What do topological insulators have to do with hall currents?

[nonequilibrium]

Hello,

So a topological insulator can induce a magnetic field when an electric charge is near to it (I can give a reference if necessary), but the thing is, the paper interprets the origin of this magnetic field as being the hall currents on the surface of the topological insulator.

Now I don't see the connection between hall currents and topological insulators? Is it obvious that there should be a thing as a hall current on the surface? Or is it only understandable through teneous quantum mechanical calculations relying on spin-orbit coupling?

Note that I know a little about what quantum hall effect and quantum spin hall effect have to do with topological insulators (the latter being a topological insulator), but in each of these cases, it didn't come across to me that the hall current was playing a role in the story. So maybe I'm overlooking something at that basic level. The easiest "solution" would be "the edge current on the boundar of a quantum hall effect state and e.g. vacuum is a hall current", but I don't think that is true.

 

[eljose79]

Hello,

Thank you for bringing up this interesting topic. The connection between hall currents and topological insulators may not be immediately obvious, but it is an important aspect to consider.

First, let's define what a topological insulator is. It is a material that behaves as an insulator in its bulk, but has conducting states on its surface or edges. These conducting states are protected by topology, meaning they cannot be easily destroyed by external perturbations. This is where the hall currents come into play.

In a topological insulator, the surface or edge states are characterized by a spin-momentum locking, meaning that the spin of the electron is locked to its momentum. This is a result of the strong spin-orbit coupling in these materials. As a charged particle moves along the surface or edge of the topological insulator, it experiences a Lorentz force due to the interaction between its spin and the external magnetic field. This results in the generation of a hall current, which is perpendicular to both the direction of motion and the external magnetic field.

This hall current is a unique feature of topological insulators and is directly related to the spin-momentum locking of the surface or edge states. In fact, the hall conductivity in topological insulators is quantized, just like in the quantum hall effect, further highlighting the connection between the two.

In conclusion, the hall currents on the surface or edge of a topological insulator are a direct result of the spin-momentum locking of its conducting states. It is not just a tenuous quantum mechanical calculation, but a fundamental aspect of these materials. I hope this helps clarify the role of hall currents in topological insulators.