Theoretical Study On Electronic Properties Of Graphene Moiré Superlattice

In recent years,two-dimensional materials have been widely studied for their unique physical and chemical properties.Different from bulk counterparts,2D materials have significant confinement effects,that is,electrons can only move in the 2D atomic plane,and are strongly constrained in the third dimension,rendering a plethora of novel emergent electrical,magnetic,thermal,optical and mechanical properties in 2D materials.Compared with traditional 2D materials,2D moire superlattice materials,obtained through van der Waals weak stacking two/multiple 2D atomic layers,have new lattice periodicity formed by lattice mismatch or twist between unit cells of constituent layers.The important tuning on electronic properties due to periodic superlattice potential gives rise to a myriad of novel properties such as unconventional superconductivity,strong correlation,quantum anomalous Hall effect and so on.What’s more,many tunable degrees of freedom in moire superlattices can diversify physical properties through numerous stacking choices such as constituent material selectivity,stacking geometry,twisted angle and number of layers.Theoretical study on the physical properties of moire superlattice materials is a key step to interpret the experimental phenomena and predict the new states of matter.Recently,there have been intensive studies on the existence of correlated insulating states and superconducting states in alternating twisted bilayer/trilayer graphene and such novel phenomena are mostly related to the existence of flat bands and magic angles.Whether it still stands in more generic multilayer systems remains unknown.Therefore,it is necessary to systematically study alternating twisted multilayer graphene.In this thesis,the effective continuum model is constructed for alternating twisted multilayer graphene and electronic properties in alternating twisted multilayer graphene are studied.It is found that there exist flat bands and magic angles in alternating twisted multilayer graphene and each pair of flat bands can be perceived as the zeroth pseudo-Landau-levels in two dimensional Dirac fermions,electron in the flat band pair can feel a pseudo-magnetic field with the same magnitude but the opposite sign.When the twisted angle between layers is ajusted so that the area of the envelope of AA region is equal to n times the flat band electrons cyclotron area in the pseudomagnetic field,the twisted angle between layers is the nth magic algles of the system.At the same time,alternating twisted multilayer graphene systems have non-trivial flat band topology and are potential materials for realizing novel quantum devices.In addition to the moiré superlattices formed by graphene homojunction,graphene/h-BN and graphene/MoS2 hetrojunctions have been widely reported and fractal Landau spectrum and non-trivial topological properties have been studied.However,these are the single moiré superlattices formed by graphene and other 2D materials.In this thesis,we studied the dual moiré superlattice in h-BN/graphene/h-BN and correlated properties.Using the effective continuum model to calculate the band structures of the system,we find that there are three isolated bands in the valence bands of hBN/graphene/h-BN.One of the isolated flat bands can be split by Coulomb interaction,which results in complex fractal Landau spectrum.Moreover,the intervalley coherent state is found to form in h-BN/graphene/h-BN,which opens a new avenue for the study of strong correlated state of dual moiré superlattices.All the above studies are made on the van der Waals stacked moiré superlattices of common 2D materials.Coupling 2D materials with artificial superlattice potential serves as an alternative effective means for artificial quantum simulation of moire superlattices and tuning the physical properties of moiré superlattices.In this thesis,we studied the electronic structures of graphene/dielectric artificial lattices and Bernel stacked(AB-)graphene/dielectric artificial lattices.The results show that there are high-order van Hove singularities in graphene/dielectric triangle artificial lattices.By further introducing effective Rashba spin-orbit coupling with different strengths,we find that different types of high-order van Hove singularities are generated in both band structures of graphene/dielectric triangle artificial lattices and AB-graphene/dielectric triangle artificial lattices.Compared with ordinary van Hove singularities,density of states of high-order van Hove singularities diverges much stronger.At the same time,because of the high tunability of the artificial lattices,it is possible to measure more diversified correlated insulating states and superconducting states in experiment.