Topological zero-dimensional defect and flux states in three-dimensional insulators

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Mechanics

Background:

• Topological electronic states were previously identified in insulating crystals at defects with lower dimensionality.
• The classification of topological defect states requires further extension to encompass higher-order phenomena.

Purpose of the Study:

• To extend the classification of topological defect states by identifying higher-order end (HEND) states.
• To demonstrate that HEND states are intrinsic topological consequences of bulk electronic structure.
• To introduce new bulk topological invariants predictive of HEND dislocation states.

Main Methods:

• Theoretical analysis of crystalline defects with integer Burgers vectors.
• Introduction of novel bulk topological invariants.
• Investigation of topological states in PbTe monolayers and SnTe crystals.
• Relating analysis to magnetic flux insertion in insulating crystals.

Main Results:

• Demonstrated the binding of 0D HEND states with anomalous charge and spin at the corners of crystalline defects.
• Established HEND states as intrinsic topological consequences of bulk electronic structure.
• Identified first-order 0D defect states in PbTe monolayers and HEND states in 3D SnTe crystals.
• Found that π-flux tubes in helical higher-order topological insulators bind Kramers pairs of spin-charge-separated HEND states.

Conclusions:

• HEND states represent a new class of topological defect states with unique properties.
• The introduced bulk topological invariants can predict HEND dislocation states in materials.
• The observed HEND states in SnTe crystals and their relation to magnetic flux tubes offer observable signatures of anomalous surface half quantum spin Hall states.