Landau quantization and Fermi velocity renormalization in twisted graphene bilayers

Abstract

Currently there is a lively discussion concerning Fermi velocity renormalization in twisted bilayers and several contradicted experimental results are reported.Here we study electronic structures of the twisted bilayers by scanning tunneling microscopy (STM) and spectroscopy (STS). The interlayer coupling strengths between the adjacent bilayers are measured according to energy separations of two pronounced low-energy van Hove singularities (VHSs) in the STS spectra.We demonstrate that there is a large range of values for the interlayer interaction in different twisted bilayers. Below the VHSs, the observed Landau quantization in the twisted bilayers is identical to that of massless Dirac fermions in graphene monolayer, which allows us to measure the Fermi velocity directly. Our result indicates that the Fermi velocity of the twisted bilayers depends remarkably on both the twisted angles and the interlayer coupling strengths.This removes the discrepancy about the Fermi velocity renormalization in the twisted bilayers and provides a consistent interpretation of all current data.

Structure of twisted and buckled bilayer graphene

“…In particular, it has been theoretically suggested that the twist in the BLG may lead to a renormalization of the Fermi velocity [17], possible appearance of the flat electronic bands [18], neutrino-like oscillation of Dirac fermions [19] as well as localization of electrons [20]. Moreover, TBLG when placed in a magnetic field, exhibits a fractal spectrum of the Landau levels [21].…”

Experimental evidence for non-Abelian gauge potentials in twisted graphene bilayers

“…3a. Consequently, it is expected to observe Landau quantization of massless Dirac fermions in twisted bilayers with larger rotation angles 16,28 . This is demonstrated explicitly in our experiment, where the observed Landau levels sequence in the 3.1° bilayer, as shown in Fig.…”

Landau quantization of Dirac fermions in graphene and its multilayers

“…• ), the twisted bilayers behave as two decoupled single-layer graphene sheets with a Fermi velocity of v F ≈ 1.1 × 10 6 m/s [181,182]. At a small rotation angle (θ < 6…”

“…• ), the electronic states near the Dirac cones of two layers couple with a reduced interlayer hopping amplitude of t θ ≈ 0.4t ⊥ (t ⊥ is the interlayer hopping for AB-stacked layers) [179,182,193]. As a result, the two Dirac cones intersect and hybridize at the energy of ± v F ∆K, generating two saddle points in the energy bands [ Fig.…”