Quantization of intraband and interband Berry phases in the shift current

The theory of the shift current has thus far been geometrical without being topological. This means that the real-space displacement of a photoexcited quasiparticle depends on the geometric Berry phase, but the Berry phase is not quantized to a rational multiple of 2π in any known material. The author rectifies this s00ext00exa00ext00exu00exs q00exu00exo by introducing a new class of topological insulators whose wave-function topology is only compatible with materials lacking a center of inversion.