[QE-users] Question marks (?) in band representations
박민규
minkyupark at ulsan.ac.kr
Thu Jan 21 10:09:58 CET 2021
Dear all,
I observed that question marks (?) appear in the middle of band representations (see below).
It seems similar problem occurs for the last band in some cases ( https://www.mail-archive.com/users@lists.quantum-espresso.org/msg31534.html ), but I can’t guess the reason for this case.
The material is GaAs with space group F-43m (216) and I attach scf input.
Does anyone know why they are not classified properly?
The below excerpt is on the path along Gamma to L.
**************************************************************************
xk=( 0.00641, 0.00641, 0.00641 )
double point group C_3v (3m)
there are 6 classes and 3 irreducible representations
the character table:
E -E 2C3 -2C3 3s_v -3s_v
G_4 2.00 -2.00 1.00 -1.00 0.00 0.00
G_5 1.00 -1.00 -1.00 1.00 0.00 0.00
G_6 1.00 -1.00 -1.00 1.00 0.00 0.00
imaginary part
E -E 2C3 -2C3 3s_v -3s_v
G_4 0.00 0.00 0.00 0.00 0.00 0.00
G_5 0.00 0.00 0.00 0.00 1.00 -1.00
G_6 0.00 0.00 0.00 0.00 -1.00 1.00
the symmetry operations in each class and the name of the first element:
E 1
-E -1
2C3 2 3
-2C3 -2 -3
3s_v 4 5 -6
3s_v 6 -4 -5
Band symmetry, C_3v (3m) double point group:
e( 1 - 3) = -8.82709 eV 3 --> G_4 L_6
e( 1 - 3) = -8.82709 eV 3 --> ?
e( 4 - 4) = -8.82688 eV 1 --> ?
e( 5 - 6) = -8.39671 eV 2 --> G_4 L_6
e( 7 - 9) = -8.35227 eV 3 --> G_4 L_6
e( 7 - 9) = -8.35227 eV 3 --> ?
e( 10 - 10) = -8.35203 eV 1 --> ?
e( 11 - 12) = -6.25322 eV 2 --> G_4 L_6
e( 13 - 14) = 5.88934 eV 2 --> G_4 L_6
e( 15 - 16) = 6.17226 eV 2 --> G_4 L_6
e( 17 - 17) = 6.22576 eV 1 --> ?
e( 18 - 18) = 6.22593 eV 1 --> ?
e( 19 - 20) = 6.33992 eV 2 --> G_4 L_6
e( 21 - 22) = 9.71086 eV 2 --> G_4 L_6
e( 23 - 24) = 9.90063 eV 2 --> G_4 L_6
e( 25 - 26) = 9.90114 eV 2 --> G_5 L_4
e( 25 - 26) = 9.90114 eV 2 --> G_6 L_5
e( 27 - 28) = 13.62609 eV 2 --> G_4 L_6
e( 29 - 29) = 16.14546 eV 1 --> ?
e( 30 - 31) = 16.14624 eV 2 --> G_4 L_6
e( 32 - 32) = 16.14710 eV 1 --> ?
e( 33 - 34) = 17.64099 eV 2 --> G_4 L_6
e( 35 - 36) = 17.67265 eV 2 --> G_4 L_6
**************************************************************************
**************************************************************************
xk=( 0.01282, 0.01282, 0.01282 )
Band symmetry, C_3v (3m) double point group:
e( 1 - 1) = -8.82718 eV 1 --> ?
e( 2 - 3) = -8.82700 eV 2 --> G_4 L_6
e( 4 - 4) = -8.82677 eV 1 --> ?
e( 5 - 6) = -8.39672 eV 2 --> G_4 L_6
e( 7 - 7) = -8.35236 eV 1 --> ?
e( 8 - 9) = -8.35219 eV 2 --> G_4 L_6
e( 10 - 10) = -8.35190 eV 1 --> ?
e( 11 - 12) = -6.25187 eV 2 --> G_4 L_6
e( 13 - 14) = 5.85998 eV 2 --> G_4 L_6
e( 15 - 16) = 6.11074 eV 2 --> G_4 L_6
e( 17 - 17) = 6.22366 eV 1 --> ?
e( 18 - 18) = 6.22401 eV 1 --> ?
e( 19 - 20) = 6.42336 eV 2 --> G_4 L_6
e( 21 - 22) = 9.71374 eV 2 --> G_4 L_6
e( 23 - 24) = 9.90214 eV 2 --> G_4 L_6
e( 25 - 26) = 9.90418 eV 2 --> G_5 L_4
e( 25 - 26) = 9.90418 eV 2 --> G_6 L_5
e( 27 - 28) = 13.63476 eV 2 --> G_4 L_6
e( 29 - 29) = 16.13092 eV 1 --> ?
e( 30 - 31) = 16.13239 eV 2 --> G_4 L_6
e( 32 - 32) = 16.13413 eV 1 --> ?
e( 33 - 34) = 17.64113 eV 2 --> G_4 L_6
e( 35 - 36) = 17.68244 eV 2 --> G_4 L_6
**************************************************************************
**************************************************************************
xk=( 0.01923, 0.01923, 0.01923 )
Band symmetry, C_3v (3m) double point group:
e( 1 - 1) = -8.82726 eV 1 --> ?
e( 2 - 3) = -8.82701 eV 2 --> G_4 L_6
e( 4 - 4) = -8.82664 eV 1 --> ?
e( 5 - 6) = -8.39674 eV 2 --> G_4 L_6
e( 7 - 7) = -8.35240 eV 1 --> ?
e( 8 - 9) = -8.35222 eV 2 --> G_4 L_6
e( 10 - 10) = -8.35171 eV 1 --> ?
e( 11 - 12) = -6.24960 eV 2 --> G_4 L_6
e( 13 - 14) = 5.80725 eV 2 --> G_4 L_6
e( 15 - 16) = 6.06587 eV 2 --> G_4 L_6
e( 17 - 17) = 6.22024 eV 1 --> ?
e( 18 - 18) = 6.22076 eV 1 --> ?
e( 19 - 20) = 6.50855 eV 2 --> G_4 L_6
e( 21 - 22) = 9.71854 eV 2 --> G_4 L_6
e( 23 - 24) = 9.90470 eV 2 --> G_4 L_6
e( 25 - 25) = 9.90923 eV 1 --> ?
e( 26 - 26) = 9.90934 eV 1 --> ?
e( 27 - 28) = 13.64913 eV 2 --> G_4 L_6
e( 29 - 29) = 16.10805 eV 1 --> ?
e( 30 - 31) = 16.11011 eV 2 --> G_4 L_6
e( 32 - 32) = 16.11272 eV 1 --> ?
e( 33 - 34) = 17.63003 eV 2 --> G_4 L_6
e( 35 - 36) = 17.70956 eV 2 --> G_4 L_6
**************************************************************************
Best regards,
============================================
Minkyu Park
Research Institute of Basic Sciences, University of Ulsan,
93, Daehak-ro, Nam-gu, Ulsan, 44610 Republic of Korea
minkyupark at ulsan.ac.kr<mailto:minkyupark at ulsan.ac.kr>
+82-52-259-1473
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