[QE-users] Phonon calculations of point defect in 2D hBN

[Ken Sharman]

Hello QE users,

I am trying to calculate the phonon properties of different point defects in monolayer (2D) hBN. As a test calculation, I am considering the neutral VnNb defect (nitrogen vacancy with a neighboring boron replaced by a nitrogen). For testing purposes, I am considering a small 17-atom unit cell with 15 A of vacuum.

In order to obtain a relaxed structure, it appears that I cannot enforce cell_dofree='ibrav+2Dxy' and instead use cell_dofree='2Dxy'. The resulting forces acting on each atom are zero up to and including the sixth decimal plane. The pw.x output states that the stresses are 0.00000000 Ry/bhor^3 for each component, expect for the zz component (0.00000086 Ry/bohr^3), which is treated using assume_isolated='2D'.

My issue is that ph.x calculates negative frequencies for the first two modes (-50 cm^{-1} and -12 cm^{-1}). It doesn't appear to be an issue related to negative frequencies at the Gamma point, because these two modes have very little dispersion across the Brillouin zone. I have performed a similar calculation for pristine hBN (also using ibrav=0 to verify this isn't the issue) and obtain all positive frequencies. Am I treating the 2D slab correctly? Any thoughts on why the phonon code indicates there is instability?

pw.x input:
&CONTROL
calculation = 'scf'
restart_mode = 'from_scratch'
prefix = 'hBN'
pseudo_dir = './pseudo/'
outdir = './TMP_DIR/'
etot_conv_thr = 1.0E-12
tstress = .true.
tprnfor = .true.
/
&SYSTEM
ibrav = 0,
nat = 17,
ntyp = 2,
ecutwfc = 50.0
ecutrho = 600.0
occupations = 'smearing'
smearing = 'm-p'
degauss = 0.0002
assume_isolated = '2D'
nosym = .true.
/
&ELECTRONS
diagonalization = 'cg'
conv_thr = 1.0E-14
/
&IONS
ion_dynamics="bfgs"
/

ATOMIC_SPECIES
  B 10.811  B.pbe-n-kjpaw_psl.1.0.0.UPF
  N 14.0067 N.pbe-n-kjpaw_psl.1.0.0.UPF

ATOMIC_POSITIONS (crystal)
B             0.1236294548        0.2288517946        0.5000000000
B             0.1088156910        0.5613303716        0.5000000000
B             0.1072329417        0.8927673484        0.5000000000
B             0.4864819943        0.2526124675        0.5000000000
N             0.4361682614        0.5638317166        0.5000000000
B             0.4386698609        0.8911844944        0.5000000000
B             0.7855708745        0.2144293085        0.5000000000
B             0.7473878305        0.5135182681        0.5000000000
B             0.7711482933        0.8763705944        0.5000000000
N             0.2442446869        0.1315370037        0.5000000000
N             0.2243740862        0.4579580637        0.5000000000
N             0.2160185581        0.7839816944        0.5000000000
N             0.5616626235        0.1119836884        0.5000000000
N             0.5420420278        0.7756259377        0.5000000000
N             0.8946390297        0.1053610363        0.5000000000
N             0.8880165315        0.4383375889        0.5000000000
N             0.8684632701        0.7557555456        0.5000000000

K_POINTS automatic
 2 2 2 0 0 0

CELL_PARAMETERS angstrom
   7.591938503  -0.231222917   0.000000000
  -3.995637427   6.459556319   0.000000000
   0.000000000   0.000000000  15.000000000

ph.x input:
Phonon dispersions for hBN
&inputph
  prefix   = 'hBN'
  outdir   = './TMP_DIR/1',
  fildvscf = 'dvscf'
  fildyn   = 'hBN.dyn'
  tr2_ph   = 1.0d-16
  recover=.true.,
  alpha_mix(1) = 0.1
  search_sym = .true.
  amass(1)=10.811,
  amass(2)=14.0067,
  ldisp=.true.,
  nq1=2, nq2=2, nq3=2,
  start_q=1, last_q=1
/

Thanks,
Ken
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