B Time reversal symmetry in topological insulator

[limarodessa]

Hi all

My question:

I have read:

Topological Insulators: Dirac Equation in Condensed Matters

...momenta. A topological insulator preserves time reversal symmetry. Due to the Kramers...

But also I have read:

Observation of a Discrete Time Crystal

...breaking of translation symmetry in time and the emergence of a "time crystal"...

Is it different situations ?

 

[radium]

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.

 

[limarodessa]

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 ?

 

[radium]

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.