How do you explain one of the biggest open problems in the physics of condensed matter: what causes a certain substance to conduct an electric current, and another substance to function as an insulator? with the help of elephants and giraffes
How do you fit four elephants into a used Volkswagen Beetle? Answer: Through the door. And how do you fit four giraffes into a Volkswagen Beetle? Answer: It is not possible to enter the giraffes, because the elephants are already inside.
This old story can illustrate one of the great open problems in condensed matter physics: What makes one material conduct electricity, and another material act as an insulator? Prof. Alexander Finkelstein, from the Department of Condensed Matter Physics at the Weizmann Institute of Science, recently took a significant step in the long journey to find the answer to this basic question. The findings of his research were published in the scientific journal "Science".
An initial explanation for the phenomenon of the existence of conductive and insulating materials, which was proposed as early as the 30s, was based on the band theory derived from quantum theory, according to which the particles of the material are, at the same time, waves.
According to these theories, the wave function (in other words, the "presence") of an electron present in a crystal of a condensed substance, is stretched across the entire width of the crystal. Since electrons can be found at different energy levels, each group of electrons with similar energy creates a kind of "band" of presences (wave functions). But even between electrons from the same group there are small differences in energy levels. These differences create several "tracks" in the "pass". When electrons can move in the "tracks" of these "stripes", we say that this material conducts an electric current.
Here we can return to the example of elephants and giraffes in the used car. Electrons will not be able to flow in a "band" whose "tracks" (energy levels) are populated by electrons ("there is no room for giraffes, because the elephants are already inside"). On the other hand, the flow is not possible even in a completely empty "strip", simply because there are no electrons to flow in it. In fact, only in a "band" that some of its energy levels (orbits) are occupied, the electrons can jump from an "occupied" orbit to an empty orbit - and flow through it.
This beautiful explanation ignores the basic fact that electrons have a negative electrical charge, which causes them to repel each other. Sir Neville Mott found that this rejection causes each "band" to actually split into two bands. The division into two bands is due to another characteristic of the electrons, called spin (a kind of vortex attack). The spin works in two directions: up, or down, and the electrons are divided into two groups. When each such group rejects the other group, the "lane" is divided into two separate "lanes", the flow through which is also possible only when they are partially populated.
The fact that the splitting is related to the spin property means that interesting magnetic phenomena occur in the material that goes from an insulator to a conductor. But even Mott's explanation does not stand the test of reality when there are impurities in the crystal of the material, or when the crystal itself is not organized in perfect order. Phil Anderson found that in such crystals, the electrons cannot be stretched across the entire crystal, and are located around a small group of atoms only. In these cases, the lack of "strips" and "tracks" prevents the possibility of electron flow, which causes the material to function as an insulator.
These explanations earned Sir Neville Mott, Phil Anderson, and John Hasbrouck and Van Welk the Nobel Prize in Physics for 1977. The problem is that in real matter, both electron repulsion and disorder exist at the same time. Prof. Finkelstein recently made a significant step in this field, when he found a way to explain how these two phenomena - disorder in the crystals of the condensed matter, and the repulsion that works between the electrons - affect each other. This explanation also includes the place of the spin in the phenomenon, (which causes the splitting of each "band" into two separate bands).
Naturally, this mutual influence is dynamic and changes according to different conditions, and Prof. Finkelstein's explanation is based on a set of mathematical equations that define the interrelationships between the phenomena. He also found that, since the electrons repel each other, their tendency to "localize" around a relatively small group of atoms (that is, to avoid flow), decreases, so that the metallic state, in which the material conducts, stabilizes. According to this explanation, the scientists predicted a transition of material ( in thin layers) from a conductor to an insulator. This prediction has been verified in recent experiments. Prof. Finkelstein's new theory also manages to explain magnetic phenomena observed in experiments.
