Unconventional valley-dependent optical selection rules and landau level mixing in bilayer graphene

摘要

Illustration of the trigonal-warped BLG band structure with a bandgap Δ in the K valley. Evolution of Landau level energies calculated by a continuum model with Δ = 80 meV. We use red and green colors to label K and K′ valleys, respectively, throughout the paper. Solid and dashed arrows illustrate inter-LL transitions obeying the usual selection rule of Δ| | = ± 1. Photocurrent spectra with a displacement field of  = 0.874 Vm at  = 0, 2, and 4 T. The 0 T spectrum features two exciton peaks near the bandgap and a flat spectrum above the bandgap. Oscillations corresponding to inter-LL transitions emerge at 2 T with an alternated high-low pattern. The contrast between high and low peaks increases at 4 T, where splittings of peaks also appear. A 2D color plot of photocurrent spectra as the magnetic field is continuously tuned. Dashed curves trace high peaks in , which grow stronger towards higher magnetic fields and we label them by branch A-H (only branch A-D are shown in ). These strong transitions obey the usual optical selection rule of Δ | | = ± 1. The low peaks in evolve into weak transitions between dashed lines, whose optical selection rules will be discussed later.