Time-Reversal Invariance at M Point of Surface Brioullin Zone

[fk08]

Hello,

i have a question on the M point of a surface brioullin zone. why is that point a point with time-reversal invariance?

Thanks

 

[kanato]

Time reversal symmetry means $$\psi_{k} = \psi_{-k}^*$$. Periodicity in reciprocal space means that we can translate a point on the surface of the first BZ to a point on the opposite surface, ie. -k + G = k would give exactly the same wavefunction. So that means that $$\psi_{-k}^* = \psi_{k}^* = \psi_{k}$$

 

[fk08]

Consider triangular BZ. How can i see, that Gamma and M has time reversal and K not?