Fig. 1: Topologically-protected states in bilayer graphene.
From: Interplay between topological valley and quantum Hall edge transport
a, b Atomic force microscopy image (a) and scattering-type scanning near-field microscopy image (b) of a bilayer graphene flake, with high-resolution zoom-in scans on the right. The scale bars are 0.5 μm. c Freestanding dually gated bilayer graphene devices schematically shown with (left) and without domain wall (right) connecting the contacts. Topological valley transport along the domain wall is shown in blue and red in the \({{{{{\rm{K}}}}}}\)- and \({{{{{\rm{K}}}}}}{^\prime}\)-valley, respectively. d, e Resistance map as a function of top and bottom gate voltage for device D1-DW (d with domain wall) and D2 (e without domain wall). Insets: Electronic band structure of bilayer graphene with (d) and without a domain wall (e) for an applied electric field. ∆ is the electric field induced bandgap, EF the Fermi level and the blue (red) lines indicate topologically protected, doubly spin degenerate chiral states in the \({{{{{\rm{K}}}}}}\)(\({{{{{\rm{K}}}}}}{^\prime}\))-valley. f, g Trace of the resistance as a function of Vb for various Vt with steps of 1 V shown for device D1-DW (f) and D2 (g). The dashed lines indicate the envelope of the resistance and are a guide to the eye.
