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

[Asad Mahmood]

No one replies :-(
I also write my affiliation now at the end of email. Still no reply



Asad Mahmood,
Research Student,
Department of Physics,
QAU, Islamabad,
Pakistan


On Fri, Sep 28, 2018 at 4:26 PM Asad Mahmood <amahmood at phys.qau.edu.pk>
wrote:

> 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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