Frozen Electrons


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


Every kid today knows what a crystal is - a perfectly regular lattice formed by ions in a solid. A crystal exists only when the temperature is sufficiently low. When heated, it will melt, turning into a liquid and, eventually, a gas.


For many decades, researchers have been trying to find out if it is possible to build a crystal not of the heavy particles in the core of atoms but, instead, of the much lighter electrons. Already in the 1930s, E. Wigner predicted this effect which is now commonly called "Wigner crystallization". And, in fact, in the 1970s electron crystals have been experimentally observed on the surface of helium droplets cooled to very low temperature. In recent years, the remarkable progress in the computer and communication industry continuously demands more memory and faster processors which is being achieved by using smaller and smaller chips. However, this miniaturization is becoming increasingly difficult and costly. This has stimulated the search for new types of devices working on the scale of a few nanometers (one millionth of a meter) and, among others,

renewed the interest in small electron crystals.


The idea is simple: electrons, being the carriers of electric current, are responsible for the peration of all devices. But, if they are trapped in a rigid lattice, they will not be able to move and will act as an insulator. If one would be able to "switch", in a controlled manner, the behavior of a few electrons between crystal-like and liquid-like, one could build extremely small devices such as switches and transistors.


Details of the crystallization of small electron clusters consisting of 20 and fewer electrons have now been completely uncovered by a group of Russian and German researchers. Due to their strong Coulomb repulsion, the electrons were confined by a spherical electrostatic potential. The first observation is that the particles arrange themselves in spherical shells. The innermost shell hosts 6 electrons. Adding another electron will open a second shell and so on - analogously to the famous Mendeleyev table for atoms.


Usually, the electron positions on the shell are not fixed the particles perform oscillations and may jump from one place to another. If the temperature is lowered below a critical value, the magnitude of these vibrations was found to drop rapidly - the cluster freezes into a crystal where electrons cannot leave their lattice sites anymore. It turned out, though, that still one shell as a whole can rotate against the other(s). Decreasing the temperature further, eventually a second transition takes place where also these rotations freeze out, and the radially ordered (RO) crystal transforms into a completely (orientationally ordered, OO) Wigner crystal.


The researchers have rigorously computed the complete boundary of the two crystal phases which turned out to be surprising even for many specialists. For example, this is what happens when

the electron cluster is compressed at constant temperature below the critical one: electrons, at low density behaving like a classical gas, become a liquid and then turn into a crystal (RO phase).

On further compression the crystal transforms into the completely ordered (OO) phase. When the crystal is compressed further, the quantum mechanical nature, i.e. the cloud-like spatial extension of the electrons becomes important: the individual electron begins to feel the "cloud" of the neighboring particles. Overlapping clouds are equivalent to quantum fluctuations. At a critical density, again the shells can rotate with respect to each other, which is so-called "cold" orientational melting. With still further compression the electron overlap grows and the (RO) crystal melts completely.


Another interesting feature is that the temperature and densities where orientational and radial melting occure strongly depend on the number of electrons in the cluster. Some clusters which are called "magic" ones have unusually high stability against orientational melting (for example,

the cluster with 19 electrons melts at a temperature thousands of times higher than the 20 electron cluster). This opens a third road to the crystal phase (besides changing the temperature or density) which has intriguing applications: addition (removal) of a single electron to (from) the cluster.


After the principal picture of Wigner crystallization in few-electron clusters is understood, now the main task is to find situations where this effect could be realized experimentally more easily.





Pictures of the electron crystal

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