Electronic Properties of Twisted Trilayer Graphene

TL;DR

This paper investigates the electronic properties of twisted trilayer graphene with mixed stacking, revealing angle-dependent band gaps and Dirac cone shifts, and introduces an effective Hamiltonian model for these phenomena.

Contribution

It provides a detailed analysis of the electronic spectrum in twisted trilayer graphene with Bernal stacking, including a new effective Hamiltonian model for low-energy properties.

Findings

Gap in parabolic bands increases as twist angle decreases

Shift in Dirac cone depends on twist angle

Effective Hamiltonian accurately describes low-energy electronic behavior

Abstract

We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twisted-like Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twisted-like Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated twisted bilayer, which is due to the loss of electron-hole symmetry caused by sublattice mixing in the rotated geometry. Using a tight-binding and a continuum model, we derive an effective Hamiltonian which accounts for the relevant low-energy properties of this system.