First Principles And K·p Model On A New Two-dimensional Topological Insulator RuO₂

Since the discovery of the quantum spin Hall effect（QSHE）,the study of topological insulators has become a hot issue in the field of condensed matter physics.Among them,two-dimensional（2D）topological insulators exhibit exotic electrical properties due to their non-trivial topological boundary states.The high-speed ordered and dissipation-free transport of electrons at the boundary in such materials makes topological insulator materials have great potential for the development of high-speed low-power electronic devices.However,there are still very few experimentally prepared 2D topological materials,so theoretically exploring more new 2D topological materials with simple structure and chemical stability is still a major direction for topological materials research.In this paper,based on first-principles calculations,it is predicted that 2D Ru O₂ is a topological insulator under 3%tensile strain applied along the lattice a-axis,which provides more optional materials for the preparation of high-speed and low-energy electronic devices.Meanwhile,the k·p model,as a semi-empirical energy band analysis method,is increasingly applied to the analysis of topological materials because it can consume less computational resources and obtain more detailed energy band information locally.However,the process of constructing the Hamiltonian matrix and solving the parameters of this model is tedious,so this paper develops a program to help construct the k·p model of topological materials quickly.The main research contents and conclusions of the paper are as follows:1.Pykp is a general-purpose program based on Python to quickly construct and solve the material k·p model.k·p models,as a semi-empirical analysis method,can effectively obtain the local energy band structure of materials by solving Hamiltonian matrices analytically.The program builds the user interface through Py Qt5 and generates the Hamiltonian matrix by qsymm library based on the self-built 32-point group information database.And by fitting the genetic algorithm with the band results of first-principles calculations,the program can solve the unknown parameters in the Hamiltonian matrix.The paper uses the typical topological insulator Bi₂Se₃ as an example to compare and verify the accuracy and feasibility of the program.Pykp is expected to be an efficient and general tool for constructing k·p models and based on Object-Oriented programming,the program can be enriched with more material calculation functions in the future.2.A 2D transition metal chalcogenides Ru O₂ with the 1T’phase has been studied based on first-principles calculations,and the stability,electrical properties,and topological properties of the material have been calculated.The computational results show that the material has excellent thermodynamic and kinetic stability.The mechanical properties exhibit anisotropy and the maximum value of Young’s modulus is 213 N/m,and the calculated results of the elastic modulus satisfy the mechanical stability criterion of the 2D orthorhombic crystal system,indicating that it is mechanically stable.The material is topologically banal in the state without applied strain and transforms from a topologically banal state to a topologically nontrivial state when 3%tensile strain is applied on the a-axis.Its topological properties are verified by the topological index Z₂ and the topological boundary states,its topological phase transition is analyzed,and finally,a k·p model is constructed for the energy band near theΓpoint of this topological system using the Pykp.This discovery provides a new research platform for the strain-regulated topological phase transition and new alternative material for the study of topological insulators.