Polarization and Weak Topology in Chern Insulators

Area of Science:

• Condensed matter physics
• Materials science
• Quantum mechanics

Background:

• Topological insulators and Chern insulators pose challenges for constructing localized electronic Wannier functions.
• This difficulty complicates the determination of electric polarization in these materials.

Purpose of the Study:

• To demonstrate that topological insulators exhibit phenomena consistent with bulk electric polarization.
• To investigate the quantization of polarization changes in crystalline domains of strong topological insulators.

Main Methods:

• Theoretical analysis of electronic properties in topological insulators.
• Investigation of bound charges and adiabatic currents.
• Examination of polarization changes across crystalline domain walls.

Main Results:

• Topological insulators exhibit bound charges and adiabatic currents, indicating measurable bulk polarization.
• The change in electric polarization across crystalline domains in strong topological insulators is quantized.
• Crystalline symmetries play a crucial role in the observed quantization.

Conclusions:

• Despite challenges with Wannier functions, bulk electric polarization is a valid concept for topological insulators.
• Quantized polarization changes in domains offer a new perspective on topological properties and potential applications.
• The findings bridge the gap between theoretical concepts and observable phenomena in topological materials.