Angle Dependent Van Hove Singularities in Slightly Twisted Graphene Bilayer

TL;DR

This study investigates how the energy difference between Van Hove singularities in slightly twisted graphene bilayers depends on the twist angle, revealing unexpected deviations from theoretical predictions and providing insights into electronic properties.

Contribution

It provides experimental evidence of angle-dependent Van Hove singularities in twisted graphene bilayers and challenges existing band structure predictions regarding Fermi velocity reduction.

Findings

Energy difference vhs follows vhs   \u2206K between 1.0b0 and 3.0b0

Fermi velocity remains largely unchanged with twist angle, contrary to predictions

At .3b0, vhs is significantly less than expected, indicating a reduction in Van Hove singularity energy separation

Abstract

Recent studies show that two low-energy Van Hove singularities (VHSs) seen as two pronounced peaks in the density of states (DOS) could be induced in twisted graphene bilayer. Here, we report angle dependent VHSs of slightly twisted graphene bilayer studied by scanning tunneling microscopy and spectroscopy. We show that energy difference of the two VHSs follows \DeltaEvhs ~ \hbar{\nu}F\DeltaK between 1.0^{\circ} and 3.0^{\circ} (here {\nu}F ~ 1.1\times106 m/s is the Fermi velocity of monolayer graphene, \DeltaK = 2Ksin(\theta/2) is the shift between the corresponding Dirac points of the twisted graphene bilayer). This result indicates that the rotation angle between graphene sheets not results in significant reduction of the Fermi velocity, which quite differs from that predicted by band structure calculations. However, around a twisted angle \theta ~ 1.3^{\circ}, the observed \DeltaEvhs ~ 0.11 eV is much less than the expected value \hbar{\nu}F\DeltaK ~ 0.28 eV at 1.3^{\circ}. The origin of the reduction of \DeltaEvhs at 1.3^{\circ} is discussed.