What is it about?
To describe the solution to a quantum-mechanical problem a choice for the basis set has to be made depending on the type of system investigated. For example electrons in a molecule can be well described by localised orbitals, whereas electrons in a metal can be depicted as plane waves. In this article I present a "middle way" for describing electrons in a crystalline solid.
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Why is it important?
The functions I introduce respect the translational invariance of the crystal, like a plane wave, yet they are reminiscent of the localised orbital from which they originated. This characteristic is useful when dealing with "crystalline topological materials", that is crystalline solids whose properties are qualitatively different from those of the atoms that make up the material. The claim I make is that the discovery of crystalline topological materials can be aided by using the methods in the article.
Perspectives
The study of theta functions that I employ is a fascinating research field in its own right, originating in the 19th century and spanning different areas of mathematics. Their rich mathematical properties can help us discover new mechanisms that underlie the existence of topological materials.
Emanuele Maggio
Scuola Superiore Meridionale
Read the Original
This page is a summary of: Exploiting ϑ-functions for the identification of topological materials, AIP Advances, August 2025, American Institute of Physics,
DOI: 10.1063/5.0256857.
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