Hi, I am a PhD student in condensed matter physics and I am studying the Lattice.m module, particularly the function GTBZPath, which implements the nodes of the irreducible Brillouin zone path for a fixed set of lattices.

The question is basically how the coordinates of the nodes already implemented relate to the reciprocal lattice vectors, since they do not show any dependence on the dimension of such reciprocal lattice vectors. Given a set of lattice vectors {v1,v2,v3} I compute the reciprocal basis {k1,k2,k3} using GTReciprocalBasis. Now, given that the nodes have coordinates like {a,b,c}, is this set of numbers like the reduced coordinates of the nodes?, in the sense that the actual coordinates of such node would be n=a*k1+b*k2+c*k3.

If it is not the case, how can I relate this set of points to any set of reciprocal lattice vectors?

Thank you very much in advance.

Currently, GTBZPath gives special points in the Brillouin zone in Cartesian coordinates and in units of 2Pi/a. The reciprocal lattice is in agreement with the corresponding real space lattice provided by GTBravaisLattice. The initial version of GTBZPath is aimed to simplify running the examples for band structure calculations in our book. We are considering extending and generalizing the command (as well as other related modules). Reduced coordinates as mentioned by you are probably the best choice for such an extension.