Scientists from Friedrich Schiller University Jena and the University of Regensburg (Germany) have proposed a method that uses light to measure a quantum property of electrons that until now has been difficult to determine experimentally. This concerns Berry curvature - a quantity describing the geometric features of electrons' quantum states. The work was published in the journal Nature Photonics.
In a crystal, electrons do not behave like small balls rolling along set trajectories. Their behavior is determined by quantum states, and researchers group their geometric properties under the term "quantum geometry." Berry curvature is one of the key parameters: among other things, it influences how electrons respond to light and electric fields.
Until now, Berry curvature was mainly calculated theoretically or studied using complex experimental methods. The group from Jena and Regensburg took a different path: it combined optical measurements with an analytical model and was able to quantitatively estimate the local Berry curvature of a material.
"We wanted to make accessible a quantum property that until now has been difficult to determine experimentally," says lead author Nele Tornov of the Institute of Solid State Physics at the University of Jena. "The special feature of our approach is that we combine an optical experiment with a theoretical model and obtain a concrete value for Berry curvature."
For the experiment, tungsten diselenide was used - a semiconductor whose studied layer is thinner than one nanometer. Such atomically thin materials respond especially strongly to light and are well suited to nonlinear optical experiments.
Two ultrashort laser pulses were directed at the sample. The first changes the material's electronic states for a fraction of a second; the second optically records this change. As a result, light is produced with twice the frequency of the incident light. From its polarization - simply put, from how the light oscillates - the researchers obtain information about Berry curvature.
The effect occurs within a few hundred femtoseconds. A femtosecond is one millionth of one billionth of a second. If the direction of rotation of the first laser pulse with circular polarization is changed, the sign of the measured signal also reverses. From the measurement data, the scientists determined the Berry curvature, and the result matched theoretical calculations.
"This optical method makes it possible to study such properties on extremely short time scales," notes Giancarlo Soavi of the Institute of Solid State Physics and the Abbe Center of Photonics at the University of Jena. "In the future, this will give us the opportunity to track how a material's quantum geometry changes during very fast processes."
Although the experiment was performed on tungsten diselenide, the authors emphasize that the principle is not limited to this class of materials. Both the measurement method and the model developed jointly with colleagues from Regensburg are in principle applicable to other materials as well. In the future, the approach could help study the geometric properties of electronic states in more detail and better understand their behavior in fast optical processes.