Real-Space Berry Phases - Skyrmion Soccer
  Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures - skyrmions - are tailormade to study these Berry phase effects. 
Karin Everschor-Sitte and Matthias Sitte
cond-mat.str-el