Parallel transport and band theory in crystals

2014/03/31 by Michel Fruchart, David Carpentier, Krzysztof Gawędzki · 33 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Berry connection and curvature #Natural (archaeology) #Parallel transport #Quantum and electron transport phenomena #Topological Materials and Phenomena #Transport theory #cond-mat.mes-hall #cond-mat.quant-gas #math-ph #math.MP

paper · pdf · doi:10.1209/0295-5075/106/60002

published in Europhysics Letters (EPL) 106(6), 60002 (Institute of Physics) · 5 pages, 1 figure ; minor update

openalex publication_date 2014/06/01 · arxiv created 2014/06/19 · arxiv updated 2014/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We show that different conventions for Bloch Hamiltonians on non-Bravais lattices correspond to different natural definitions of parallel transport of Bloch eigenstates. Generically the Berry curvatures associated with these parallel transports differ, while physical quantities are naturally related to a canonical choice of the parallel transport.

Citations

• Berry’s phase for energy bands in solids
• Quantized Hall Conductance in a Two-Dimensional Periodic Potential
• Holonomy, the Quantum Adiabatic Theorem, and Berry's Phase
• Quantal phase factors accompanying adiabatic changes
• Berry phase effects on electronic properties
• Remarks on the tight-binding model of graphene

Cited by

• Measuring Chern numbers in Hofstadter strips
• Geometry of projected connections, Zak phase, and electric polarization