Landau level properties of two prototypical bilayer graphenes 邱裕煌，何彥宏，林明發 成功大學 物理系 Introduction Tight-binding Model Results and Discussions Conclusions 1/33

hybridization of atomic orbitals 2/33

various dimensionality 3/33

achievement of few-layered sheets Mechanical exfoliation of highly oriented pyrolytic graphite Science 306, 666 (2004) Epitaxial growth on silicon carbide Science 312,1191 (2006) 4/33

stacking consequence AA Simple hexagonal stacking Bernal stacking 5/33

low-energy bands: monolayer & bilayer Science 313, 951 (2007) 6/33

angle-resolved photoelectron spectroscopy (ARPES) 7/33

Landau quantization 2DEG 8/33

experimental observation of Landau levels in graphene 1. Quantum Hall conductivity 2. Scanning tunneling spectroscopy 3. Magnetooptical transmission (excitations between Landau levels) Nature 438, 197 (2005) Nat. Phys. 3, 623 (2007) PRL 97, 266405 (2006) 9/33

Tight-binding model Phys. Rev. 109, 272 (1958) monolayer graphene γ0 bilayer Bernal graphene γ0 γ4 γ1 γ3 γ6 10/33

zero-gap semiconductor semimetal

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Monolayer graphene

γ0 13/33

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Optical absorption function Velocity matrix element 18/33

Monolayer

AB-bilayer

AB-bilayer Selection rules

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Selection rules

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Conclusions: Two prototypes of bilayer graphenes, AA- and AB-stacking bilayer graphenes, exhibit different Landau level spectra, which reflect the fact that the magneto-electronic properties strongly depend on the stacking configurations. The Landau wave functions of AA- and AB-stacking bilayer graphenes show dissimilar features and the dissimilarities are reflected in the magneto-optical absorption spectra, such as the distinct selection rules and different field-dependent absorption frequencies. 33/33

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