Why am I getting DOS like this in Quantum ESPRESSO?

Question

I am working on $\ce{GeHfTe}$ and in the case of a non-collinear calculation, I am getting the DOS in the attached photo. I have already relaxed my structure with VC-relax and it is converged with respect to k-points, EOS parameter, and degauss value.

If any one can guide me what is wrong in the DOS obtained it will be very helpful. I am not quite sure about the two sharp peaks around $\pu{-25eV}$.

&CONTROL
  calculation = 'scf'
  restart_mode  = 'from_scratch'
  etot_conv_thr =   1.0000000000d-13
  forc_conv_thr =   1.0000000000d-09
  outdir = './'
  prefix = 'GeHfTe'
  pseudo_dir = '/home/yash/project/qe-6.7-ReleasePack/qe-6.7/pseudo'
  tprnfor = .true.
  tstress = .true.
  verbosity = 'high'
/
&SYSTEM
  degauss =   0.001
  ecutwfc =   150
  ibrav = 0
  nat = 6
  ntyp = 3
  occupations = 'smearing'
  smearing = 'cold'
 noncolin=.true.
  lspinorb=.true.
/
&ELECTRONS
  conv_thr =   1.2000000000d-15
  mixing_beta =   4.0000000000d-01
/
&IONS
/
&CELL
/
ATOMIC_SPECIES
Ge     72.64  Ge.rel-pz-dn-rrkjus_psl.0.2.2.UPF
Hf     178.49 Hf.rel-pz-spn-rrkjus_psl.1.0.0.UPF
Te     127.6 Te.rel-pz-dn-rrkjus_psl.0.2.2.UPF

CELL_PARAMETERS (angstrom)
   3.799849132   0.000000000   0.000000000
   0.000000000   3.799849132   0.000000000
   0.000000000   0.000000000   8.387787463

ATOMIC_POSITIONS (crystal)
Hf            0.0000000000        0.5000000000        0.7536986859
Hf            0.5000000000        0.0000000000        0.2463013141
Ge            0.0000000000        0.0000000000       -0.0000000000
Ge            0.5000000000        0.5000000000        0.0000000000
Te            0.5000000000        0.0000000000        0.6218959934
Te            0.0000000000        0.5000000000        0.3781040066

K_POINTS (automatic)
10 10 10 0 0 0

Answer 1

I suspect that these are the $5s$ and $5p$ states of $\ce{Hf}$, which are treated as valence in the pseudopotential you're using. These states will be fairly tightly bound to the nucleus, which always show up as sharp peaks in the DOS.

The reason why tightly-bound states show up like this can be understood by noting that if the potential $V$ is large compared to the kinetic term $T$, then the Hamiltonian $H$ can be approximated as:

$$H\approx V$$

The energy $E$ of a wavefunction $\psi_{k}$ at k-point $k$ is,

\begin{align} E & \approx \int d^3 r \psi^\ast_k(r)V(r)\psi_k(r)\\ &= \int d^3 r V(r)\psi^\ast_k(r)\psi_k(r)\\ &= \int d^3 r V(r)\left\vert \psi_k(r)\right\vert^2\\ \end{align}

Now, recall that k-points are introduced when we apply Bloch's theorem, and write,

$$\psi_k(r)=u_k(r)e^{ik\cdot r}$$

where $u_k$ is the Bloch function, which does not explicitly depend on $k$. Substituting into the energy expression, we have

\begin{align} E & \approx \int d^3 r V(r)\left\vert u_k(r)\right\vert^2\\ \end{align}

In other words, the phase factor is irrelevant and the dependence on the phase $k$ has disappeared! The energy does not depend on $k$ at all, and the state has the same energy regardless of $k$. This means that the density of states for this state is a delta-function at $E$ -- which is essentially what you're seeing in your DOS plots.