Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators

Understand

Bosonic topological insulators (BTI) in three dimensions are symmetry-protected topological phases (SPT) protected by time-reversal and boson number conservation {symmetries}.

• BTI in three dimensions were first proposed and classified by the group cohomology theory which suggests two distinct root states, each carrying a $\mathbb{Z}_2$ index.
• Soon after, surface anomalous topological orders were proposed to identify different root states of BTI, which even leads to a new BTI root state beyond the group cohomology classification.
• In this paper, we propose a universal physical mechanism via \textit{vortex-line condensation} {from} a 3d superfluid to achieve all {three} root states.