Theoretical Study Of Topological Flat Bands In Twisted Multilayer Graphene

Flat bands in Moir(?) van der Waals heterostructures have drawn great reasearch interest very recently.The celebrated example is the twisted bilayer graphene(TBG),where a small twist between two graphene layers can produce a long-range Moir(?) pattern.When θapproaches the so-called “magic angles”,a pair of narrowly dispersing Moir(?) flat bands with extremely large DOS appears near Fermi surface isolated from other high energy bands.Due to the quite reduced bandwidth and quenched kinetic energy of the Moir(?) flat band,the mutual Coulomb repulsion between electrons dominates over the kinetic energy and drive the system into various strongly correlated states,e.g.Mott insulator states and superconducting states.As we all know,correlated electron interaction and topology are two core problems in condensed matter physics.We find that in our study of the twisted multilayer graphene heterostructure,both the band topology and the flat band with electron interaction are obtained,and the system can be easily manipulated by an external electric field.The unique properties of twisted Van der Waals heterojunction may open a new playground for correlate electricity in a two-dimensional platform.The major works is as below:1.We study a simplest realistic topological flat band system,i.e.,the twisted trilayer graphene,where one monolayer graphene is placed on the top of a bilayer graphene and they are twisted with each other by a nonzero angle θ.We numerically calculate the band structure and the valley Chern number of the twisted trilayer graphene based on the continuum model.Different from the twisted bilayer graphene,twisted can induce a small gap at all the Dirac points,which can be further tunable by a perpendicular electric field.we plot the phase diagram of the valley Chern number for the first electron band and hole band.We find that the Chern number of the twisted trilayer graphene strongly depends on the twisted angle and the applied electric field.2.We theoretically study a richer and highly controllable flat band structure of Moir(?) superlattice system: twisted few-layer graphite.The twisted few-layer graphite system consists of two few-layer graphites stacked on top of each other with a small twisting angle.We find that the energy band structure of the twisted few-layer graphite mainly depends on the layer number of its composed few-layer graphites and the twisted angle.Our results show that there are always two Moir(?) flat bands coexisting a few pairs of linear or parabolic narrowed dispersive bands near the magic angle.When a proper perpendicular electric field applied on the twisted few-layer graphites system,we can get four isolated nearly flat band with nonzero Chern number.3.We study a new family of Moir(?) heterostructures,double-twisted few layer graphite.The double-twisted few layer graphite is composed of three few layer graphite stacked with two twist angles.According to the rotation direction of the two twist angles,we calculate two kinds of double-twisted few layer graphite,alternately twisted and chirally twisted.Our result show that once the middle few layer graphene of the double-twisted few layer graphite is greater than or equal trilayer,both kinds of the double-twisted few layer graphite can host two pairs of Moir(?) flat bands at the charge neutral point,twice that of the twisted bilayer graphene.More Moir(?) flat bands lead to higher DOS at the charge neutral point,which implies much stronger correlation effects than the twisted bilayer graphene.When a proper perpendicular applied on the twisted few-layer graphites system,the degeneracy of Moir(?) flat band will be lefted,and the isolated Moir(?) flat band have nonzero valley Chern number.4.We discover a new kind of wave localization mechanism in periodic wave system.Using this mechanism,we can get a flat band in a spatially continuous system.Two examples are given and their band structures and eigenfunctions are calculated by the finite difference method and the commercial software package COMSOL MULTIPHYSICS.The first example we design a quasi one dimensional waveguid with special periodic confinement potential.Through calculation,we find that the electrons can be completely localized in an open waveguide by reasonably designing the geometry of the local potential field.We explain this phenomenon by introducing a concept of self-localized orbit.It is this self-localized orbit that leads to flat bands in the electron waveguide.Then,we design a metal waveguide array and find that a similar flat band can be easily realized in the electromagnetic wave system.Our research extends the concept of flat band to space continuous system.