Theoretical Study Of Topological Flat Bands In Multilayer Graphene/hBN Moiré Heterostructures

Recently,Moiré flat bands in twisted graphene have received a lot of attention.In fact,Moiré flat band is not only present in twisted graphene systems,but also in multilayer graphene boron nitride heterostructures.When graphene is placed on boron nitride,a longrange Moire pattern is formed between the layers due to lattice mismatches,which in turn periodically modulate the band structure near the graphene Dirac point,resulting in the formation of Moiré band.It was found that when an appropriate vertical electric field was applied,the Moiré flat band would appear near the Fermi surface of the multilayer graphene/h BN heterostructures with a nonzero topological Chern number.Ashoori,Wang Feng and others observed the fractional quantum Hall effect,Mott insulator and superconducting state in the ABCstacked trilayer graphene/BN heterostructures,which made the ABCstacking trilayer graphene/h BN heterostructures become the focus of recent research.Graphene with different stacking order has different band structures.In this paper,we systematically studied the effect of stacking sequence on the Moiré band of graphene/h BN heterostructures,focusing on the changes of Moire flat band of ABA and ABCstacking graphene/h BN heterostructures under the regulation of electric field and rotation Angle.The main research results of this paper are as follows:(1)Starting from the tight binding model and using the continuous effective model to describe the interaction between layers,we systematically studied the band structure of ABAstacking trilayer graphene/h BN heterostructures.Through theoretical calculation,we found that four Moire bands,including two linear dispersion bands and two secondary dispersion bands,would appear near the Fermy surface of bernal stacking graphene/h BN heterostructures,and the Moire bands are coupled at the Dirac point.When a vertical voltage is applied,the band gap of the two linear bands becomes larger with the increase of bias voltage,and the two secondary dispersive bands appear as partially flat band near the Dirac point.The bandwidth of the flat band can be adjusted by changing the electric field intensity.The presence of partially flat bands indicates that strong correlations can also be in ABAstacking graphene/BN heterostructures.(2)We investigated the effects of the layer number and the stacking order of graphene on the topological properties of heterostructures.Under a appropriate vertical voltage,a flat band with C=4 and a flat band of C=0 will appear near the Fermi surface in the ABCA stacking fourlayer graphene/h BN system.Change the direction of the vertical bias voltage,and the Chern number of conduction band and valence band will be reversed.We found similar properties when we calculated 5layer and 6layer graphene/h BN systems.It can be inferred that there would be a flat band with a Chern number of n and a flat band with a Chern number of 0 in rhombohedral stacked multilayer graphene/h BN heterostructures,n is the number of layers of graphene.However,for Bernal stacking graphene/h BN heterostructures,the Valley Chern number of the two Moire bands near the Fermi surface is not directly related to the layer number of graphene.For example,in the ABA stacking trilayer graphene/h BN heterostructures,the Chern numbers of conduction band and valence band are 2 and 1,respectively.After changing the electric field direction,the Chern numbers do not flip.All these indicate that the stacking order of graphene has an important effect on the band structure and topological properties of the system.(3)We investigated the effect of relative rotation Angle on the band structure of multilayer graphene/h BN heterostructures.When the rotation Angle is changed with fixed stacking order and bias voltage,the band structure and bandwidth will not change significantly if the relative rotation Angle is not too large(? < 1°).This is true for bilayer,trilayer or higher layers of graphene/h BN heterostructures.That is to say,compared with the twisted graphene system,the multilayer graphene/h BN heterostructures does not require precise Angle control.By changing the vertical bias voltage,the band structure and topological properties can be fully modulated,which reduces the difficulty of the experiment.We may say this system is promising in studying the topological properties of the Moiré band and the strong correlation effect.