Geometric phases and Wannier functions of Bloch electrons in 1-dimension

Abstract

We present a formal expression for Wannier functions of composite bands of 1-D Bloch electrons in terms of parallel-transported Bloch functions and their non-Abelian geometric phases. Spatial decay properties of these Wannier functions are studied in the case of simple bands of 1-D model insulator and metal. Within first-principles density functional theory, we illustrate the formalism through the construction of Wannier functions of polyethylene and polyacetylene.

4 pages, 4 figures

References in corpus (4)

• Band-structure trend in hole-doped cuprates and correlation with Tcmax
• Exponential decay properties of Wannier functions and related quantities
• Electron localization in the insulating state: application to crystalline semiconductors
• Electron localization : band-by-band decomposition, and application to oxides

Cited by in corpus (5)

• Maximally localized Wannier functions: Theory and applications
• Wannier-based definition of layer polarizations in perovskite superlattices
• Raman anomalies as signatures of pressure induced electronic topological and structural transitions in black phosphorus: Experiments and Theory
• Activation of Graphenic Carbon due to Substitutional Doping by Nitrogen: Mechanistic Understanding from First-principles
• Optimally localized Wannier functions for quasi one-dimensional nonperiodic insulators