Quantitative relationship between polarization differences and the zone-averaged shift photocurrent

@article{Fregoso2016QuantitativeRB,
  title={Quantitative relationship between polarization differences and the zone-averaged shift photocurrent},
  author={Benjamin M. Fregoso and Takahiro Morimoto and Joel E Moore},
  journal={Physical Review B},
  year={2016},
  volume={96},
  pages={075421}
}
A relationship is derived between differences in electric polarization between bands and the ``shift vector'' that controls part of a material's bulk photocurrent, then demonstrated in several models. Electric polarization has a quantized gauge ambiguity and is normally observed at surfaces via the surface charge density, while shift current is a bulk property and is described by shift vector gauge invariant at each point in momentum space. They are connected because the same optical… 

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