Topological Weaire-Thorpe models of amorphous matter

Area of Science:

• Condensed Matter Physics
• Materials Science
• Computational Chemistry

Background:

• Amorphous solids lack systematic classification within topological materials discovery.
• Existing models for topological materials are often not analytically tractable for amorphous structures.
• Realistic models for amorphous solids need to incorporate fixed coordination numbers.

Purpose of the Study:

• Introduce analytically tractable models for amorphous topological materials.
• Enable prediction of spectral gaps and topological phase diagrams in amorphous systems.
• Develop a framework for classifying amorphous topological states.

Main Methods:

• Defined the topological Weaire-Thorpe class of models on amorphous lattices.
• Utilized fixed coordination numbers, characteristic of covalently bonded amorphous solids.
• Employed symmetry under orbital permutation to compute topological phase diagrams.
• Introduced symmetry indicators for amorphous systems to determine quantized observables.

Main Results:

• Analytically predicted spectral gaps based on short-range properties of the models.
• Analytically computed topological phase diagrams, revealing quantized observables like circular dichroism.
• Demonstrated generalizability of models and procedures to higher dimensions and coordination numbers.

Conclusions:

• The developed models provide a route to classifying amorphous topological states.
• This work opens avenues for systematic discovery of new amorphous topological materials.
• The methodology allows for real-space classification using quasilocal properties.