Of course. Moreover, the topological insulator state could be due to the Rashba splitting.

Thanks, but when will it occur in a topological insulator..

When there is a large internal electric field of the crystal perpendicular to the k. It can be at a surface or in a bulk of complicated crystal. This mechanism can be seen in my paper:

https://www.researchgate.net/publication/273758820_A_Simplified_Approach_to_the_Problems_of_Room-Temperature_Superconductivity

If you put a normal electric field to effect of Rashba splitting in TI there will be no special effects, because the internal field has a much more value.

Article A Simplified Approach to the Problems of Room-Temperature Su...

Hi!

The band inversion is necessary condition and nontrivial Chern number is sufficient condition. If RSOI does not break these two conditions it can exist in TI.

Best Regards

H.Simchi