How To Track Topological Properties

An ultrafast optical process tickles critical information out of quantum materials.

Topological insulators are exotic quantum materials that, thanks to a special electronic structure, conduct electrical current along their surfaces and edges like a metal. Its interior, on the other hand, is an insulator and not conductive. Scientists at the Max Born Institute for Nonlinear Optics and Short Pulse Spectroscopy (MBI) have now been able to show for the first time how to distinguish such topological materials within a femtosecond (millionth of a billionth of a second) from conventional materials by irradiating them with ultrafast laser pulses. The process could open up new possibilities for using such materials as logical building blocks in light-triggered electronics, allowing information to be processed tens of thousands of times faster than previously possible.

The best known representation of the concept of topology is based on an elastic pretzel, which can be arbitrarily pulled apart, bent or twisted. However they are deformed, it is impossible to make a bagel from a pretzel or add holes without tearing them. The number of holes in a pretzel is fixed and contains topological information about the shape of the pretzel.

In a solid, the laws of quantum physics determine which energies can have electrons. This leads to the formation of so-called electronic bands, which have either allowed or forbidden energies. Using the concept of topology, physicists can now describe complex shaped bands of allowed energies and assign them a specific topological number. A special topology of the electronic band structure in a material system shows up in corresponding exotic properties - such as in the surface conductivity of topological insulators.

"The most extraordinary aspect of topology is its robustness: it protects properties caused by topology," explains Dr. Álvaro Jiménez-Galán from the MBI, one of the two main authors of the article. Just as one can not change the number of holes in a pretzel without tearing them, impurities and other defects - which otherwise affect the electrical conductivity of a material - do not detract from the high electron mobility on topological insulator surfaces. This insensitivity to contamination is the reason why the electronics industry has been very interested in topological materials for some time.

How electrons reveal their topology
Although the topology of a system is closely related to the behavior of the electrons contained in it, the influence of topological properties on the dynamics of the electrons on the time scale of about one femtosecond has not yet been demonstrated. Using numerical simulations and theoretical analyzes, the research team at MBI has now been able to show how information about the topology of such a system is encoded in its ultrafast electron dynamics. This information can be obtained by first exciting the electrons with laser radiation and then analyzing the light they emit.

"If we imagine the electrons in a solid moving along certain energy bands like runners on a race track, then our method allows us to determine the topology of this race track simply by measuring the acceleration of the runners," explains Prof. Dr. Olga Smirnova, head of a theory group at the MBI, said the ultrashort laser pulses excite the electrons in the system to jump from one energy band to a higher one, accelerating on the new "race track." The accelerated electrons emit Light and fall quickly back to the lower lane, the whole process takes only fractions of a second but is long enoughthat an electron can "feel" the subtle difference between the energy structures of ordinary and topological insulators and transmit that information to the emitted light.

On the way to ultra-fast lightwave electronics
The new study shows how to distinguish between ordinary and topological insulators with ultrashort pulses and how to read out the topological information of the system using laser spectroscopy. In the next step, the MBI researchers want to use this knowledge to transform a common insulator into a topological one with the help of laser radiation and vice versa - ie to "write" the topological information accordingly into the material. Theoretical proof of this effect could advance the use of topological materials in optically controlled electronics, where the speed of information processing is limited only by the rate of reaction of the electrons to light.