First-principles Predictions Of Nodal Surface Nodal Line Hybrid Phonons And Two-dimensional Van Der Waals Superconductors

Topological and superconducting materials are one of the research hotspots in condensed matter physics,material science and information science in recent years.Such materials not only exhibit new physical phenomena,but also have broad prospects in applications such as new principle devices and quantum information technology.On one hand,the rapid development of band theory and first-principles calculations has advanced the prediction of topological materials ahead of experimental synthesis,becoming one of the most important branches of computational condensed matter physics.With the in-depth study of various symmetries,the classification of topological states has become more and more complete,and the research scope of topological materials has also been extended from the fermion systems represented by electrons to the boson systems represented by phonons and photons.On the other hand,two-dimensional superconducting materials have attracted a lot of attention in the past decade with the progress of thin-film fabrication methods.Atomically thick superconducting materials provide ideal conditions for studying quantum critical phenomena,and two-dimensional superconductors with high superconducting transition temperature T_c are desirable for the construction of quantum devices.Therefore,the researches and predictions of novel topological materials（such as phononic materials）and two-dimensional superconductors may not only provide new carriers for the researches in the field of fundamental physics,but also provide meaningful references for the implementation of condensed matter physics experiments.Based on the above background,this thesis takes topological physics as the main line and is based on the first-principles calculations.This thesis（1）explored the ubiquitous nodal surface nodal line hybrid phonons in solid materials,which enriches the research of topological semimetals in boson systems;（2）predicted a class of two-dimensional van der Waals superconductors with relatively high T_c,and studied the coexisting topological properties;（3）proposed a scheme for manipulating the topological properties of graphene through nanochain patterning from the perspective of structural units;（4）investigated the tight binding model and topology of cycloaddition reactions from the interdisciplinary perspective.In addition,based on the study of two-dimensional van der Waals superconductors and combined with the demands of scientific research,the properties of tantalum disulfide in charge density wave phase were studied in cooperation with experiments.The main research results are as follows:1.Based on analysis of symmetry and compatibility relations,the configurations and space groups of all nodal surface nodal line hybrid phonons which are describable by two bands are given,and the three-dimensional Dirac points,Dirac nodal lines and hourglass phonons in four band situations are discussed.Meanwhile,by screening the phonon database and first-principles calculations,candidate materials possessing various nodal surface nodal line hybrid phonons are predicted.This work has the following two aspects of theoretical value:First,taking C₄N of space group 113 as an example,the Berry-field-driven surface states of nodal surface are revealed.The quadratic nodal line acts as a hub of the Berry fields between two nodal surfaces,leading to a non-zero and opposite Berry flux for each nodal surface.The surface states between two nodal surfaces are in a unique two-segment manner,which are stabilized by the intermediate bulk states,but are not protected by topological charges.Second,it is confirmed that the nodal surface nodal line hybrid phonons composed of simple two bands can generate complex topological surface states.For example,K₂Pt I₆ of space group 128 presents surface arcs including nodal surface to nodal line 1,nodal surface to nodal line 2,and nodal line 1 to nodal line 2.These topological surface states make it possible to observe a variety of surface states and their transformations in a certain frequency range.2.Through preliminary screening of the two-dimensional material database C2DB,a new class of two-dimensional van der Waals superconductors have been found:transition metal monohalides（MX）with four atomic layers.First-principles calculations of electron-phonon coupling revealed that MX（M=Zr,Mo;X=F,Cl）have a relatively high T_c（5.9–12.4 K）and strong electron-phonon coupling coefficient（λ>1）due to the rich mechanisms of phonon softening.Anisotropic Migdal-Eliashberg theory based analysis demonstrated that the orbital composition of Fermi surface should determine the characteristics of superconducting gaps（i.e.,single-gap or two-gap）.The study also found that MX（M=Zr,Mo;X=F,Cl）all have a nontrivial electronic topological invariant Z₂=1,where Mo Cl and Mo F are candidates for realizing topological superconductivity.The existence of two-dimensional Dirac phonons at Brillouin zone boundaries and the distinct phonon edge states with a w-shape make Zr Cl and Mo Cl promising for the edge-enhanced superconductivity.The exploration of Janus monolayer Zr₂FCl further revealed the roton-like phonon softening caused by the chiral modes.This work provides a valuable reference for studying the coexistence of two-dimensional van der Waals superconductivity with topological properties and chiral phonons.3.A scheme towards manipulating Dirac fermions of graphene by one-dimensional nano-patterning is proposed.Combining the k·p Hamiltonian with the tight-binding model,this study found that two-dimensional graphene can be broken into coupled armchair carbon chains first,and then the inter-chain coupling strength are adjustable to create tilted type-I and strongly anisotropic type-II/type-III two-dimensional Dirac fermions.First-principles calculations identified that the aforementioned theoretical model should be realized by the selective adsorption of atoms on graphene.This method can be extended to other group-IVA monolayer,which exhibits the universality.The calculations of static electrical conductance via Green’s function revealed that one-dimensional patterning significantly change the transport properties of graphene.This work provides a new idea for studying the topological properties of materials under symmetry breaking and designing functional nanostructures.4.A research on the tight binding model of molecular reaction and its application in cycloaddition reactions.Inspired by Woodward and Hoffmann’s theory,a tight-binding model of molecular reactions has been proposed.With the parameters fitted from first-principles calculations,the simplified Hamiltonian has the characteristics of the frontier orbitals of corresponding molecules and is used to construct a multi-molecular system.When frontier orbitals of the composite system changes with the reaction parameter（bonding strength）,whether the energy levels of occupied states and empty states have a crossing or not determines that the reaction is topologically allowed or topologically obstructed.Using this method,the classical ethylene-cis-butadiene reaction and the r PAMY-pentacene reaction discovered by experimental collaborators can be explained.This work provides a new idea for understanding the cycloaddition reactions and the topology inside.5.Combined with experimental observations,various properties of the normal states,defect states and domain wall states of 1T-tantalum disulfide in the charge density phase have been studied.In this work,the atomic force microscopy and scanning tunneling microscopy simulations agreed well with experiments.At the atomic scale,it explains the structural defects,charge defects and the domain wall states of tantalum disulfide.These results provide a valuable reference for the research of charge density wave systems by combing atomic force microscopy and first-principles calculations.