The Electronic Properties Of Twisted Bilayer Kagome And Lieb Lattices

Since the discovery of unconventional superconductivity in twisted bilayer graphene in 2018,the peculiar properties of graphene got extensive attention once again.The rotation operation breaks the original symmetry of the crystal lattice,and a longrange orderly periodic Moiré pattern will be formed at some certain angles.The flat band of magic-angle graphene will bring about multi-body correlation phenomena,which provides a simple platform for the study of flat band system and helps to explain the unconventional superconductivity mechanism represented by copper oxide.In addition to graphene,there are many other two-dimensional(2D)thin-film materials.Inspired by twisted bilayer graphene,the properties of other 2D twisted bilayer thinfilm materials were effectively regulated.As a result,a new field appeared as twistronics.This paper mainly focuses on the electronic properties of 2D thin-film materials such as twisted bilayer Kagome lattice and Lieb lattice.This paper is divided into five chapters.The first chapter mainly describes some typical 2D thin films represented by graphene.At the same time,the development and application of some 2D thin films that use rotation operations to change their electronic properties in recent years are described in detail like twisted bilayer graphene especially.The second chapter elaborates the two calculation methods and principles we mainly use,which are the first-principle calculations and tight-binding approximation theory.In Chapter 3,we rotate two layers of Kagome graphene.Due to the similarity between the Kagome lattice and the hexagonal lattice,the Moiré patterns are basically the same at small angles.The particularity of the Kagome lattice is that the Kagome band is formed by coupling the Dirac band and the flat band together.After rotation,flat bands are separated from the Kagome band by the influence of interlayer van der Waals forces,and become isolated.As the angle decreases,the number of flat bands increases.Each flat band is almost a band without dispersion and corresponds to a kind of Wigner crystallization.The local radius of the charge density changes from small to large,showing us colorful patterns.The generation of isolated flat bands makes it easier to study flat bands,and at the same time it solves the problem that Kagome lattices represented by Kagome graphene cannot obtain isolated flat bands.Chapter 4 rotates the two layers of Lieb lattice.We obtain Moiré patterns that are completely different from the Kagome lattice,but its electronic properties are relatively similar.In other words,we also obtain several completely isolated flat bands,most of which are distributed in near Fermi level.when the angle decreases,this phenomenon becomes apparently.Meanwhile,the Wigner crystallization patterns belonging to the Lieb lattice are also found.So,we develop the field of twistronics.Chapter 5 summarizes the work of this thesis and assume prospects for future research at the same time.