Topological insulators in three dimensions
Three-dimensional time-reversal-invariant insulators can have robust surface Dirac states.
$$(\nu_0;\nu_1\nu_2\nu_3)$$
What this means
Three-dimensional time-reversal-invariant insulators can have robust surface Dirac states.
Deep dive: mathematical and physical mechanism
Four $\mathbb Z_2$ indices characterize strong and weak band topology in the standard noninteracting classification. A strong topological insulator has an odd number of surface Dirac cones modulo symmetry-compatible surface perturbations. Spin–orbit coupling often drives band inversion.
How it appears in quantum phenomena
Bi-based topological insulators and surface-state spectroscopy.
Assumptions, caveats and limitations
A surface may be gapped by time-reversal breaking or modified by interactions and disorder.
Connect the ideas
For context, see the Topological Band Theory topic guide and the reading references.