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Example 2: Disturbed Diamond Supercell

Disturbed \(2 \times 2 \times 2\) Diamond

Now we consider a more realistic case of a disturbed SC where unfolding weights are not only 0 or 1. In this example, we are going to unfold the band structure of a disturbed \(2\times 2 \times 2\) diamond SC to the PC k-path \(\Gamma (0, 0, 0) - M (0.5 ,0,0.5)\).

Geometry

lattice_vector 0.0000000000000000 3.5370480743960000 3.5370480743960000 
lattice_vector 3.5370480743960000 0.0000000000000000 3.5370480743960000 
lattice_vector 3.5370480743960000 3.5370480743960000 0.0000000000000000 
atom_frac 0.0034522138685516 0.0010265461377090 0.0096830381856692 C
atom_frac 0.5107673460286567 -0.0040894299438661 -0.0152942515572113 C
atom_frac 0.0026513963582662 0.4801543341478594 0.0113654454191475 C
atom_frac 0.4962265395199286 0.4979453568455721 0.0009603430783825 C
atom_frac -0.0011785475591161 0.0165193747626418 0.4913997525804544 C
atom_frac 0.4954348644380653 -0.0148694573814163 0.5036124496712057 C
atom_frac 0.0011624231033274 0.4966670514782747 0.4929239964416142 C
atom_frac 0.4816744102276218 0.5029554493216754 0.5136817103554485 C
atom_frac 0.1437809870942692 0.1201530788816737 0.1218779580192683 C
atom_frac 0.6226940144564765 0.1178104186848227 0.1334367931239557 C
atom_frac 0.1143995502453649 0.6376281355472183 0.1471419277881658 C
atom_frac 0.6235394485319055 0.6233509357056823 0.1228684277218698 C
atom_frac 0.1248922061558824 0.1247955400420933 0.6121137499973340 C
atom_frac 0.6288765039017798 0.1355352218462510 0.6167725376498303 C
atom_frac 0.1272098977741730 0.6376059045876353 0.6168866468147000 C
atom_frac 0.6244167458548475 0.6268115393361741 0.6205694747101654 C
This structure is originated from a prototype of a \(2\times 2 \times 2\) diamond SC but with disturbed atomic positions. In comparison, the PC structure is:

lattice_vector -0.0000000000000000 1.7685240371980000 1.7685240371980000 
lattice_vector 1.7685240371980000 -0.0000000000000000 1.7685240371980000 
lattice_vector 1.7685240371980000 1.7685240371980000 -0.0000000000000000 
atom 0.0000000000000000 0.0000000000000000 0.0000000000000000 C
atom 0.8842620185990002 0.8842620185990002 0.8842620185990002 C

As usual, we can check the reference band structures before the band unfolding calculation:

The SC band structure is much more complex than in the previous example, as the degenerate bands are split due to the symmetry breaking in a distorted cell.

Control tags

output band                        -0.5 -0.0 -0.5 0.5 0.0 0.5 65
bs_unfolding                       True

Other input files

2 0 0
0 2 0
0 0 2


1
1
1
1
1
1
1
1
9
9
9
9
9
9
9
9
Here the 1-8 SC atoms corresponding to the same PC atom as the SC atom 1 and the 9-16 SC atoms corresponding to the same PC atom as the SC atom 9. Aware that the mapping relation in unfolding_map.dat must be consistent with the geometry.in.

If one re-shuffle the atomic order in the geometry.in, the unfolding_map.dat must be updated simultaneously. For instance, another geometry file with different atomic order can be:

lattice_vector 0.0000000000000000 3.5370480743960000 3.5370480743960000 
lattice_vector 3.5370480743960000 0.0000000000000000 3.5370480743960000 
lattice_vector 3.5370480743960000 3.5370480743960000 0.0000000000000000 
atom_frac 0.0034522138685516 0.0010265461377090 0.0096830381856692 C
atom_frac 0.1437809870942692 0.1201530788816737 0.1218779580192683 C
atom_frac 0.5107673460286567 -0.0040894299438661 -0.0152942515572113 C
atom_frac 0.6226940144564765 0.1178104186848227 0.1334367931239557 C
atom_frac 0.0026513963582662 0.4801543341478594 0.0113654454191475 C
atom_frac 0.1143995502453649 0.6376281355472183 0.1471419277881658 C
atom_frac 0.4962265395199286 0.4979453568455721 0.0009603430783825 C
atom_frac 0.6235394485319055 0.6233509357056823 0.1228684277218698 C
atom_frac -0.0011785475591161 0.0165193747626418 0.4913997525804544 C
atom_frac 0.1248922061558824 0.1247955400420933 0.6121137499973340 C
atom_frac 0.4954348644380653 -0.0148694573814163 0.5036124496712057 C
atom_frac 0.6288765039017798 0.1355352218462510 0.6167725376498303 C
atom_frac 0.0011624231033274 0.4966670514782747 0.4929239964416142 C
atom_frac 0.1272098977741730 0.6376059045876353 0.6168866468147000 C
atom_frac 0.4816744102276218 0.5029554493216754 0.5136817103554485 C
atom_frac 0.6244167458548475 0.6268115393361741 0.6205694747101654 C
In this case, the corresponding unfolding_map.dat is:

1
2
1
2
1
2
1
2
1
2
1
2
1
2
1
2
The atomic order will not affect the unfolding results, as long as the mapping relation is correct.

Run the calculation

A parallel simulation with N processes can be launced by typing

mpirun -n N your_aims.x > aims.out
The binary name your_aims.x should be replaced by your FHI-aims binary file.

Checking the result

The format of output files are exactly the same as the previous example. After post-processing, we can visualize the unfolded band:

The color transparency indeicates the unfolding weight, in this case the unfolded weights are fractional due to the symmetry breaking, which can be understood as the electron spectral function.

Solutions

You find all the solution to all the above exercises by clicking on the button below.

Show solutions to Part 2