A solid crystal contains an innumerable number of electrons which give rise to various interesting and functional properties.

The geometric nature of electrons in solids, known as Bloch electrons, provides novel nonlinear and nonequilibrium phenomena, making its understanding crucial. Therefore, a group of researchers from Japan has recently reviewed the latest developments in the research of such phenomena in solids, with a focus on their geometrical aspects.

The geometrical phase of Bloch electrons is quantified by a parameter called the Berry connection, which measures the coordinate of a Bloch state located away from the center of the unit cell. Engineering the geometrical phase of electrons in crystals generates shift current, a bulk photovoltaic effect and nonreciprocal current, a nonlinear transport phenomenon.

While the Berry connection describes the nonlinear responses of electrons in bulk crystals, the nonequilibrium phenomena can be accounted for using the Floquet theory. It explains the time-evolution of an electron in an oscillating electromagnetic field, characteristic of periodically-driven systems.

The researchers highlight that by illuminating intense laser light, it is possible to drastically change the geometric properties of electrons in trivial materials to develop materials with interesting properties, such as topological insulators, magnets, and superconductors.

Furthermore, geometric nonlinear phenomena in inversion symmetry-broken materials have potential applications in several areas, such as solar panels made of bulk crystals, highly efficient photodetectors, and novel diodes. Also, light induced topological superconductivity could provide a new platform for quantum computing.

In summary, understanding the geometric aspects of nonlinear optical phenomena in crystals would facilitate advanced materials with novel applications.