Flat Bands in Slightly Twisted Bilayer Graphene (1012.4320v1)

Abstract: The bands of graphite are extremely sensitive to topological defects which modify the electronic structure. In this paper we found non-dispersive flat bands no farther than 10 meV of the Fermi energy in slightly twisted bilayer graphene as a signature of a transition from a parabolic dispersion of bilayer graphene to the characteristic linear dispersion of graphene. This transition occurs for relative rotation angles of layers around $1.5^o$ and is related to a process of layer decoupling. We have performed ab-initio calculations to develop a tight binding model with an interaction Hamiltonian between layers that includes the $\pi$ orbitals of all atoms and takes into account interactions up to third nearest-neighbors within a layer.

• The paper demonstrates that slight twists (~1.5°) induce flat electronic bands near the Fermi level, marking a transition in dispersion characteristics.
• It employs a tight-binding model with up to third nearest-neighbor interactions to replicate density functional theory results accurately.
• The study highlights that precise twist angle control in bilayer graphene can tailor electronic properties, paving the way for novel electronic device applications.

Flat Bands in Slightly Twisted Bilayer Graphene

The paper "Flat Bands in Slightly Twisted Bilayer Graphene" presents a detailed investigation into the electronic properties of bilayer graphene structures subjected to slight rotational misalignment between the layers. Utilizing both ab initio calculations and a parameterized tight-binding model, the authors explore the transition in electronic dispersion characteristics as a function of the twist angle.

Bilayer graphene (BLG), particularly with AB stacking, usually exhibits a quadratic dispersion relation, contrasting the linear dispersion seen in monolayer graphene. These differing band structures lead to distinct charge carrier dynamics, wherein the latter behaves as massless Dirac fermions. The paper focuses on how introducing a slight twist angle impacts the electronic properties, especially in close proximity to the Fermi level.

Key Findings

1. Transition in Electronic Dispersion: The researchers predict the presence of non-dispersive flat bands close to the Fermi energy for twist angles around 1.5 degrees. The transition from a parabolic to a linear band dispersion occurs within the range of 1 to 2 degrees. Notably, for angles between 2 to 10 degrees, there is a linear dispersion but with a renormalized Dirac fermion velocity.
2. Critical Angle and Flat Bands: A rapid flattening of the bands is documented when the twist angle is approximately 1.5 degrees. Around this critical angle, the energy separation between van Hove singularities reaches a minimum, indicating a significant alteration in electronic properties tied to the loss of a degree of freedom due to layer decoupling.
3. Model Development: The authors developed a tight-binding model to accommodate the complex unit cells that arise from commensurate twisting. The model includes interlayer interactions of π orbitals and considers up to third nearest-neighbors interactions within a layer, ensuring an accurate reproduction of band structure consistent with density functional theory (DFT) results.
4. Implications of Commensurable Rotations: By adopting a commensurable rotation approach based on predefined lattice vectors, the paper can explore the impact of stacking configurations, further validating the observed dispersion transitions across various twist angles.

Implications and Future Directions

The identification of flat bands in slightly twisted bilayer graphene at certain angles has substantive implications for potential applications and theoretical explorations. The presence of these flat bands suggests possibilities for tailoring electronic properties through precise angular control, which could have implications for novel electronic and optoelectronic devices. It also echoes the significance of extended van Hove singularities, known for their potential roles in phenomena like superconductivity.

From a theoretical perspective, the critical angle at which electronic transition occurs highlights an area for further investigation. The intersection of quantum confinement and layer decoupling presents a compelling playground for exploring new quantum mechanical behaviors in two-dimensional materials.

In culmination, this paper elucidates the delicate balance of interactions and structural nuances that dictate the electronic properties of bilayer graphene. Future research might extend upon this work by investigating the effects of additional factors such as strain, external fields, or other types of atomic alignment, contributing to the broader understanding and technological exploitation of two-dimensional materials.