Nearly flat bands in twisted triple bilayer graphene

TL;DR

This paper explores how twisting and stacking configurations in triple bilayer graphene can produce nearly flat electronic bands, which are crucial for studying correlated electron phenomena.

Contribution

It provides a detailed analysis of how interlayer coupling, twist angle, potential difference, and stacking affect flat band formation in twisted triple bilayer graphene.

Findings

Flat bands can be achieved at twist angles below 2 degrees.

Finite interlayer potential difference helps isolate flat bands.

Stacking configurations influence Coulomb interactions and topological properties.

Abstract

We investigate the electronic structure of alternating-twist triple Bernal-stacked bilayer graphene (t3BG) as a function of interlayer coupling $\omega$, twist angle $\theta$, interlayer potential difference $\Delta$, and top-bottom bilayers sliding vector $\boldsymbol{\tau}$ for three possible configurations AB/AB/AB, AB/BA/AB, and AB/AB/BA. The parabolic low-energy band dispersions in a Bernal-stacked bilayer and gap-opening through a finite interlayer potential difference $\Delta$ allows the flattening of bands in t3BG down to $\sim 20$~meV for twist angles $\theta \lesssim 2^{\circ}$ regardless of the stacking types. The easier isolation of the flat bands and associated reduction of Coulomb screening thanks to the intrinsic gaps of bilayer graphene for finite $\Delta$ facilitate the formation of correlation-driven gaps when it is compared to the metallic phases of twisted trilayer graphene under electric fields. We obtain the stacking dependent Coulomb energy versus bandwidth $U/W \gtrsim 1$ ratios in the $\theta$ and $\Delta$ parameter space. We also present the expected $K$-valley Chern numbers for the lowest-energy nearly flat bands.