are, however, highly dependent on the type of deformation and setups considered, it is important to identify the relevant factors determining optimal operation and detection of valley currents. In this paper, we present a comprehensive comparison of two typical deformations commonly found in graphene samples: local centrosymmetric bubbles and extended folds/wrinkles. Using the Dirac model for graphene and the second-order Born approximation, we characterize the scattering properties of the bubble deformation, while numerical transmission matrix methods are used for the foldlike deformations. In both cases, we obtain the dependence of valley polarization on the geometrical parameters of deformations and discuss their possible experimental realizations. Our study reveals that extended deformations act as better valley filters in broader energy ranges and present more robust features against variations of geometrical parameters and incident current directions.