Electricity is created by electrons flowing through materials. Materials that allow electrons to travel through, like copper wires, are called conductors, whereas materials that inhibit electron flow, like rubber, are called insulators. However, the models behind our understanding have been incomplete. To understand which materials permit electron movement, scientists have investigated the patterns of electron motion in materials.

Electrons do not behave like macroscopic objects. While we can use Newton’s equations (force equals mass times acceleration) to know exactly where a macro-object will move, electrons obey a different equation called *Schrödinger’s Equation. *This equation can only tell us the probability of where the electron will be. With a large number of electrons, we can predict the distribution of electrons in the material. The best-known distribution is called the bell-curve, and predicts that most of the numbers in the distribution are piled up near the center (see figure). In an insulator, we see that electrons have this bell curve. Since their distribution shows a high probability to be around one point, the electrons are localized in the material; that is, we don’t expect electrons to move around much. For a conductor, the predicted distribution is nearly uniformly-spaced. We expect the electrons to be spread evenly throughout the conductor rather than ‘trapped’ in space. Therefore, materials that yield peaked distributions are insulators, whereas materials with flat distributions are conductors. This model supports our long-held theories about conductors and insulators, and can be used to identify better conductive material.

And finding materials that are excellent conductors is a lucrative business. As electrons move through materials, they can bump into atoms and lose energy which hurts the efficiency of power distribution. The materials that do not lose energy, called *superconductors*, must operate at temperatures far colder than what can be achieved for power grids. Physicists are actively searching for materials that can be superconducting near room temperature, which would greatly reduce the cost of energy. In order to find optimal conductors that function at temperatures reachable outside of a laboratory setting, scientists must first understand the underlying principles of these materials. This paper moves us further along in that direction.

**Managing Correspondent**: Cari Cesarotti

**Read More:** Universal Pattern Explains Why Materials Conduct

**Image Credits:** Bulat Burganov, Binomial Distribution (bell curve). Wolfram MathWorld.

Thank you for your explanation! It help me a lot in better understanding the conductivity of materials. But I still have some questions. Since electrons follow the bell-curve distribution, does that mean that electrons can still move around the center location? If it is true, then what’s the range of the movement length? Or in another word, what’s the lateral scale of the bell-curve figure? And the last question is that, if we inject some free electrons into an ideal insulator, how do they move around? I would be quite appreciate for your replying!