Topological quantum chemistry.

Area of Science:

• Condensed Matter Physics
• Materials Science
• Quantum Chemistry

Background:

• Topological insulators and semimetals exhibit unique electronic properties due to their topology.
• Current methods have identified only a limited number of topological materials, questioning existing discovery approaches.
• A gap exists in understanding the fundamental principles governing the prevalence of topological properties in materials.

Purpose of the Study:

• To propose a comprehensive electronic band theory that connects material topology with local chemical bonding.
• To establish a framework for classifying all possible band structures across different crystal symmetries.
• To identify a broader range of topological materials beyond those currently known.

Main Methods:

• Developed a theory of topological quantum chemistry, integrating graph theory for reciprocal space and group theory for real space.
• Classified band structures arising from local atomic orbitals for all 230 crystal symmetry groups.
• Identified band structures exhibiting non-trivial topology.

Main Results:

• Established a universal description of band structures and weakly correlated materials based on fundamental chemical and crystallographic principles.
• Successfully classified topologically non-trivial band structures across all crystal symmetry groups.
• Provided new insights into the nature of known topological insulators.

Conclusions:

• The theory of topological quantum chemistry offers a complete electronic band theory, unifying topology and local chemical bonding.
• This approach significantly expands the predicted number of topological materials, suggesting their prevalence is underestimated.
• The framework provides a powerful tool for the systematic discovery of novel topological quantum materials.