Energy spectrum and Landau levels in bilayer graphene with spin-orbit interaction

Details Energy spectrum and Landau levels in bilayer graphene with spin-orbit interaction Energy spectrum and Landau levels in bilayer graphene with spin-orbit interaction

2012-03-06

arxiv.org/abs/1203.1094v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

23 pages, 5 figures

Scientific paper

We present a theoretical study of the bandstructure and Landau levels in bilayer graphene at low energies in the presence of a tranverse magnetic field and Rashba spin-orbit interaction. Within an effective low energy approach (L\"owdin partitioning theory) we derive an effective Hamiltonian for bilayer graphene that incorporates the influence of the Zeeman effect, the Rashba spin-orbit interaction, and inclusively, the role of the intrinsic spin-orbit interaction at the same footing. Particular attention is spent to the energy spectrum and Landau levels. Our modeling unveils the strong influence of the Rashba coupling $\lambda_R $ in the spin-splitting of the electron and hole bands. We found that graphene bilayer with weak Rashba spin-orbit interaction shows a spin-splitting linear in momentum and proportional to $\lambda_R $, but scales inversely proportional to the interlayer hopping energy $\gamma_1$. However at robust spin-orbit coupling $\lambda_R $ the energy spectrum shows a strong warping behavior near the Dirac points. We find the bias-induced gap in bilayer graphene to be decreasing with increasing Rashba coupling, a behavior resembling a topological insulator transition. We further predicted an unexpected assymetric spin-splitting and crossings of the Landau levels due to the interplay between the Rashba interaction and the external bias voltage. Our results are of relevance for interpreting magnetotransport and infrared cyclotron resonance measurements, including also situations of comparatively weak spin-orbit coupling.

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