Concept of Quantum Geometry in Optoelectronic Processes in Solids: Application to Solar Cells

The concept of topology is becoming more and more relevant to the properties and functions of electronic materials including various transport phenomena and optical responses. A pedagogical introduction is given here to the basic ideas and their applications to optoelectronic processes in solids. A pedagogical review on the geometry in the quantum theory of electrons in solids is presented. The Bloch wavefunction in momentum space is characterized by the Berry phase, i.e., the connection between the neighboring crystal momenta, which acts as the intracell coordinate. The optical transition induces the shift of this intracell coordinate to result in a DC current in noncentrosymmetric crystals called the shift current.