Playing billiards with excitons – a milestone towards quantum simulators

18 June 2020

Photo: UHH/Schmelcher, MPQ München

Left is the exciton, consisting of a hole (blue, positively charged) and an electron (red, negatively charged) visible. It has just trapped a second electron (right) and forms a trion, which is a quasiparticle consisting of three particles. The illustration on the right shows how freely moving electrons in two-dimensional semiconductors gather around an exciton (center) and altogether form a larger quasiparticle, a so-called polaron.

Semiconductors play an important role in electronics, optoelectronics or photovoltaics. But like other solids they are quantum many-particle systems. Therefore, calculating their properties with computers is very challenging and sometimes impossible. However, this task could be performed by a quantum system with comparable properties that is fully controllable from outside: a quantum simulator. In a collaboration of the Max Planck Institute of Quantum Optics in Munich with colleagues at Universität Hamburg and ETH Zürich, scientists were able to explain certain properties of an ultra-flat semiconductor. Researchers now have a new toolbox at their disposal to describe these two-dimensional semiconductors in theory, which is an important milestone in the development of corresponding quantum simulators.

Not only in human society in general, but also in physics there are different "cultures". The Munich-Hamburg-Zürich collaboration creates a connecting link between two such physics cultures: quantum optics and solid-state physics. And it is part of a research field that is developing a kind of analogue quantum computer, a so-called quantum simulators. This idea goes back to the famous American theoretical physicist Richard Feynman and is a long-cherished dream.

The current work has now been published as an editor's suggestion in "Physical Review B". It deals with a solid-state system with special properties that were first observed in ultracold quantum gases a few years earlier. Such gases are a popular object of investigation in quantum optics and, as a quantum simulator, have enabled a prediction to be made for a special system of solid-state physics, which has recently been demonstrated experimentally.

The exciton as a billiard ball

In an ultracold quantum gas, the atoms collide like hard billiard balls. In order to be able to apply a corresponding quantum simulator to a solid, it would be helpful if there were also particles in the solid-state system that interact like billiard balls. In fact, these exist in the form of so-called excitons. These particles can be found in any normal semiconductor, for example in a luminous LED or vice versa in a photovoltaic system producing electricity.

For example, an exciton occurs when a quantum of light hits an electron in a semiconductor. If the energy of the photon matches, the electron absorbs this energy, detaches from its atom and moves freely through the semiconductor. This happens when light is converted into electricity. In the original place of the electrons a hole develops, which can also effectively move through the crystal lattice as an electrically positive charge. The electron and the hole attract each other electrically and together they form a so-called quasi-particle, the exciton, which can now also move freely through the semiconductor.

"You can imagine it roughly like a hydrogen atom," explains Prof. Peter Schmelcher from the Cluster of Excellence "CUI: Advanced Imaging of Matter" at Universität Hamburg.  "The hole corresponds to the proton in its atomic nucleus." And this exciton behaves more like a billiard ball, which can only hit another ball in direct contact - like the atoms in a cold quantum gas. However, the electron and the hole of the exciton in ordinary semiconductors are quite far apart. "That could be ten or more nanometers," says Dr. Christian Fey, a former doctoral student at the Center for Optical Quantum Technologies at Universität Hamburg and now a postdoctoral fellow in the Munich group and first author of the scientific paper. When there are other freely moving electrons in a normal, three-dimensional semiconductor, then these not only surround the exciton, they penetrate and destroy it quite quickly. This happens, for example, at electron densities that are technically relevant.

Ultra-flat semiconductors as ideal simulation objects

A two-dimensional semiconductor, on the other hand, is so flat that there are no electrons above and below the exciton that can weaken it. These properties make it the ideal simulation object. The exciton can even survive in a stable condition when there are additional electrons nearby. And not only that: it can also influence the electrons around it in such a way that a so-called polaron is created. This is a many-particle object in which the exciton is "clad" in a cloud of electrons. The mass of the exciton is effectively increased, because it must pull this cloud through the solid.  As an alternative to polaron formation, the exciton can also form a larger quasiparticle, a "trion", with another electron as a third particle.

This state has not yet been found experimentally, but together with other physical properties of a two-dimensional semiconductor crystal it is described in the new collaboration toolbox. This toolbox has already passed an experimental test: It can explain the data for the absorption of light measured on the two-dimensional semiconductor molybdenum diselenide (MoSe2).

"This story from the productive clash of two cultures in physics thus demonstrates a successful application of quantum simulation to a solid-state system. An important milestone in the development of quantum simulators has been reached," Schmelcher says. Text: CUI. For a long version of the text please visit the following web site: https://www.mpq.mpg.de/6275398/playing-pool-with-excitons?c=4455309

Publication

C. Fey, P. Schmelcher, A. Imamoglu, R. Schmidt

"Theory of exciton-electron scattering in atomically thin semiconductors"

Phys. Rev. B 101, 195417 (2020),

DOI: 10.1103/PhysRevB.101.195417