Generalized Wannier Functions

Abstract

We consider single particle Schrodinger operators with a gap in the en ergy spectrum. We construct a complete, orthonormal basis function set for the inv ariant space corresponding to the spectrum below the spectral gap, which are exponentially localized a round a set of closed surfaces of monotonically increasing sizes. Estimates on the exponential dec ay rate and a discussion of the geometry of these surfaces is included.

References in corpus (3)

• Maximally-localized generalized Wannier functions for composite energy bands
• Analytic structure of Bloch functions for linear molecular chains
• Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators

Cited by in corpus (5)

• On the construction of composite Wannier functions
• Existence and computation of generalized Wannier functions for non-periodic systems in two dimensions and higher
• The Iterated Projected Position Algorithm for Constructing Exponentially Localized Generalized Wannier Functions for Periodic and Non-Periodic Insulators in Two Dimensions and Higher
• Localization of generalized Wannier bases implies Chern triviality in non-periodic insulators
• Ultra-generalized Wannier bases: Are they relevant to topological transport?