First-principles And Model Studies Of Ordered States In Quasi-two-dimensional Graphene-based And Iron-based Systems

Ordered states and their associated phase transitions in materials are crucial re-search contents in condensed matter physics.The order states and phase transitions in quasi-two-dimensional material are of particular interest due to their unique layered structures compared with two-dimensional or three-dimensional materials,which en-dow us with some new ways to tune the properties of ordered states or induce phase transitions.This superiority implies possible wide applications of the ordered states of quasi-two-dimensional material in the future.Therefore,to clarify the nature of some ordered phase transition phenomena in quasi-two-dimensional material,to study the tunability of ordered states in quasi-two-dimensional material,to establish an unified theory for understanding the ordered phenomena in a class of quasi-two-dimensional material,and to develop theoretical methods to handle the strong correlation effects in quasi-two-dimensional material are of great significance.Multilayer graphenes are the simplest class of quasi-two-dimensional material,and iron-based high-temperature superconductors are the most popular class of materials at present,whose character-istic layers host a quasi-two-dimensional structure.In multilayer graphenes,the or-dered states play a crucial role in the formation of a band gap.However,until now,some ordered phase transition phenomena have not been well explained,the effects of these ordered states on band gap opening have not been studied as well.In iron-based high-temperature superconductors,the superconductivity often emerges in close prox-imity to a state with antiferromagnetism.Because of this close relationship between superconductivity and magnetism,it is widely believed that understanding the origin of magnetism is the key to reveal the origin of superconductivity in iron-based super-conductors.However,there are currently different opinions on the origin of magnetism in iron-based superconductors.In addition,it is necessary to develop some methods,which do not require much computational resources and are more accurate than the mean-field approximation,to study the strong correlation effect in iron-based super-conductors.Therefore,in this dissertation,combining first-principles calculations with model analysis of both tight-binding model and Hubbard model,We have carried out a series of studies on the charge-ordered or spin-ordered phenomena in these two classes of quasi-two-dimensional material and on the development of multi-orbital method for strongly correlated effect.Our main findings are as follows:（1）We have investigated the ordered phase transition phenomenon which ex-hibits non-monotonic behavior of resistance with electric field in AB-stacked bilayer graphene.Using a simple model,we demonstrate that the ground state of AB-stackd bilayer graphene is most likely a charge-ordered state with intralayer charge dispropor-tionations in the absence of an external field,which leads to band inversion near the Fermi surface and opens a band gap.The conduction-band minimum and valence-band maximum of this charge-ordered insulating state will approach,touch,and then move away from each other when applying an electric field.As a result,the resistance changes non-monotonically with the external electric field.Combining density functional theory calculations with modeling of interlayer Van der Waals interactions,we reveal that the interlayer van der Waals interactions may be responsible for the intralayer charge dis-proportionations.Besides,the strength of interlayer van der Waals interactions has been estimated to be on the order of 10 me V.Our results can well explain the phenomenon of resistance changing non-monotonously with electric field mentioned above and pro-vide some theoretical guidance for the correct understanding of the ground state of this material at low temperature.These will be shown in chapter 3.（2）We have clarified the effect of the ordered state on the band gap opening in twisted bilayer graphene and have studied its band gap tunability.Taking the twisted bilayer graphene with a twisted angle ofθ_R=38.21°as an example,we show the effect of external tuning parameters,such as a transverse homogeneous pressure,an in-plane biaxial tensile strain,or a transverse electric field on gap opening.We found that there is an intrinsic intralayer charge disproportionation（CD）in this material,which,together with the effective interlayer hopping and interlayer charge disproportionation,increase the band gap.By studying the effect of interlayer hoppings and on-site potentials in specific regions of the moi（?）e supercell on gap opening using the tight-binding model,we propose that a periodic transverse inhomogeneous pressure can open a gap of over100 me V in this system.Our work clarify for the first time the effect of intralayer charge disproportionation on the gap opening in this system,study systematically the tunability of band gap,and provide a way to open a large band gap experimentally in this system.These findings will be demonstrated in chapter 4.（3）We have investigated the effects of As’s height from the Fe atomic plane,elec-tronic interactions,and Cu doping on the magnetic ground state of Cu Fe As.The mag-netic ground state of Cu Fe As was investigated using density functional theory calcu-lations,with the correlation effect taken into account using the generalized gradient approximation plus U approach.When Cu Fe As has a small hight of As to the Fe plane h_As,the ground state is a striped antiferromagnetic state,but when h_Asis is big,the ground is ferromagnetic.Due to the occurrence of numerous competing magnetic or-dered states in Cu Fe As with an intermediate value of h_As,electronic interactions play a significant role in determining a specific magnetic ground state.The electronic in-teractions will favor a double-striped antiferromagnetic state.This state will further be stabilized and exhibits a non-zero net magnetic moment when Cu vacancy exists.Our results can well explain the magnetic ground state in Cu Fe As observed experimen-tally and reveal that the electronic interactions play an important role in determining the ground state of iron-based superconductors with an intermediate value of anion height.It also provides some theoretical guidance for understanding correctly the weak mag-netism in iron-based superconductors.These will be illustrated in chapter 5.（4）We have found an unified minimal model which can explain qualitatively the magnetic states in iron-based and cuprate superconductors.Using the mean-field ap-proximation to study the single-orbital Hubbard model with nearest-neighbor hoppings and next-nearest neighbor hoppings in a square lattice,we show that all the antifer-romagnetic states,which are observed in iron-based superconductors and cuprate su-perconductors,can be found from the U/t₁—t₂/t₁phase diagram.Two new antiferro-magnetic phases are detected at intermediate strength of Hubbard U and relative strong frustration of t₂/t₁,named double-striped antiferromagnetic state and plaquette antifer-romagnetic state,both of which are stable even at electron doping and finite temperature.We argue that the antiferromagnetism of iron-based and cuprate superconductors can be understood qualitatively by this unified minimal model.This work provides theoretical guidance for an unified understanding of the magnetic ground state in high-temperature superconductors.These findings are presented in chapter 6.（5）We have developed the multiorbital coherent potential approximation,which does not require much computational resources and is more accurate than the mean-field approximation,to handle the strong correlation effects of multi-orbital materials.Our developmental works include two-orbital paramagnetic coherence potential approxima-tion without the effects of spin flip and pair hopping terms,two-orbital paramagnetic coherence potential approximation with the effects of spin flip and pair hopping terms,and three-orbital paramagnetic coherence potential approximation with the effects of spin flip and pair hopping terms.Our study provides a theoretical approach to the multi-orbital correlation problem,which may have important implications for dealing with the multi-orbital correlation effect problem.These will be shown in chapter 7.In conclusion,the order states and phase transitions in two typical quasi-two-dimensional material,namely,multilayer graphenes and iron-based superconductors,are investigated in this dissertation.For multilayer graphenes,AB-stacked bilayer graphene and twisted bilayer graphene with a large twisted large are studied.we have found that intralayer charge disproportionation exists in these two system and has sig-nificant effect on their properties.For iron-based superconductors,Cu Fe As is investi-gated.We have found that the electronic interactions play an important role in deter-mining a specific magnetic ground state when there are numerous competing magnetic ordered states in the system.Then,we have proposed an unified minimal model with electronic interactions to describe qualitatively the magnetic ground state of iron-based and cuprate superconductors.In addition,we have developed the multiorbital coherent potential approximation to handle the correlation effects of multiorbital materials such as iron-based superconductors.Our works provide theoretical guidances for the cor-rect understanding of the ordered phenomena in quasi-two-dimensional material such as multilayer graphenes and iron-based superconductors.We also provide a theoretical approach to the correlation problem in multi-orbital materials.