The Berry phase rectification tensor and the solar rectification vector

@article{Matsyshyn2021TheBP,
  title={The Berry phase rectification tensor and the solar rectification vector},
  author={Oles Matsyshyn and Urmimala Dey and Inti Sodemann and Yan Sun},
  journal={Journal of Physics D: Applied Physics},
  year={2021},
  volume={54}
}
We introduce an operational definition of the Berry Phase Rectification Tensor as the second order change of polarization of a material in response to an ideal short pulse of electric field. Under time reversal symmetry this tensor depends exclusively on the Berry phases of the Bloch bands and not on their energy dispersions, making it an intrinsic property to each material which contains contributions from both the inter-band shift currents and the intra-band Berry Curvature Dipole. We also… 
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