Application Of First-principles Calculations In The Study Of Structural Phase Transitions And Topological States

Since the birth of the first-principles calculations,it has played a more and more important role in the study of condensed matter physics.Because of the least reliance on the empirical parameters,it can provide the reference for the parameters in theoretical models and experiments.For example,the many-body studies on materials often start from the electronic structure from first-principles calculations.After the development of the topological band theory,the combination of first-principles calculations and experiments has made a great success in the progress of the studies of topological states and the discovery of topological materials due to the global nature of topological states and the stability against perturbation.This thesis includes two works using the first-principles calculations.First is the research on the structural phase transition and metal-insulator transition of GaTa4Seg.Second is the systematic research on topological states of Chevrel Phase materials.These two kinds of materials have a common feature,i.e.,there is a cluster molecule as the basic unit in their crystal structure.Here,we call them cluster-assembled materials.In GaTa4Se8,the cluster is Tao.For Chevrel phase materials,such as BaMo6Sg,the cluster is Mo6S8.The electrons near the Fermi level mainly come from the molecule clusters.As a result,when we analyze the low-energy effective electronic structures,the molecular orbitals are a better starting point than the atomic orbitals.For example,the symmetry of molecular orbitals is consistent with the point group of the crystal,i.e.,the molecular orbitals belong to the irreducible representations of the corresponding point group.The problem of structural phase transition of GaTa4Se8 at low temperatures has a long history.Here,we studied three crystal structures(i.e.F43m,R3m and P421m space group)using first-principles calculations.The phonon spectra of the F43m phase have imaginary frequencies in the whole Brillouin zone,which indicates that the F43m phase is dynamically unstable.There is no gap at the Fermi level in the electronic structure of the first-principles calculations with the single-particle approximation.By analyzing one of the soft modes at Γ point,we got the R3m phase.The phonon spectra of the R3m phase have no imaginary frequency,which indicates that the R3m phase is dynamically stable.There is no gap at the Fermi level in the electronic structure with the single-particle approximation.By considering the on-site Coulomb interaction of Ta4 clusters and using the dynamical mean-field theory,we opened a gap near the Fermi level,which indicates that the R3m phase GaTa4Se8 is a Mott insulator.There is no imaginary frequency in the phonon spectra of the P421m phase GaTa4Se8,which indicates that this phase is dynamically stable.Because the primitive unit cell of the P421m phase GaTa4Se8 is enlarged four times,there is a gap near the Fermi level with the single-particle approximation.This indicates that the P421m phase GaTa4Se8 is a band insulator rather than a Mott insulator.The crystal structure of Chevrel phase materials is R3 at room temperatures.When lowing the temperatures,most of these compounds take a structural phase transition from the R3 phase to the P1 phase.There are many intriguing physical properties of these materials,such as superconductivity and the anomalous resistance-temperature behavior.However,besides numerous preceding studies on these materials in the last decades,their topological states have not drawn the attention of researchers.Here we systematically studied the topological states of these compounds,and analyzed BaMo6S8,as an example,in detail.For BaMo6S8,SrMo6S8,and Mo6S8,which have time-reversal symmetry,they are topological insulators.For EuMo6S8 without time-reversal symmetry,it is an axion insulator in the R3 phase,while a normal insulator in the P1 phase.