electron-phonon matrix elements are not hermitian

[simba2828]

Dear experts,

From my EPW calculation, the electron-phonon matrix elements at q = 0 are not Hermitian, i.e,

g_{n,m}^\nu ≠ g_{m,n}^\nu*

Could anyone please tell the possible reason?

I am using EPW6.0 where I can print the complex electron-phonon matrix elements.

Sincerely,
Shubham

[Shashi]

Dear Shubham,

You may want to check the behavior at a finite q-point instead of Gamma, since q = 0 can sometimes be special (e.g., degeneracies or phase/gauge issues) that may affect the apparent Hermiticity.

Also, does your system preserve time-reversal symmetry? This can influence the symmetry properties of the electron–phonon matrix elements.

In addition, please check the quality of your Wannierization (e.g., spreads, band interpolation), as poor Wannierization can also lead to such inconsistencies.

It would be useful to verify these points and see if the issue persists away from gamma.

Best regards,
Shashi

[simba2828]

Dear Shashi,

Thank you for your reply. Yes the system is TRS preserved. I haven't checked the q\=0 case but will definitely check.

Meanwhile I am trying to print the el-ph matrix elements from PHonon routine of ph.x. Is there any way I can print the matrix elements for given k points. I am using the following ph.in file but I can print only one k point at a time. Is there any tag from which I can print all the k points together.
Currently I am doing nscf calculation for some k points and then using the following input I can print el-ph matrix elements individually.

Code: Select all

&inputph
  tr2_ph=1.0d-14
  prefix=aiida'
  fildvscf = 'dvscf'
  amass(1)= 118.71
  amass(2)= 78.96
  outdir='./out/'
  fildyn=aiida.dyn'
  electron_phonon = 'prt'
  el_ph_sigma=0.04
  el_ph_nsigma = 25
  ldisp = .true.
  nq1 = 5
  nq2 = 5
  nq3 = 1
  start_q =1
  last_q =1
  trans = .false.
  kx = -0.5000000
  ky = -0.4885337
  kz = 0.0000000
 /

I also tried nk1, nk2, nk3 for isotropic grid but that too did not work. ALso, the above input file, read only 2pi/alat kpoints and not the crystal coordinates.

Please let me know if there is any functionality through which I can print the matrix elements in one go.


Thanks very much.

Regards,
Shubham

[simba2828]

Dear Shashi,
As you suggested I checked the matrix elements away from the Gamma point, and found that they are not Hermitian even there. Also, the system (monolayer h-BN) is TRS preserved, and the modes in prefix.dyn1 are completely real. However the matrix elements are not Hermitian.

Here is my input file, epw.in. Could you please suggest if there is any tag that might be missing?

Code: Select all

--
&inputepw
  prefix      = 'bn',
  amass(1)    = 10.811,
  amass(2)    = 14.0067,
  outdir      = './out/'

  elph        = .true.
  epwwrite    = .false.
  epwread     = .true.

  nbndsub     =  7,
  !nbndskip = 0
  !bands_skipped = 'exclude_bands = 55-58,65-68'

  wannierize  = .false.
  num_iter    = 1000
  dis_froz_max= 11.0
  dis_froz_min= -13.0


  wdata(1)   = 'dis_mix_ratio   = 1.0'
  wdata(2)   = 'dis_num_iter    = 3000'
  wdata(3)    = 'bands_plot : true'
  wdata(4)    = 'bands_num_points : 300'
  wdata(5)    = 'bands_plot_format : xmgrace gnuplot'
  wdata(6)    = 'begin kpoint_path'
  wdata(7)    = 'G 0.0 0.0 0.0 M 0.5 0.0 0.0'
  wdata(8)    = 'M 0.5 0.0 0.0 K 0.3333 0.3333 0.0'
  wdata(9)    = 'K 0.3333 0.3333 0.0 G 0.0 0.0 0.0'
  wdata(10)    = 'end kpoint_path'
  wdata(11)   = 'write_tb = true'

  efermi_read = .true.
  fermi_energy = -0.711418
  phonselfen = .true.
  delta_approx= .true.
  temps = 100
  degaussw    = 0.04 ! eV ~  1/4 of fsthick
  fsthick     = 7.5  ! eV ~ 4 times the maximum phonon frequency
  prtgkk = .true.

  dvscf_dir   = '../ph/save'

  filqf = 'kpt1.dat'
  filkf = 'hex_kmesh.dat'

  !nkf1 = 32
  !nkf2 = 32
  !nkf3 = 1

  nk1         = 16
  nk2         = 16
  nk3         = 1

  nq1         = 8
  nq2         = 8
  nq3         = 1
/

Here is the scf.in:

Code: Select all

&CONTROL
  calculation = 'scf'
  outdir = './out/'
  prefix = 'bn'
  pseudo_dir = '../pseudo/'
  verbosity = 'high'
/
&SYSTEM
  degauss =   2.0000000000d-02
  ecutrho =   4.8000000000d+02
  ecutwfc =   6.0000000000d+01
  ibrav = 0
  nat = 2
  ntyp = 2
  occupations = 'smearing'
  smearing = 'cold'
/
&ELECTRONS
  conv_thr =   4.0000000000d-12
  electron_maxstep = 150
/
ATOMIC_SPECIES
B      10.811 B_ONCV_PBE-1.2.upf
N      14.0067 N_ONCV_PBE-1.2.upf
ATOMIC_POSITIONS crystal
B            0.3333333432       0.6666666864       0.2017712537
N            0.6666666865       0.3333333432       0.2017712537
K_POINTS automatic
16 16 1 0 0 0
CELL_PARAMETERS angstrom
      2.5128455762       0.0000000000       0.0000000000
     -1.2564227881       2.1761881047       0.0000000000
      0.0000000000       0.0000000000      16.7633022130

Thank you very much.

Sincerely,
Shubham