  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.
