Topological phase transitions in antimony without gap parity reversal

A common feature for all three-dimensional topologically nontrivial materials is an inverted band gap. Transitioning to a topological state typically involves a gap reversal caused by a strong spin-orbit coupling (SOC), and is accompanied by the appearance of topological surface states. A distinctly different behavior in antimony (Sb), where the topological transition does not involve gap reversal and the surface states survive the transition, is investigated. First-principles calculations are used to determine the electronic band structure of Sb for various SOC strengths. The results illustrate a new type of topological phase transition despite the same underlying Z₂ topological order.