Strong Coupling Theory of Magic-Angle Graphene: A Pedagogical Introduction

TL;DR

This paper reviews a strong coupling theory of magic-angle graphene that unifies insulating and superconducting states, providing analytical insights into their electronic structure, topological features, and potential for novel quantum phases.

Contribution

It introduces a comprehensive strong coupling framework for magic-angle graphene that captures both insulating and superconducting phenomena with analytical treatment.

Findings

The theory explains flavor ordered insulators at integer fillings.

It predicts the emergence of fractional Chern states at fractional fillings.

Superconductivity can be achieved by disordering the sigma model, with estimated T_c values.

Abstract

We give a self contained review of a recently developed strong coupling theory of magic-angle graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. We begin by reviewing the electronic structure of magic angle graphene's flat bands, in a limit that exposes their peculiar band topology and geometry. We highlight how similarities between the flat bands and the lowest Landau level give insight into the effect of interactions. For example, at certain fractional fillings, we note the promise for realizing fractional Chern states. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Unexpectedly, topological textures of the sigma model carry electric charge which allows us to extend the same theory to describe the doped phases away from integer filling. We show how this approach can lead to superconductivity on disordering the sigma model, and estimate the T$_c$ for the superconductor. We highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. Seeking to enhance this coupling helps predict new superconducting platforms, including the recently discovered alternating twist trilayer platform. We also contrast our proposal from strong coupling theories for other superconductors.