[QE-users] Finding Parity of Different Bands in Topological Insulator

[Asad Mahmood]

Here is the input file:

  &control
    calculation = 'scf'
    restart_mode='from_scratch',
pseudo_dir = './../../../Pseudo',
prefix='arsenene',
verbosity = 'high'
/
&system
       ibrav = 4,
 nat= 2, ntyp= 1,
 ibrav=  4,
    celldm(1) =7.8,
    celldm(3) =6.103648,

ecutwfc =30.0,
occupations='smearing',
smearing='gauss', degauss=0.02,
lspinorb=.true
noncolin=.true
nbnd = 20
/
&electrons
!diagonalization='david'
electron_maxstep = 300
!mixing_mode = 'plain'
mixing_beta = 0.7
conv_thr = 1.0d-10
/
ATOMIC_SPECIES
As  74.9216  As.rel-pbe-n-rrkjus_psl.0.2.UPF
ATOMIC_POSITIONS crystal
As 0.333333333  0.666666666  0.524859275
As 0.666666666  0.333333333  0.475140725
K_POINTS crystal
1
0.5 0.0 0.0 1


Note that in the above highlighted portion I am using one of the TRIM
points, i.e. M1. Where other TRIM points are M2, M3 and G with coordinates
0.0 0.5 0.0, -0.5 0.0 0.0 and 0.0 0.0 0.0 respectively.
After SCF (pw.x) calculation, I run the bands,x calculation. The relevant
portion of the output is :

 **************************************************************************

                    xk=(  -0.50000,   0.28868,   0.00000  )

     double point group C_2h (2/m)
     there are  8 classes and  4 irreducible representations
     the character table:

       E     -E    C2    -C2   i     -i    s_h   -s_h

G_3+   1.00 -1.00  0.00  0.00  1.00 -1.00  0.00  0.00
G_4+   1.00 -1.00  0.00  0.00  1.00 -1.00  0.00  0.00
G_3-   1.00 -1.00  0.00  0.00 -1.00  1.00  0.00  0.00
G_4-   1.00 -1.00  0.00  0.00 -1.00  1.00  0.00  0.00

     imaginary part

       E     -E    C2    -C2   i     -i    s_h   -s_h

G_3+   0.00  0.00  1.00 -1.00  0.00  0.00  1.00 -1.00
G_4+   0.00  0.00 -1.00  1.00  0.00  0.00 -1.00  1.00
G_3-   0.00  0.00  1.00 -1.00  0.00  0.00 -1.00  1.00
G_4-   0.00  0.00 -1.00  1.00  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

     C2            2

     -C2          -2

     i             3

     -i           -3

     s_h           4

     -s_h         -4


     Band symmetry, C_2h (2/m)  double point group:

     e(  1 -  2) =    -14.19192  eV     2   --> G_3-
     e(  1 -  2) =    -14.19192  eV     2   --> G_4-
     e(  3 -  4) =    -12.67503  eV     2   --> G_3+
     e(  3 -  4) =    -12.67503  eV     2   --> G_4+
     e(  5 -  6) =     -6.29105  eV     2   --> G_3+
     e(  5 -  6) =     -6.29105  eV     2   --> G_4+
     e(  7 -  8) =     -5.79866  eV     2   --> G_3-
     e(  7 -  8) =     -5.79866  eV     2   --> G_4-
     e(  9 - 10) =     -4.65984  eV     2   --> G_3-
     e(  9 - 10) =     -4.65984  eV     2   --> G_4-
     e( 11 - 12) =     -2.39948  eV     2   --> G_3+
     e( 11 - 12) =     -2.39948  eV     2   --> G_4+
     e( 13 - 14) =     -0.22470  eV     2   --> G_3-
     e( 13 - 14) =     -0.22470  eV     2   --> G_4-
     e( 15 - 16) =      0.10174  eV     2   --> G_3+
     e( 15 - 16) =      0.10174  eV     2   --> G_4+
     e( 17 - 18) =      2.74250  eV     2   --> G_3+
     e( 17 - 18) =      2.74250  eV     2   --> G_4+
     e( 19 - 20) =      3.59948  eV     2   --> G_3-
     e( 19 - 20) =      3.59948  eV     2   --> G_4-

Is highlighted K point in the output file okay?? since I used 0.5 0 0 but
it is xk=(  -0.50000,   0.28868,   0.00000  ).
Moreover, I get the same result for M2 and M3 (which should not happen
because then Z2 = 0 which contradicts the dedfinitions of TI)

Please help.


On Thu, Sep 27, 2018 at 4:19 PM Asad Mahmood <amahmood at phys.qau.edu.pk>
wrote:

> Hi everyone,
>
> I am working with 2D materials, applying biaxial strain. At some strain
> value, the electronic structure exhibits the band diagram similar to that
> of a Topological Insulator (as I could observe band inversion from partial
> DOS too).  The material I am working with has inversion symmetry which
> implies that I can find parity eigen values at different bands(then I can
> find Z2 Topological Invariant using parity eigen values).
> My question is:
>
> How can we obtain parities (or directly Z2 values, if possible) using
> Quantum Espresso for a given band diagram?
>
> Regards,
> Asad Mahmood,
> Physics Department,
> Q.A.U, Islamabad,
> Pakistan
>
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