# Time reversal symmetry in topological insulator

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• limarodessa
In summary, the conversation discusses two different types of topological insulators: Z2 topological insulators, which preserve time reversal symmetry, and Chern insulators, which have broken time reversal symmetry due to the presence of a magnetic field. The second paper mentioned refers to a driven system with periodic time correlations, while the first paper discusses the preservation of time reversal symmetry in Z2 topological insulators. Ultimately, the term "topological insulator" is a general term that can refer to both Z2 topological insulators and Chern insulators, but Z2 topological insulators are the most commonly associated with the term.
Yes. Z2 topological insulators must preserve time reversal symmetry in order for there to be edge states since Kramer's degeneracy occurs in systems with time reversal and an odd number of electrons. The second paper refers to a driven system which has periodic time correlations at some frequency.

Yes. Z2 topological insulators must preserve time reversal symmetry in order for there to be edge states since Kramer's degeneracy occurs in systems with time reversal and an odd number of electrons. The second paper refers to a driven system which has periodic time correlations at some frequency.

1. Does there is broken time-reversal symmetry in Chern insulator or time-reversal symmetry in Chern insulator is preserved ?

2. Does Chern insulator is the topological insulator or it is not such ?

The word topological insulator is actually more general and is technically used to describe a state which is insulating in the bulk and has conducting edge states
The one people most associate with the word topological insulator is thenZ2 topological insulator, which preserves time reversal symmetry. Given the above definition, a chern insulator (like the Haldane model) does not have time reversal symmetry since it is broken by the second nearest neighbor terms from the presence of a magnetic field (the flux from the nearest neighbor terms in the honeycomb is zero, but the flux through the next nearest neighbor terms is not). The Z2 topological insulator is like one copy of the Haldane for each spin (considering spin orbit coupling acting as an effective magnetic field for each spin), so together time reversal is preserved. Time reversal basically transforms The up spins into down spins vice versa. For the field if you think of it microscopically (via the current producing it, it is odd under time reversal.

## 1. What is time reversal symmetry?

Time reversal symmetry is a fundamental principle in physics that states that the laws of physics should be the same regardless of whether time is moving forwards or backwards. In other words, if a physical process can occur in one direction of time, it should also be able to occur in the opposite direction with the same probability.

## 2. What are topological insulators?

Topological insulators are materials that have an insulating interior but conduct electricity along their surface. This unique property is due to the topological order of the material's electronic structure, which is protected by time reversal symmetry.

## 3. How does time reversal symmetry affect topological insulators?

Time reversal symmetry plays a crucial role in the behavior of topological insulators. It ensures that the electronic states on the surface of the material are protected from backscattering, meaning they cannot be reflected back into the bulk of the material. This allows for the efficient flow of electrons along the surface, making topological insulators promising for future applications in electronics and quantum computing.

## 4. Can time reversal symmetry be broken in topological insulators?

While time reversal symmetry is a fundamental principle, it can be broken in certain systems, including topological insulators. This can occur through the application of external magnetic or electric fields, which can alter the electronic structure of the material and disrupt the protection of the surface states.

## 5. What are the practical implications of understanding time reversal symmetry in topological insulators?

Understanding time reversal symmetry in topological insulators is important for further advancing the field of topological materials and potentially developing new technologies. It could also shed light on other areas of physics, such as the study of quantum mechanics and the behavior of matter at the atomic level.

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