Spread-balanced Wannier functions: Robust and automatable orbital localization

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...

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.

Wannier orbital overlap population (WOOP), Wannier orbital position population (WOPP) and the origin of anomalous dynamical charges.

Most d(0) transition metal (TM) oxides exhibit anomalously large Born dynamical charges associated with off-centering or motion of atoms along the TM-O chains. To understand their chemical origin, we introduce "Wannier orbital overlap population" (WOOP) and "Wannier orbital position population" (WOPP) in terms of the Wannier function based description of electronic structure obtained within fir...

Partly occupied Wannier functions: Construction and applications