HOPPING.x

This script prints input_hr.dat hamiltonian from the wannier90 package to block-divided form between orbitals.

Usage

python HOPPING.py input out.dat

As an example let's consider PBE band structure of Cu2GeO4 system [Phys. Rev. B 100, 214401 (2019)], which was parametrized by Wannier functions based on Cu(d), O(p) and Ge(s) initial projectors. Total number of Wannier functions is 46, corresponding to 20(5x4) d orbitals of copper, 24(3x8) p orbitals of oxygen and 2(1x2) s orbitals of germanium atoms:

input.json file contains the following information:

   "cell_vectors": [[5.596748, 0.000000,  0.000000], [0.000000,  5.596748,  0.000000], [2.798374, 2.798374, 4.700648]],
   "number_of_atoms": 14,
   "max_sphere_num": 10,
   "print_complex": 0,
   "positions": [[2.79837,   4.19756,   1.17516], [6.99593,   5.59675,   3.52549], [2.79837,   1.39919,   1.17516], [4.19756,   5.59675,   3.52549], [5.59675,   6.94556,   3.37506], [1.44956,   5.59675,   1.02474], [5.59675,   4.24793,   3.37506], [4.14719,   5.59675,   1.02474], [2.79837,   4.24793,   3.67591], [1.44956,   2.79837,   1.32558], [2.79837,   6.94556,   3.67591], [4.14719,   2.79837,   1.32558], [0.00000,   0.00000,   0.00000], [5.59675,   2.79837,   2.35032]],
   "wanniers": [5,5,5,5,3,3,3,3,3,3,3,3,1,1]

• cell_vectors - (3x3)(dfloat) array of unit cell vectors (in Ang);
• number_of_atoms - (int) total number of atoms, parametrized by Wannier functions;
• positions - (3 x number_of_atoms)(dfloat) array of cartesian coordinates of these atoms (in Ang);
• wanniers - (number_of_magnetic_atoms) (int) array of Wannier functions numbers of these atoms;
• max_sphere_num - (int) maximum number of coordination sphere to print the hamiltonian blocks between pair of atoms;
• print_complex - (0 or 1) print the imaginary part of hamiltonian blocks.

As a result, one can find out.dat file, which contains the information from input.json file and output data:

==================================================================

Hopping <a|H|b> between atom 0 (000)<-->atom 0 ( 0 0 0 ) in sphere # 0 with radius 0.000000 -- 1:
Radius vector is: 0.000000 0.000000 0.000000

$$\begin{pmatrix} 7.184363 & 0.000004 & 0.051011 & -0.019062 & -0.000001 \\\ 0.000004 & 6.784132 & 0.000001 & -0.000013 & -0.051461 \\\ 0.051011 & 0.000001 & 6.735531 & -0.040079 & 0.000000 \\\ -0.019062 & -0.000013 & -0.040079 & 6.224034 & 0.000001 \\\ -0.000001 & -0.051461 & 0.000000 & 0.000001 & 7.065857 \end{pmatrix}$$

Hopping <a|H|b> between atom 0 (000)<-->atom 5 ( 0 0 0 ) in sphere # 1 with radius 1.949268 -- 1:
Radius vector is: -1.348810 1.399190 -0.150420

$$\begin{pmatrix} 0.128273 & 0.321582 & -0.328282 \\\ 0.457768 & -0.118238 & 0.154528 \\\ -0.485105 & 0.112035 & -0.064925 \\\ 0.008259 & 0.491431 & 0.435576 \\\ 0.213296 & 0.854884 & -0.889601 \end{pmatrix}$$

...

==================================================================

For example, the last table gives the hamiltonian block 5x3 <Cu(d)|H|O(p)> between atom 0 (Cu(d)) and atom 5 (O(p)) with the distance between them 1.949268 Å and radius vector R = (-1.348810, 1.399190, -0.150420)Å.