Time-reversal symmetry protection

[sagitta]

Hi there! I'm a third-grade physics student and I'm trying to understand the physics of topological insulators, I have found this thread, where somebody else has already asked this question, but in that thread it wasn't really answered in details, they concentrated on other issues.

My question is: What does time-reversal invariance protection mean? As I understand intuitively, it means that if I apply magnetic field to my system or do anything with it, it doesn't change the topological phase, doesn't become simple insulator etc. But I don't really understand why. I know that some quantities are odd under t -> -t transformation and some are even, but I don't know what is the connection between this symmetry and stability of the system.

 

[BigJDubs]

Can you please explain it in more detail?Time-reversal invariance protection is a property of topological insulators that helps to maintain their exotic properties. This means that even if some external perturbations are applied to the system, such as a magnetic field, the topological properties of the system remain unchanged. This is because time-reversal symmetry dictates that certain quantities must be even under a time-reversal operation, meaning that they remain the same after the operation. For example, the Hamiltonian of a system with time-reversal symmetry must still possess time-reversal symmetry after any perturbation is applied. As such, the topological properties of the system remain protected.