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irreducible-representations / irrep

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zero eigenvalue for inversion symmetry #34

Closed bfocassio closed 3 years ago

bfocassio commented 3 years ago

Dear all,

I'm trying to compute the eigenvalues for the inversion symmetry operator for MoS2 in the TMDC-H' structure.

The problem is that I'm getting eigenvalues equal to zero at some TRIM points.

The output is:

'NoneType' object has no attribute 'split'

 ----------INFORMATION ABOUT THE UNIT CELL----------- 

Primitive vectors : 
 [[ 5.722851  0.        0.      ]
 [ 0.        3.173255  0.      ]
 [ 0.        0.       20.16    ]] 
 Atomic positions: 
 [[0.802497 0.75     0.49631 ]
 [0.197503 0.25     0.50369 ]
 [0.083583 0.75     0.586158]
 [0.578635 0.25     0.565937]
 [0.421365 0.75     0.434063]
 [0.916417 0.25     0.413842]] 
 Atom type indices: 
 [1, 1, 2, 2, 2, 2]
 Reciprocal lattice:
 [[1.09791174 0.         0.        ]
 [0.         1.98004425 0.        ]
 [0.         0.         0.31166594]]
reading symmetries
Placing origin at  [0. 0. 0.]
where [0. 0. 0.] = [0. 0. 0.] + [0. 0. 0.] x refUC

The transformation to the convenctional cell is given by:
        |   1.0000  0.0000  0.0000 |
refUC = |   0.0000  1.0000  0.0000 |    shiftUC = [-0. -0. -0.]
        |   0.0000  0.0000  1.0000 |

Lattice vectors of DFT (a) and reference (c) cells:
a(0)=[  5.7229  0.0000  0.0000 ]    c(0)=[  5.7229  0.0000  0.0000 ]
a(1)=[  0.0000  3.1733  0.0000 ]    c(1)=[  0.0000  3.1733  0.0000 ]
a(2)=[  0.0000  0.0000 20.1600 ]    c(2)=[  0.0000  0.0000 20.1600 ]
Efermi = -2.5126 eV
WAVECAR contains 4 k-points and 44 bands.
 Saving 36 bands starting from 1 in the output
Energy cutoff in WAVECAR :  400.0
Energy cutoff reduced to :  50.0
0 0
10 1055
20 3927
30 6151
0 0
10 1044
20 3912
30 6128
0 0
10 1028
20 3952
30 6148
0 0
10 1028
20 3966
30 6188

 ---------- INFORMATION ABOUT THE SPACE GROUP ---------- 

Space group P2_1/m (# 11) has 4 symmetry operations  

 ### 1 

rotation : |  1   0   0 |
           |  0   1   0 |
           |  0   0   1 |

spinor rot.         : | 1.000+0.000j  0.000+0.000j |
                      | 0.000+0.000j  1.000+0.000j |
spinor rot. (refUC) : | 1.000+0.000j  0.000+0.000j |
                      | 0.000+0.000j  1.000+0.000j |

translation         :  [   0.0000   0.0000   0.0000 ] 

axis: [0. 0. 1.] ; angle =  0 , inversion : False

 ### 2 

rotation : | -1   0   0 |
           |  0   1   0 |
           |  0   0  -1 |

spinor rot.         : | 0.000+0.000j -1.000+0.000j |
                      | 1.000+0.000j  0.000+0.000j |
spinor rot. (refUC) : |-0.000+0.000j  1.000-0.000j |
                      |-1.000+0.000j -0.000+0.000j |

translation         :  [   0.0000   0.5000   0.0000 ] 

axis: [0. 1. 0.] ; angle = 1 pi, inversion : False

 ### 3 

rotation : | -1   0   0 |
           |  0  -1   0 |
           |  0   0  -1 |

spinor rot.         : | 1.000+0.000j  0.000+0.000j |
                      | 0.000+0.000j  1.000+0.000j |
spinor rot. (refUC) : | 1.000+0.000j  0.000+0.000j |
                      | 0.000+0.000j  1.000+0.000j |

translation         :  [   0.0000   0.0000   0.0000 ] 

axis: [0. 0. 1.] ; angle =  0 , inversion : True

 ### 4 

rotation : |  1   0   0 |
           |  0  -1   0 |
           |  0   0   1 |

spinor rot.         : | 0.000+0.000j -1.000+0.000j |
                      | 1.000+0.000j  0.000+0.000j |
spinor rot. (refUC) : |-0.000+0.000j  1.000-0.000j |
                      |-1.000+0.000j -0.000+0.000j |

translation         :  [   0.0000   0.5000   0.0000 ] 

axis: [0. 1. 0.] ; angle = 1 pi, inversion : True

reading symmetries

k-point   1 :[0. 0. 0.] 
 number of states = 328
   Energy  |   degeneracy  |        irreps        | sym. operations  
           |               |                      |     1        2        3        4    
 -14.0380  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000   0.0000   2.0000   0.0000
 -13.0505  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000   0.0000  -2.0000   0.0000
 -12.3138  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000   0.0000  -2.0000  -0.0000
 -12.2332  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000   0.0000
  -5.9864  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000  -0.0000  -2.0000  -0.0000
  -5.3411  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000  -0.0000
  -4.5843  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000   0.0000
  -4.4817  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000   0.0000  -2.0000   0.0000
  -3.3463  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000   0.0000  -2.0000  -0.0000
  -3.2443  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000   0.0000
  -2.8413  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000   0.0000
  -2.4726  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000   0.0000   2.0000   0.0000
  -1.9148  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000   0.0000  -2.0000   0.0000
  -1.2695  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000   0.0000  -2.0000   0.0000
  -0.9933  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000  -0.0000
  -0.4827  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000  -0.0000
  -0.3277  |        2      | -GM5(1.0), -GM6(1.0) |   2.0000   0.0000  -2.0000   0.0000
  -0.0962  |        2      | -GM3(1.0), -GM4(1.0) |   2.0000  -0.0000   2.0000   0.0000
inversion is # 3
number of inversions-odd Kramers pairs :  8
Gap with upper bands :  0.531060616569321
reading symmetries

k-point   2 :[0.5 0.  0. ] 
 number of states = 324
   Energy  |   degeneracy  |       irreps       | sym. operations  
           |               |                    |     1        2        3        4    
 -13.3479  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000   0.0000   2.0000  -0.0000
 -13.3346  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000   0.0000  -2.0000  -0.0000
 -12.8518  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000   0.0000  -2.0000   0.0000
 -12.3087  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000   0.0000   2.0000  -0.0000
  -5.4570  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000   0.0000  -2.0000  -0.0000
  -5.1012  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000  -0.0000   2.0000  -0.0000
  -4.6896  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000  -0.0000  -2.0000   0.0000
  -3.7471  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000  -0.0000  -2.0000   0.0000
  -3.5145  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000   0.0000   2.0000  -0.0000
  -3.2163  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000  -0.0000  -2.0000  -0.0000
  -2.9178  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000  -0.0000   2.0000   0.0000
  -2.5203  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000   0.0000   2.0000  -0.0000
  -2.0585  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000   0.0000  -2.0000  -0.0000
  -1.2484  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000   0.0000  -2.0000  -0.0000
  -1.1488  |        2      | -Y5(1.0), -Y6(1.0) |   2.0000  -0.0000  -2.0000   0.0000
  -1.0747  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000   0.0000   2.0000   0.0000
  -0.8511  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000  -0.0000   2.0000   0.0000
  -0.6662  |        2      | -Y3(1.0), -Y4(1.0) |   2.0000   0.0000   2.0000  -0.0000
inversion is # 3
number of inversions-odd Kramers pairs :  9
Gap with upper bands :  0.9114263180867801
reading symmetries

k-point   3 :[0.  0.5 0. ] 
 number of states = 324
   Energy  |   degeneracy  |  irreps  | sym. operations  
           |               |          |     1        2        3        4    
 -12.4507  |        4      | -Z2(2.0) |   4.0000   0.0000   0.0000   0.0000
 -11.9693  |        4      | -Z2(2.0) |   4.0000  -0.0000   0.0000   0.0000
  -5.2404  |        4      | -Z2(2.0) |   4.0000   0.0000  -0.0000   0.0000
  -4.8488  |        4      | -Z2(2.0) |   4.0000  -0.0000   0.0000   0.0000
  -4.1170  |        4      | -Z2(2.0) |   4.0000   0.0000  -0.0000   0.0000
  -3.0178  |        4      | -Z2(2.0) |   4.0000  -0.0000   0.0000   0.0000
  -2.9034  |        4      | -Z2(2.0) |   4.0000   0.0000  -0.0000   0.0000
  -1.9015  |        4      | -Z2(2.0) |   4.0000   0.0000  -0.0000   0.0000
  -1.2046  |        4      | -Z2(2.0) |   4.0000   0.0000  -0.0000   0.0000
inversion is # 3
number of inversions-odd Kramers pairs :  9
Gap with upper bands :  3.217323964361185
reading symmetries

k-point   4 :[0.5 0.5 0. ] 
 number of states = 324
   Energy  |   degeneracy  |  irreps  | sym. operations  
           |               |          |     1        2        3        4    
 -12.5529  |        4      | -C2(2.0) |   4.0000  -0.0000  -0.0000   0.0000
 -11.8329  |        4      | -C2(2.0) |   4.0000  -0.0000   0.0000   0.0000
  -6.0358  |        4      | -C2(2.0) |   4.0000  -0.0000  -0.0000   0.0000
  -4.5667  |        4      | -C2(2.0) |   4.0000   0.0000   0.0000   0.0000
  -3.8684  |        4      | -C2(2.0) |   4.0000   0.0000   0.0000   0.0000
  -3.1708  |        4      | -C2(2.0) |   4.0000  -0.0000   0.0000   0.0000
  -2.3999  |        4      | -C2(2.0) |   4.0000   0.0000  -0.0000   0.0000
  -1.8984  |        4      | -C2(2.0) |   4.0000   0.0000  -0.0000   0.0000
  -0.8169  |        4      | -C2(2.0) |   4.0000  -0.0000   0.0000   0.0000
inversion is # 3
number of inversions-odd Kramers pairs :  9
Gap with upper bands :  2.604040594501429
number of inversions-odd Kramers pairs IN THE LISTED KPOINTS:  35   Z4=  3
Minimal direct gap: 0.531060616569321  eV
indirect  gap: 0.3413834160661504  eV
stepan-tsirkin commented 3 years ago

This is normal, all irreps for thiese kpoints are 2dimi sional with the trace of the inversion matrix equal to zero. IMG_20211019_101253 Plus TRS doubles the degeneracy to 4.

bfocassio commented 3 years ago

Thank you very much