A Unified View of Topological Phase Transition in Band Theory
arXiv:1904.06003
Abstract
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.
arXiv comment13 pages, 4 figures
References in corpus (13)
- Topological Insulators
- Topological insulators and superconductors
- Topological Order and the Quantum Spin Hall Effect
- Colloquium: Topological Band Theory
- High temperature fractional quantum Hall states
- Acoustic topological insulator and robust one-way sound transport
- Catalogue of Topological Electronic Materials
- Towards ideal topological materials: Comprehensive database searches using symmetry indicators
- Computing topological invariants without inversion symmetry
- Nearsightedness of Electronic Matter
- Topological modes bound to dislocations in mechanical metamaterials
- Epitaxial growth of large-gap quantum spin Hall insulator on semiconductor surface
- Topological states of non-Dirac electrons on triangular lattice