Symmetry-adapted closest Wannier modeling based on complete multipole basis set

TL;DR

This paper introduces a symmetry-adapted Wannier modeling method using a complete multipole basis, enabling accurate, symmetry-respecting tight-binding models and revealing hidden electronic multipole interactions.

Contribution

The authors develop a non-iterative, symmetry-preserving Wannier modeling approach based on a complete multipole basis, enhancing electronic structure analysis.

Findings

Successfully modeled monolayer graphene under electric field

Restored symmetry in Wannier Hamiltonians

Quantified symmetry breaking and electronic multipole effects

Abstract

We have developed a method to construct a symmetry-adapted Wannier tight-binding model based on the closest Wannier formalism and the symmetry-adapted multipole theory. Since the symmetry properties of the closest Wannier functions are common to those of the original atomic orbitals, symmetry-adapted multipole basis (SAMB) can be defined as the complete orthonormal matrix basis set in the Hilbert space of the closest Wannier functions. Utilizing the completeness and orthonormality of SAMBs, the closest Wannier Hamiltonian can be expressed as a linear combination of SAMBs belonging to the identity irreducible representation, thereby fully restoring the symmetry of the system. Moreover, the linear coefficients of each SAMB (model parameters) related to crystalline electric fields, spin-orbit coupling, and electron hoppings are determined through simple matrix projection without any iterative procedure. Thus, this method allows us to unveil mutual interplay among hidden electronic multipole degrees of freedom in the Hamiltonian and numerically evaluate them. We demonstrate the effectiveness of our method by modeling monolayer graphene under a perpendicular electric field, highlighting its utility in symmetrizing the closest Wannier model, quantifying symmetry breaking, and predicting unusual responses. The method is implemented in the open-source Python library SymClosestWannier, with the codes available on GitHub (https://github.com/CMT-MU/SymClosestWannier).