Broken-Symmetry Quantum Hall States in Twisted Bilayer Graphene.

Youngwook Kim,Takashi Taniquchi,Jun Sung Kim,Jong Mok Ok,Hee Cheul Choi,Jaesung Park,Younjung Jo,Intek Song,Suyong Jung,Kenji Watanabe,Dong Su Lee

doi:10.1038/srep38068

Abstract

Twisted bilayer graphene offers a unique bilayer two-dimensional-electron system where the layer separation is only in sub-nanometer scale. Unlike Bernal-stacked bilayer, the layer degree of freedom is disentangled from spin and valley, providing eight-fold degeneracy in the low energy states. We have investigated broken-symmetry quantum Hall (QH) states and their transitions due to the interplay of the relative strength of valley, spin and layer polarizations in twisted bilayer graphene. The energy gaps of the broken-symmetry QH states show an electron-hole asymmetric behaviour, and their dependence on the induced displacement field are opposite between even and odd filling factor states. These results strongly suggest that the QH states with broken valley and spin symmetries for individual layer become hybridized via interlayer tunnelling, and the hierarchy of the QH states is sensitive to both magnetic field and displacement field due to charge imbalance between layers.

Highlights

Bilayer two-dimensional electron gas system (2DES), a pair of 2DESs in close proximity, reveals various intriguing quantum Hall (QH) phenomena arising from the additional layer degree of freedom[1,2,3,4,5,6]
Our observations clearly demonstrate that the interaction energies above B = 9 T follow the hierarchy of Δvalley >Δspin > ΔSAS
Our study shows that the behaviour of the broken-symmetry QH states is very sensitive to the external magnetic field as well as the interlayer displacement field

Summary

Introduction

Bilayer two-dimensional electron gas system (2DES), a pair of 2DESs in close proximity, reveals various intriguing quantum Hall (QH) phenomena arising from the additional layer degree of freedom[1,2,3,4,5,6]. The merging of two Dirac cones of each layer at very small twist angles (θ < 2°) drastically alters the low-energy electronic structure[7,8,9,10,11,12,13], in most cases with large twist angles the low energy states of the two layers are only tunnel-coupled, similar to the double quantum well in semiconductor heterostructures This breakdown of interlayer coherence[14] unties the layer degree of freedom from spin and valley counterparts for each layer, providing eight-fold degeneracy in the LLs. This breakdown of interlayer coherence[14] unties the layer degree of freedom from spin and valley counterparts for each layer, providing eight-fold degeneracy in the LLs This contrasts to the case of zeroth LL in Bernal-stacked bilayer graphene where spin, valley and orbital degrees of freedom introduce the eight-fold degeneracy with the layer degree of freedom tied to the valley. We have found that the hierarchy of the broken-symmetry QH states is sensitive to external magnetic field and internal displacement field between layers from charge imbalance

Methods

Results

Conclusion