Hofstadter butterfly and Floquet topological insulators in minimally twisted bilayer graphene

Yang-Zhi Chou,Sankar Das Sarma,Fengcheng Wu

doi:10.1103/physrevresearch.2.033271

Yang-Zhi Chou, Sankar Das Sarma + Show 1 more

Open Access

https://doi.org/10.1103/physrevresearch.2.033271

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Abstract

We theoretically study the Hofstadter butterfly of a triangular network model in minimally twisted bilayer graphene (mTBLG). The band structure manifests periodicity in energy, mimicking that of Floquet systems. The butterfly diagrams provide fingerprints of the model parameters and reveal the hidden band topology. In a strong magnetic field, we establish that mTBLG realizes low-energy Floquet topological insulators (FTIs) carrying zero Chern number, while hosting chiral edge states in bulk gaps. We identify the FTIs by analyzing the nontrivial spectral flow in the Hofstadter butterfly, and by explicitly computing the chiral edge states. Our theory paves the way for an effective practical realization of FTIs in equilibrium solid state systems.

Highlights

Orientation misalignment in twisted bilayer graphene gives rise to a moiré superlattice greatly changing the electronic band structure
We study the electronic structure of minimally twisted bilayer graphene (mTBLG) in a magnetic field Bzby calculating the Hofstadter butterfly of the network model
We demonstrate that the network model effectively realizes Floquet topological insulators (FTIs) [28,29,30], where Chern numbers of bulk bands are zero, but there are chiral edge states traversing bulk gaps

Summary

INTRODUCTION

Orientation misalignment in twisted bilayer graphene gives rise to a moiré superlattice greatly changing the electronic band structure. We study the electronic structure of mTBLG in a magnetic field Bzby calculating the Hofstadter butterfly of the network model. In the strong B field regime, the probabilities of an electron to deflect right and left at a scattering junction can be significantly different, which leads to gap opening at Dirac points. In such a case, we demonstrate that the network model effectively realizes Floquet topological insulators (FTIs) [28,29,30], where Chern numbers of bulk bands are zero, but there are chiral edge states traversing bulk gaps.

BAND STRUCTURE

HOFSTADTER BUTTERFLY AND DIRAC POINTS

FLOQUET TOPOLOGICAL INSULATORS

DISCUSSION