Upto now there are there types of available Topological insulator :
1> The chern Insulator : 2D free electron gas under magnetic field. The integar and fractional quantum hall effct. The chen number is basically the TKNN invariant of occupied band.
2> Z2 Type: As predicted by Cane ad Mele the time reversal invariant topological insulator.
3> Topological crystalline insulator: proposed by Liang Fu PRL 106, 106802 (2011) here the richness and beauty of the crystal symmetry drives the topological nature
Experiment: http://science.sciencemag.org/content/341/6153/1496
One of the common thing among this three class is that they all have non vanishing Berry Curvature !
Now there is this paper predicting a NEW TOPOLOGICAL class without Bery Curvature but Berry connection.
1> The chern Insulator : 2D free electron gas under magnetic field. The integar and fractional quantum hall effct. The chen number is basically the TKNN invariant of occupied band.
2> Z2 Type: As predicted by Cane ad Mele the time reversal invariant topological insulator.
3> Topological crystalline insulator: proposed by Liang Fu PRL 106, 106802 (2011) here the richness and beauty of the crystal symmetry drives the topological nature
Experiment: http://science.sciencemag.org/content/341/6153/1496
One of the common thing among this three class is that they all have non vanishing Berry Curvature !
Now there is this paper predicting a NEW TOPOLOGICAL class without Bery Curvature but Berry connection.
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