SCS: Hanwen Zhang (Yale), Wannier functions in electronic structure calculations

Tuesday Apr 15, 2025, 10:00 AM → 11:00 AM America/New_York

3rd floor classroom (162)

Title: Constructing optimal Wannier functions via potential theory

Abstract:

In this talk, I will present a rapidly convergent scheme for computing exponentially localized Wannier functions of isolated bands. Wannier functions are localized molecular orbitals in crystalline materials. They provide an alternative representation of a material’s electronic band structure, usually characterized by delocalized Bloch functions. Besides providing chemical insights into material properties, Wannier functions also reflect the topological properties of a band. Moreover, they are indispensable tools for many computational tasks in solid-state physics. The scheme in this talk is non-iterative and computes the desired Wannier functions via parallel transport. Relevant geometric/topological quantities, such as Berry connections and first Chern numbers, appear naturally during this process. The resulting Wannier functions can be further optimized for better localization by eliminating the divergence of the Berry connections, which can be done efficiently by solving Poisson’s equation via FFTs. I will demonstrate numerical results from both single and multi-band examples.

Hosts: Alex Barnett, Jason Kaye