Moire bands in twisted double-layer graphene

TL;DR

This paper investigates the electronic properties of twisted double-layer graphene, revealing how moire patterns lead to unique band structures, including flat bands at specific 'magic' angles, with implications for conductivity and density of states.

Contribution

It introduces a continuum Dirac model for twisted bilayer graphene, demonstrating the emergence of moire Bloch bands and identifying magic angles where bands flatten.

Findings

Moire pattern periodicity creates moire Bloch bands.

At certain twist angles, the Dirac velocity vanishes.

Flat bands occur at magic angles, enhancing density of states.

Abstract

A moire pattern is formed when two copies of a periodic pattern are overlaid with a relative twist. We address the electronic structure of a twisted two-layer graphene system, showing that in its continuum Dirac model the moire pattern periodicity leads to moire Bloch bands. The two layers become more strongly coupled and the Dirac velocity crosses zero several times as the twist angle is reduced. For a discrete set of magic angles the velocity vanishes, the lowest moire band flattens, and the Dirac-point density-of-states and the counterflow conductivity are strongly enhanced.