TRIM Points in Brillioun zone

dipole

Hello, I'm trying to find a good reference for how to find or calculate or know which points in the Brillioun zone are "TRIM" (time reversal invariant momentum) points? If anyone is familiar with this topic and could perhaps post a reference or two it would be of great help.

Thanks!

M Quack

At first look time reversal transforms k into -k. For these two points in the BZ to be equivalent, they have to be related by a reciprocal lattice vector G, e.g. -k = k + G or
k = (-)G/2. That would be pretty much all high-symmetry points on the surface of the BZ.

dipole

Thanks for the reply M Quack. I am under the impression that TRIM points are somehow a subset of high symmetry points, that they are "special" high symmetry points.

If it helps at all, TRIM points come up in the context of topological insulators, they are points where the wave function can change its parity I believe.

M Quack

Thanks, that is exactly what my quick scan of Google threw up. Unfortunately none of the papers I looked at were very clear on the definition of TRIM, so I ... improvised.

You know that the BZ is limited by planes in reciprocal space half way to the next reciprocal lattice point. Therefore any point k on the line between the origin and a neighbor reciprocal lattice G point AND on the BZ boundary will fulfill k=G/2.

For some directions the BZ boundary intersects before the half way point. Therefore TRIM points are a subset of the high-symmetry points.