# Twisted bilayer graphene: low-energy physics, electronic and optical properties

## TL;DR

This paper reviews the low-energy physics, electronic, and optical properties of twisted bilayer graphene, highlighting how layer misalignment influences electronic structure and optical responses, with a focus on small-angle rotations.

## Contribution

It provides a pedagogical overview of the theoretical framework for van der Waals heterostructures, specifically applying it to twisted bilayer graphene to analyze angle-dependent electronic and optical phenomena.

## Key findings

- Fermi velocity renormalization depends on twist angle
- Low-energy van Hove singularities emerge at specific angles
- Optical conductivity and surface plasmon-polaritons are characterized

## Abstract

Van der Waals (vdW) heterostructures ---formed by stacking or growing two-dimensional (2D) crystals on top of each other--- have emerged as a new promising route to tailor and engineer the properties of 2D materials. Twisted bilayer graphene (tBLG), a simple vdW structure where the interference between two misaligned graphene lattices leads to the formation of a moir\'e pattern, is a test bed to study the effects of the interaction and misalignment between layers, key players for determining the electronic properties of these stackings. In this chapter, we present in a pedagogical way the general theory used to describe lattice mismatched and misaligned vdW structures. We apply it to the study of tBLG in the limit of small rotations and see how the coupling between the two layers leads both to an angle dependent renormalization of graphene's Fermi velocity and appearance of low-energy van Hove singularities. The optical response of this system is then addressed by computing the optical conductivity and the dispersion relation of tBLG surface plasmon-polaritons.