Abstract
We study graphene with an adsorbed spin texture, where the localized spins create a periodic magnetic flux. The latter produces gaps in the graphene spectrum and breaks the valley symmetry. The resulting effective electronic model, which is similar to Haldane's periodic flux model, allows us to tune the gap of one valley independently from that of the other valley. This leads to the formation of two Hall plateaux and a quantum Hall transition. We discuss the density of states, optical longitudinal and Hall conductivities for nonzero frequencies and nonzero temperatures. A robust logarithmic singularity appears in the Hall conductivity when the frequency of the external field agrees with the width of the gap.
Highlights
Transport properties of neutral graphene are characterized by a semimetallic behavior with a point-like Fermi surface at two valleys
Chemical doping is an interesting direction for modifying graphene because it leads to a rich field with new properties
We focus on φ = −π/4 and compare the results with gapless graphene (M = t = 0) and with graphene with uniform gap (M = 0, t = 0)
Summary
Transport properties of neutral graphene are characterized by a semimetallic behavior with a point-like Fermi surface at two valleys. We propose a model that is based on a honeycomb lattice, where one sublattice is occupied by localized spins This leads to an effective hopping parameter with a Berry phase and reflects the equivalence of the spin texture with an effective periodic magnetic flux in the tight-binding model. The inter-valley symmetry is lifted by introducing only a next-nearest-neighbor hopping on one sublattice and a staggered magnetic flux This choice is motivated by the fact that graphene on a substrate can adsorb atoms only on one side. It is known that such spin structures provide an effective Berry phase for the electron hopping rate [27]–[29] The latter has the same effect as a periodic (staggered) flux, where the flux depends on the tilting angle of the localized spins (figures 1 and 2)
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