Theoretical Design of Some Topological and Two-Dimensional Materials

Author:Liu Zuo

Supervisor:yang jin long wang zheng fei


Degree Year:2018





Traditional condense matter physics has two conerstones:Laudau-Fermi liquid theory and Laudau phase transition theory.Under weak correlation,based on a exactly solvable Hamiltonian,Laudau-Fermi liquid treat the interaction as perturbation and derive concept such as quansiparticle and excitation spectrum.Laudau phase transition theory describes the how phase transition is accompanied by symmetry breaking,and the classical example is the gas-liquid phase transition and magnetism phase transiton.In the seventies of last century,D.J.Thouless and J.M.Kosterlitz discovered the"KT-phase transtion" when they were studing the superliquid phase transiton in two dimension.Such a phase transition was strange since there is no symmetry change during the phase transition.Time flied to the eighties.On the one hand,D.J.Thouless was studying integer quantum Hall effect and fingding that the phase transition also has no symmetry change.On the other hand,F.D.H.Haldane was studying one dimensional quantum spin chain and also discovering a phase transion with no symmetry breaking.All were new phenomena at that time.There is always new physics behind new phenomena.All the three scientists found that the mechanism behind the new phenomena was connected to the idea of topology in mathematics.If we see topology as diging a hole on a page,we can only make holes one by one,not half by half.This example tells us topology doesn’t care about size or shape,it care about one or zero.So if someone asks you why the god creat number such as integer someday,you may answer like this:maybe the god is diging holes.Because the interfiled discovery,the above three scientists ware rewarded the Nobel Prize in Physics in 2016.Before their discovery,people only know how to classify matter according to symmetry,and now we can classify matter according to topology.This brings new diagram to condense matter physics and lays a solid foundation to the search of new"topological material".In 2005~2006,two pioneering works appeared.One is the Z2 topological phase in graphene by C.L.Kane and E.J.Mele.The other is the research about HgTe quantum well by B.A.Bernevig,T.L.Hughes and S.-C.Zhang.These two researches brought the idea of topological insulator.After these work,other topopogical classification about gapped system comes into being,such as topologicalcrystalline insulator,high order topological insulator and so on.Ten years after that,the idea of topology is also extended to gapless system,ideas such as Weyl,Dirac,triple point and nodal-line semimetal are proposed.Since gapless system will always superconducting,the combination of superconductivity and topology will be a beautiful story.Alghouth now we have complete classification theory about topological material,whether a material is topological trivial or not is beyond classification theory.This is the stage of first-principle calculations.Compared to other kind of calculation,such as the value of band gap,the type of band gap,the value of carrier mobility,the cohesive energy and the adsorption energy etc,the calculation of topology is very robust and the chose of different functional has little effect on it.Over the past decades,due to the constantly updated and enhanced computer hardware,the obtaining of huge date about different kind of material in a short period of time gradually becomes a possibility.We can then filter the big date and choose the material we need.Such a method can greatly speed up the discovery of new materials and becomes a general trend these years.On the other hand,we can narrow down the possibilities based on fundamental principles,either from modeal calculation or chemical analogy.On the second stage,we make use of first-principle calculations to check what we get.This is the basic logic of this thesis and there are three parts.The first part includes chapter 1~3,mainly about first-principle calculations,basic knowledge about symmetry and topology.The second part includes chapter 4~7,mainly about realization of different topological phase in different systems.The third part include chapter 8,mainly about the design of first "Cario pentagon tiling"material.Following are the details:Chapter 1 is the basic introduction of first-principle calculations.Firstly,we introduce the Hartree-Fock method which is the most basic in the calculation of the first principles calculations,and explain the advantages and demerits of the Hatree-Fock method.Secondly,it introduces the most widely used density functional theory(DFT)in the current first-principles calculation,including the core concepts of Hohenberg-Kohn theorem,Kohn-Sham equation,exchange-correlation functional,pseudopotential and basis set,as well as implementation of density functional theory using different basis set.Finally,we briefly review the databases and softwares used in this thesis.Chapter 2 is the basic introduction of group theory which helps us gain the basic understanding about space group.Alghouth the existence of topology doesn’t rely on specific symmetry,the utility of symmetry analysis will greatly simplfy the classification of different topological phase as well as the calculation of topological number.First we give a definition about a group and all kinds of representations such as regular representation,vector representation,spinor representation as well as complex conjugate representation.Then we study the point group and space group for detail and at the same time,we spend some time on color point group and color space group which are used to describe magnetic system.Finally,we briefly give an introduction about kp theory,which is often used in model analysis.Chapter 3 is the basic introduction of topology.First we introduce the idea of differential manifold,the derivative algebraic structures such as tangent space and fiber bundle.Then we study the classicial utility of differential manifold in physics:guage field theory.The linkage between thes two is that the space of guage filed-Mikovski space-is a differential manifold,so we can define electromagnetic field on this space.After the study of differential manifold in real space,then we study the differential manifold in reciprocal space:Berry phase.The linkage behind this is that the Bloch state in periodic crystals also lives on a space and such a space is also a differential manifold.Finally,we give an example about the calculation of topological number.Chapter 4 is the design of topological insulator which has giant Rashba spin splitting as well as large topological gap based on trigonal lattice and Rashba spin-orbit coupling.There are there common lattices on 2D hexagonal crystal system:honeycomb lattice,Kagome lattice and trigonal lattice.The former two are well studies and the topological properties are well-known.The last one is less studied and our main work is to study the effect of Rashba spin-orbit coupling on topological phase.First we proposed a tilted sp2 model,study its phase diagram and find that Rashba spin-orbit coupling can coexist with topological phase.Then according first-principle calculations,we find an experimental realizable surface alloy is a good candidate.Chapter 5 is a correction calculation based on experimental results.In a recentexperiment,researches grown a single molecular crystal and found some abnormal phenomenon:the conductivity doesn’t change with respect to temperature when the applied pressure reaches a critical point.They claim that such abnormal is attributed to the come into being of Dirac point.But according to our knowledge,it is Dirac loop semimetal rather than Dirac semimetal that cause such phenomenon.Chapter 6 is a general design based on knowledge about previous chapter.We propose to use frontier orbital to construct clean Dirac loop semimetal with the imposingof pressure.Then we choose a molecular crystal in the datebase and calculate the existence of Dirac loop semimetal phase with pressure higher than 4 GPa.Chapter 7 is about the design to realize in-plane magnetization induced quantum anomalous Hall effect.As the last member of Hall family,quantum anomalous Hall effect is the hardest to realize because of two restrictions:the ferromagnetism transition temperature and the strength of spin-orbit coupling(to open a sizeble gap).Previous studies always assume a out-of-plane ferromagnetism,although a in-plane magnetization is capable of creating quantum anomalous Hall effect.The orientation of magnetization is due to magnetic anisotropic energy.Based on these analysis,start with a Weyl loop semimetal which is formed by opposite spins,we put forward the conditions to realize in-plane magnetization.Then by first-principle calculations,we find that LaCl monolayer can host the exotic in-plane magnetization induced quantum anomalous Hall effect.In contrast to quantum anomalous Hall effect induced by out-of-plane magnetization,there is exotic topological phase transition for in-plane magnetization induced quantum anomalous Hall effect.More specificly,with the orientation of magnetic moments vary,the Chern number will flip between-1 and +1.What’s more,it is Weyl semimetal that lies at the phase transition point.Chapter 8 is about the design of first "Cario pentagon tiling" fulfilled two-dimensional material.Recent years saw the raise of three kinds of two-dimensional materials:graphene,transitom metal dicogenides and phosphorene.All of them have great application in different fields:graphene guides the development of toplogical electronics,transitom metal dichalcogenides guide the development of vallytronics and phosphorene guides the development of optoelectronics.However,none of them is suitable for nanoelectronics.Graphene is gapless,transitom metal dichalcogenides have low carrier mobility and phosphorene is ambient unstable.If we can introduce intrinsic gap to graphene,graphene will be a perfect material for nanoelectronics.But as we know,the property of gapless is due to the honeycomb tiling.If we can change the tiling from honeycomb tiling to "Cario pentagon tiling",we may creat an ideal two-dimensional material for nanoelectronics.Guided by coordination chemistry,we find that penta-Pt2N4 is such a material:stability,mechanical perperties and carrier mobility are comparable to graphene,suitable gap comparable to phosphorene and what’s more,the gap is direct.After the previous discussion,we know that the basic framework about topological materials has been well established and it seem that we can never gain something new.Don’t be pessimistic! The previous discussion is just based on the breaking of the second cornerstone.What’s happes when we break the first cornerstone?In other words,is the language of topology suitable for strongly correlated system?The answer is yes,but we are far from the end.Once such a framework is finished,it is the day that the new condense matter physics takes place the traditional condense matter physics.Looking forward to that day!Finally,a few word about 2D materials.Since the discovery of graphene,more and more 2D materials are predicted by DFT calculations and synthesized by experiments.A nature question is:how much can DFT calculations help experiment?Are the synthesized 2D materials in experiments corresponds to the lowest or second lowest structure in DFT calculations?Today,there are still many problems to be solved about 2D materials.For example,can we synthesize 2D metal oxide and detect the strongly-correlated properties?We have TMD,crystal of light element(C,B,P,Te and so on),how about 2D metal oxide?Alougth there are several works reporting the liquid synthesis of 2D metal oxide,no strongly-correlated properties have ever been reported.During the preparation of this work,2D magnetic material is getting hot.Two works have found 2D ferromagnetic semiconductor,nevertheless the low Curie temperatures.How to increase the Curie temperatures?Is it easier for 2D than 3D?At last,with more and more functional 2D materials been discovered,the van der Waals junctions combining several functions will become more and more important.With the devices become smaller and smaller,our society is going to faster and faster.