Theory of composite-band Wannier states and order-N electronic-structure calculations

TL;DR

This paper develops a theoretical framework and practical algorithm for constructing composite-band Wannier states in covalent solids, enabling efficient order-N electronic-structure calculations.

Contribution

It introduces a Hamiltonian that maps Wannier state locality to impurity states, demonstrated with a practical order-N algorithm for diamond-structure solids.

Findings

Wannier states constructed efficiently in covalent systems

Hamiltonian maps Wannier locality to impurity states

Order-N algorithm validated on diamond solids

Abstract

From the order-N electronic-structure formulation, a Hamiltonian is derived, of which lowest eigen state is the generalized or composite-band Wannier state. This Hamiltonian maps the locality of the Wannier state to that of a virtual impurity state and to a perturbation from a bonding orbital. These theories are demonstrated in the diamond-structure solids, where the Wannier states are constructed by a practical order-N algorithm with the Hamiltonian. The results give a prototypical picture of the Wannier states in covalent-bonded systems.