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 2 in any known material. The author rectifies this s0{0ex}t0{0ex}a0{0ex}t0{0ex}u0{0ex}s q0{0ex}u0{0ex}o by introducing a new class of topological insulators whose wave-function topology is only compatible with materials lacking a center of inversion.