A primer on twistronics: A massless Dirac fermion's journey to moir\'{e} patterns and flat bands in twisted bilayer graphene

TL;DR

This paper provides a comprehensive, pedagogical overview of the evolution of graphene's electronic properties from Dirac fermions to the emergence of flat bands in twisted bilayer graphene, highlighting theoretical insights and experimental correlations.

Contribution

It offers a self-contained, theoretical perspective on the transition from single-particle physics to strongly-correlated phenomena in twisted bilayer graphene, connecting foundational concepts to recent discoveries.

Findings

Explanation of Dirac points and superlattice effects in graphene

Analysis of moiré patterns and their influence on electronic properties

Discussion of the origin and significance of flat bands at magic angles

Abstract

The recent discovery of superconductivity in magic-angle twisted bilayer graphene has sparked a renewed interest in the strongly-correlated physics of $sp^2$ carbons, in stark contrast to preliminary investigations which were dominated by the one-body physics of the massless Dirac fermions. We thus provide a self-contained, theoretical perspective of the journey of graphene from its single-particle physics-dominated regime to the strongly-correlated physics of the flat bands. Beginning from the origin of the Dirac points in condensed matter systems, we discuss the effect of the superlattice on the Fermi velocity and Van Hove singularities in graphene and how it leads naturally to investigations of the moir\'{e} pattern in van der Waals heterostructures exemplified by graphene-hexagonal boron-nitride and twisted bilayer graphene. Subsequently, we illuminate the origin of flat bands in twisted bilayer graphene at the magic angles by elaborating on a broad range of prominent theoretical works in a pedagogical way while linking them to available experimental support, where appropriate. We conclude by providing a list of topics in the study of the electronic properties of twisted bilayer graphene not covered by this review but may readily be approached with the help of this primer.