Extreme conditions in semiconductors

Credit: Leitenstorfer research team

Scientists from the University of Konstanz and Paderborn University have succeeded in producing and demonstrating what is known as Wannier-Stark localization for the first time. In doing so, the physicists managed to overcome obstacles that had so far been considered insurmountable in the field of optoelectronics and photonics. Wannier-Stark localization causes extreme imbalance within the electric system of crystalline solids. "This fundamental effect was predicted more than 80 years ago. But it has remained unclear ever since whether this state can be realized in a bulk crystal, that is, on the level of chemical bonds between atoms", says Professor Alfred Leitenstorfer, Professor of Experimental Physics at the University of Konstanz. Analogues of the effect have so far been demonstrated only in artificial systems like semiconductor superlattices or ultracold atomic gases. In a bulk solid, Wannier-Stark localization can only be maintained for an extremely short period of time, shorter than a single oscillation of infrared light. Using the ultrafast laser systems at the University of Konstanz, Wannier-Stark localization has now been demonstrated for the first time. The experiment was conducted in a high-purity gallium arsenide crystal grown at ETH Zurich using epitaxial growth. The research results were published in the scientific journal Nature Communications on 23 July 2018.

What is Wannier-Stark localization?

If we tried to picture the atoms of a crystal, it would have to be as a three-dimensional grid composed of small beads that repel each other and are only kept together by rubber bands. The system remains stable as long as the rubber band is as strong as the repulsion is. If this is the case, the beads neither move closer to each other, nor do they move away from each other – the distance between them remains about the same. Wannier-Stark localization occurs when the rubber bands are removed abruptly. It is the electronic state that happens at the precise moment in time when the rubber bands have already gone but the beads still remain in place: The chemical bonds that hold the crystal together have been suspended.

If this state is maintained for too long, the beads will break apart and the crystal dissolves. To analyze Wannier-Stark localization, the physicists had to remove the stabilizing structures, capture the system within a fraction of a light oscillation using light pulses, and finally to stabilize it again to prevent the atoms from breaking apart. The experiment was made possible through the highly intense electric field of an ultrashort infrared light pulse, which is present in the crystal for a few femtoseconds only. "This is what we specialize in: studying phenomena that only exist on very short time scales", explains Alfred Leitenstorfer.

"In perfect insulators and semiconductors, electronic states expand throughout the entire crystal. According to an 80-year-old prediction, this changes as soon as electrical voltage is applied", says Professor Torsten Meier from Paderborn University. "If the electric field inside the crystal is strong enough, the electronic states can be localized to a few atoms. This state is called the Wannier-Stark ladder", explains the physicist, who is also Vice-President for International Relations at Paderborn University.

New electronic characteristics

"A system that deviates so extremely from its equilibrium has completely new characteristics", says Alfred Leitenstorfer about why this state is so interesting from a scientific perspective. The short-lived Wannier-Stark localization correlates with drastic changes to the electronic structure of the crystal and results, for example, in extremely high optical nonlinearity. The scientists also assume that this state is chemically particularly reactive.

The first-ever experimental realization of Wannier-Stark localization in a gallium arsenide crystal was made possible through highly intense Terahertz radiation with field intensities of more than ten million volts per centimetre. The application of more ultrashort optical light pulses resulted in changes to the crystal's optical characteristics, which was instrumental to proving this state. "If we use suitably intense light pulses consisting of a few oscillations lasting some ten femtoseconds only, we can realize the Wannier-Stark localization for a short period of time", says Alfred Leitenstorfer. "Our readings match the theoretical considerations and simulations carried out both by my own research team and by that of my colleague, Professor Wolf Gero Schmidt", adds Torsten Meier. The researchers are planning to study the extreme state of Wannier-Stark localization on the atomic scale in more detail in the future and intend to make its particular characteristics usable.



  • Scientists from the Universities of Konstanz, Paderborn and ETH Zurich succeed in experimentally demonstrating Wannier-Stark localization in a high-purity gallium arsenide crystal grown at ETH Zurich.
  • Original publication: C. Schmidt, J. Bühler, A.-C. Heinrich, J. Allerbeck, R. Podzimski, D. Berghoff, T. Meier, W. G. Schmidt, C. Reichl, W. Wegscheider, D. Brida, A. Leitenstorfer: Signatures of transient Wannier-Stark localization in bulk gallium arsenide, Nature Communications 9, 2890 (2018), direct link: https://rdcu.be/3ntP
  • Wannier-Stark localization occurs in extremely high electric fields in solid-state crystals and results in new characteristics such as optical nonlinearity. The scientists also assume that this state exhibits extremely high chemical reactivity.
  • Implementation of Wannier-Stark localization through highly intense Terahertz radiation with field intensities of more than ten million volts per centimetre. Demonstration through ultrashort light pulses in the femtosecond range.
  • Research funded through: ERC Advanced Grant 290876 "UltraPhase" of the European Research Council (ERC, A. Leitenstorfer, Konstanz), Emmy Noether Programme of the German Research Foundation (DFG, D. Brida, Konstanz), Collaborative Research Centre SFB-TRR 142 (DFG, T. Meier and W. G. Schmidt, Paderborn), Carl Zeiss Foundation (J. Bühler, Konstanz), Swiss National Science Foundation (C. Reichl and W. Wegscheider, Zurich).

Note to editors:

You can download photos here:


Caption: Close-up of the experimental setup in the University of Konstanz's high-field Terahertz lab. Under the extreme conditions of the experiment, a bright red glow can be seen to emanate from the gallium arsenide crystal used as a semiconductor. This is due to the system's extremely high optical nonlinearity, which occurs when Wannier-Stark localization sets in.

Photo: Leitenstorfer research team


Caption: Professor Alfred Leitenstorfer, Professor of Experimental Physics at the University of Konstanz

Photo: University of Konstanz


University of Konstanz
Communications and Marketing
Phone: + 49 7531 88-3603
E-Mail: [email protected]

                                <p><strong>Media Contact</strong></p>    <p>Julia Wandt<br />[email protected]<br />


%d bloggers like this: