Are all edge states topological?

[AnGGeL]

Hey am new to this forum but I have a question regarding topologically protected states.. Let's suppose we have a 1D gapped system divided two to distinct regions that have different periodicity or different properties and that at the centre, where the two regions 'meet' states appear in the gap. The simplest example where this happens is the SSH model. But i was wondering whether this is generally true. Are these states always topological?

 

[eljose79]

Hello and welcome to the forum! That is a great question about topologically protected states. The example you mentioned, the SSH model, is indeed a common example of a topological state in a 1D system with two distinct regions. However, whether or not these states are always topological depends on the specific system and its properties.

In general, topological states are characterized by their robustness against perturbations and their non-local nature. So, in your scenario, if the states at the center of the two distinct regions are robust against perturbations and exhibit non-local behavior, then they can be considered topological states. However, if these states can be easily destroyed by perturbations or do not exhibit non-local behavior, they may not be considered topological.

There are many different types of topological states, such as topological insulators, topological superconductors, and topological semimetals, each with their own unique properties and behaviors. So, it is important to carefully analyze the specific system in question to determine if the states at the center of the two regions are topological or not.

I hope this helps answer your question. If you have any further inquiries about topologically protected states, feel free to ask and I would be happy to assist.