Z2 calculations with first principles code

Dear Sir,

I am a second-year Ph.D. student. I need some help in understanding z2 calculations using first-principles code.

How to clearly distinguish strong topological insulator with a weak topological insulator using z2 pack calculations with first principles.

What is the difference between the following two cases. What does it signify:

1. Z2 topological invariant at kz = 0: 1 Z2 topological invariant at kz = 0.5: 1 (Both 1)

2. Z2 topological invariant at kz = 0: 0 Z2 topological invariant at kz = 0.5: 1 (Only 1 at one surface)

It would be very helpful for my research work if I get some clarity on this.

With warm regards, Raagya Arora JNCASR Bangalore, India