A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene

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A primer on twistronics: A massless Dirac fermion's journey to moiré patterns and flat bands in twisted bilayer graphene


Deepanshu Aggarwal Dept. of Physics, IIT Delhi, Rohit Narula Dept. of Physics, IIT Delhi, Sankalpa Ghosh Dept. of Physics, IIT Delhi


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.

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Does the paper contain any new results or  a summary of what's been done by others?

If it's "just" a summary, what notable papers apart from the original ones by MacDonald and the early experiments, can you recommend?


It is indeed a review. But it reviewed in a way so that one can understand how magic angle twisted bilayer graphene can be seen as a natural consequence of the problem of massless Dirac fermions in a superlattice potentials. It analysed in detail a number of such works including the earlier work ( as compared to BM) by Castro Neto et al., Eugene Mele and some subsequent work by A Vishwanath et al. These works have been analysed in detail and we hope you will find it useful.

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