Valley symmetry breaking and gap tuning in graphene by spin doping

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.

Emergent Chern-Simons excitations due to electron-phonon interaction

“…Higher order terms are negligible, as the analysis of the conductivity tensor for the full Haldane model in Ref. [28] has shown. Performing a gradient expansion up to second order in the momenta, cf.…”

“…The parity between the cones is broken by exposing the system to the chemical modification, e.g. by a periodic flux [27] or a spin texture [28]. Combining fermionic operators to spinors…”

“…where t ′ is the hopping amplitude between second nearest neighbors (t ′ /t ∼ 0.1 [2]) and the matrix element of the Haldane term is given by [27,28] …”

Optical Hall conductivity of systems with gapped spectral nodes

“…Such a periodic flux can be generated by a spin texture, realized by spin doping of graphene [6]. The main effect of the periodic flux is that the mass terms in the two valleys can be tuned independently.…”

“…The main effect of the periodic flux is that the mass terms in the two valleys can be tuned independently. Then the QHE appears when the mass signs in the two valleys are different because the Hall conductivity reads [6] …”