Topological quantum number

A topological quantum number is like a special code that describes the properties of certain materials or systems. Imagine you have a toy that can change its shape or size without breaking apart or changing its behavior, like a rubber ball or a balloon. These kinds of toys are called topological objects because they have certain properties that don't change even though they can be transformed in different ways.

Now imagine that instead of a toy, we have a material that behaves like a topological object in space or time, like a crystal or a superconductor. This means that the electrons, atoms or molecules that make up the material have special configurations or connections that cannot be broken or changed without affecting their behavior. In other words, the material has a certain "topology" that can be described by mathematical rules or equations.

The topological quantum number is a way to measure how tightly linked the different parts of a material are or how resistant it is to external forces or disturbances. It can also tell us about the presence of special features or boundaries in the material, like insulators, metals or superfluids. The number itself is a whole number or fraction that has specific values depending on the material and the type of measurement or experiment used to obtain it.

By understanding the topological quantum number of a material, scientists can predict or control its behavior under different conditions or applications, like in electronics, photonics, energy storage or quantum computing. In a way, the topological quantum number is like a passport that allows us to explore the exotic and fascinating properties of matter in new and exciting ways.