Abstract
A general and beautiful picture for the realization of topological insulators is that the mass term of the Dirac model has a nodal surface wrapping one Dirac point. We show that this geometric picture based on Dirac points can be generalized to extended band degeneracies with nontrivial topological charges. As the nontrivial topological charges force the extended band degeneracies to be created or annihilated in pairs, when the nodal surface of mass wraps one such extended band degeneracy, the resulting gapped phase must be topologically nontrivial since it cannot adiabatically be deformed into a topologically trivial atomic insulator without closing the energy gap. We use nodal lines which carry a nontrivial monopole charge in three dimensions to illustrate the physics. Notably, because the wrapping surfaces for an extended band degeneracy are diverse, we find that this generalization unearths topological insulators with unconventional patterns of boundary states.
- Received 7 May 2020
- Revised 2 August 2020
- Accepted 14 September 2020
DOI:https://doi.org/10.1103/PhysRevB.102.115151
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