SeeK-path: the k-path finder and visualizer

This tool takes in input a crystal structure (in a number of different formats), and

• finds its spacegroup;
• computes the crystallographic primitive cell (i.e., always oriented according to crystallographic standard definitions);
• computes the Brillouin zone;
• provides interactive visualization of primitive cell and Brillouin zone;
• computes all high-symmetry k-points coordinates;
• for band structure plotting, provides a complete list of high-symmetry paths in the Brillouin zone going between the high-symmetry k-points;
• provides copy-paste content to input the kpoints in an external code or input file.

Alternatively, you can calculate and visualize an example.
(There is one example for each possible extended Bravais symbol, both for systems with and without inversion symmetry.)

This tool follows the definitions of the HPKOT paper. The main advantages of this work are:

• use of the crystallographic cells: The conventional cell is standardized according to the definitions that are standard in the field in crystallography: the International Tables of Crystallography (the Tables, from here on), and Parthé, Gelato, Acta Cryst. A40, 169 (1984). Just a couple of examples:
  • orientation of the axes follows the standards mentioned above, e.g., monoclinic cells are always b-axis unique.
  • order of axes is imposed only when not already imposed by symmetry, (following the prescriptions of Parthé and Gelato). E.g., for spacegroup Pmm2 (orthorhombic), the third axis is fixed by symmetry (the one with 180° rotation but no mirror plane). Therefore, we only impose a<b, with no ordering imposed on c.
• Unambiguous high-symmetry k-point labels. For rational k-points, we use the same labels as the ones defined in the Tables. For irrational k-points (not defined in the Tables), letters are chosen so as to never collide with existing letters in the Tables.
• Complete set of high-symmetry paths (band lines), using also spacegroup symmetry when needed. For instance, spacegroup Pm-3 (cubic primitive, extended Bravais lattice cP1) does not have 90° rotation symmetries, so both the lines M–X and M–X₁ must be considered.