A Unified View of Topological Phase Transition in Band Theory

We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid crystal, such as a semiconductor, we demonstrate that there exists ubiquitously an intermediate phase of topological insulator (TI), whose critical transition point displays a linear scaling between electron hopping potential and average bond length, underlined by deformation-potential theory. The validity of the scaling relation is verified in various two-dimensional (2D) lattices regardless of lattice symmetry, periodicity, and form of electron hoppings, based on a generic tight-binding model. Significantly, this linear scaling is shown to set an upper bound for the degree of structural disorder to destroy the topological order in a crystalline solid, as exemplified by formation of vacancies and thermal disorder. Our work formulates a simple framework for understanding the physical nature of TPTs with significant implications in practical applications of topological materials.Comment: 13 pages, 4 figure

Emergence of a Chern-insulating state from a semi-Dirac dispersion

A Chern insulator (quantum anomalous Hall insulator) phase is demonstrated to exist in a typical semi-Dirac system, the TiO2/VO2 heterostructure. By combining first-principles calculations with Wannier-based tight-binding model, we calculate the Berry curvature distribution, finding a Chern number of -2 for the valence bands, and demonstrate the existence of gapless chiral edge states, ensuring quantization of the Hall conductivity to 2e^2/h. A new semi-Dirac model, where each semi-Dirac cone is formed by merging three conventional Dirac points, is proposed to reveal how the nontrivial topology with finite Chern number is compatible with a semi-Dirac electronic spectrum.Comment: 12 pages, 3 figure