Transition state method and Wannier functions

Partly occupied Wannier functions.

We introduce a scheme for constructing partly occupied, maximally localized Wannier functions (WFs) for both molecular and periodic systems. Compared to the traditional occupied WFs the partly occupied WFs possess improved symmetry and localization properties achieved through a bonding-antibonding closing procedure. We demonstrate the equivalence between bonding-antibonding closure and the mini...

Generalized Wannier Functions

We consider single particle Schrodinger operators with a gap in the energy spectrum. We construct a countable set of exponentially decaying functions, which form a complete, orthonormal basis set for the states below the spectral gap. Each such function is localized near a closed surface. Estimates on the exponential decay rate and a discussion of the geometry of these surfaces is included.

Partly occupied Wannier functions: Construction and applications

Maximally localized Wannier functions for GW quasiparticles

We review the formalisms of the self-consistent GW approximation to many-body perturbation theory and of the generation of optimally localized Wannier functions from groups of energy bands. We show that the quasiparticle Bloch wave functions from such GW calculations can be used within this Wannier framework. These Wannier functions can be used to interpolate the many-body band structure from t...

Exponential localization of Wannier functions in insulators.

The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. Our proof relies on the equivalence between the existence of analytic quasi-Bloch functions and the nullity of the Chern numbers (or of the Hall current) for the system under consideration. The same equivalence implie...