Can you heat the electron

(A.V. Filinov, M. Bonitz, and Yu.E. Lozovik, Physical Review Letters 86, 3851 (2001)

Every child nowadays knows what a crystal is - a regular lattice, formed from the ions into a solid. A crystal only exists when the temperature is low enough. When heated, it melts, transforming into a liquid and - with further heating - into a gas.

For many decades researchers have tried to find out whether it is possible to form a crystal not from the heavy particles in the atomic nucleus, but from the much lighter electrons. E. Wigner had theoretically predicted this effect as early as the 1930s, which has since been referred to as Wigner crystallization. Indeed, in the 1970s, it was possible to experimentally observe such an electron crystal - on the surface of tiny helium droplets that had been cooled to very low temperatures.

In recent years, the breathtaking advances in computing and communications technology have resulted in ever-increasing demands for ever faster processors and ever more memory. Up to now, this has been achieved by constantly downsizing semiconductor chips. However, this miniaturization is technically becoming more and more complicated and expensive. For this reason, new technologies and physical principles are being sought all over the world, according to which circuits in the nanometer range (1nm = 0.000 000 001 meters) could function. In particular, one has again turned to the phenomenon of the crystallization of electrons.

The idea is simple: electrons, which transport the electric current, are crucial for the functioning of all devices and chips. If the electrons are now "trapped" in a crystal, they have no way of moving: the material behaves like an insulator. If it were also possible to selectively "switch" the behavior of a handful of electrons from crystal-like to liquid, one would be able to use it to produce extremely small electronic components such as switches or transistors.

The details of the crystallization of such small clusters of no more than 20 electrons have now been fully clarified by a group of German and Russian physicists in a cooperation between the University of Rostock and the Moscow Institute for Spectroscopy. Since the electrons repel each other very strongly, they have to be held from outside. A circular electric field was used in the calculations. The first observation was that the electrons arrange themselves in circular shells. 6 electrons can sit on the inner shell. If another is added, a second shell is formed spontaneously, etc. - very similar to the famous Mendelejev periodic table of the elements.

It turned out that the electrons are usually not firmly seated in their shell positions - they swing back and forth and can even jump from one place to another. If the temperature is now lowered below a critical value, the electron vibrations are suddenly reduced - the cluster freezes to a crystal in which the electrons can no longer leave their lattice positions. However, it is still possible that two shells with all their electrons can rotate against each other. If the temperature is now further reduced, a second phase transition occurs, in which these rotations also "freeze". The electron Wigner crystal changes from the partially ordered phase (1) to a fully ordered state (2).

The researchers succeeded in determining the melting parameters of the Wigner crystal completely and precisely, and the results came as a surprise even to many specialists. For example, it is very interesting what happens to the crystal when it is pressed together at a constant low temperature: initially the electrons behave like an ordinary gas, under pressure they transform into a liquid and finally into a phase 1 crystal Compression, the crystal goes into phase 2. If the pressure is increased even further, the laws of quantum mechanics come into play, according to which every electron has a spatial extension and thus resembles a cloud. With increasing compression, the "clouds" of neighboring electrons come closer and closer. They begin to penetrate each other, whereby the electrons suddenly have the opportunity to "jump" from one place to another. This increase in quantum fluctuations ultimately leads to the "melting" of the Wigner crystal, it even melts at a temperature of 0 degrees Kelvin.

Another very interesting observation was that the melting temperature (and pressure) are very dependent on the number of electrons in the cluster. In particular, there are "magic" clusters with a special symmetry (e.g. a cluster of 19 electrons) that have an unusually stable second phase. If only a single electron is added, the transition temperature between phase one and two drops dramatically by more than a thousand times. This opens up completely new and promising application possibilities for these systems. The crystallization of electrons can now be controlled not only in the conventional way by changing temperature or pressure, but also simply by adding or removing just a single electron.

Now that all the basic questions of Wigner's crystallization in small electron clusters have been understood, the researchers are now concerned with finding the situations in which these effects can be most easily realized in semiconductor structures.

Images of the electron crystal

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