Quantum Espesso and qe2pert Calculations with DFT+U

Before running the DFPT+U phonon calculations with Quantum Espresso, it is necessary to modify the file PHonon/PH/dnsq_bare.f90 by adding the following lines below the line reading CALL sym_dns_wrapper (ldim, dnsbare, dnsbare_all_modes) and recompile Quantum Espresso.

  !added to output symmetrized dnsbare in the pattern basis
  if(ionode) then
     CALL seqopn (iundnsbare, 'dnsbare_pattern', 'formatted', exst)
     WRITE(iundnsbare,*) dnsbare_all_modes
     CLOSE (unit=iundnsbare,status='keep')
  endif

Run the scf, nscf, phonon, and Wannier calculations as normal, specifying Hubbard parameters in the scf and nscf files. Note that ph.x is not compatible with all Hubbard options available in pw.x. For the phonon calculations, it is necessary to copy to following output files for each q point into the save folder prefix.dnsbare_pattern_q*, prefix.dnsbare_q*, prefix.dnsscf_q*, prefix.dnsorth_cart_q*, prefix.dvscf_q*, and prefix.dyn*.xml.

Then run qe2pert.x as normal. You will notice the following lines in the qe2pert.out file.

     QE2PERT
     ---------------------------
     DFPT + U calculation

Calculations on SrVO3

The calculations below look at the e-ph coupling and conductivity in the correlated metal SrVO3 and the effect of using DFT+U. For more information, see Phys. Rev. Lett. 133, 186501 (2024)

  • Run the Quantum Espresso scf, nscf, and phonon calculations, the wannier90 calculations, and qe2pert.x using the files provided and following the instructions above.

  • Run the Perturbo calculations in pert-bands, pert-phdisp, and pert-ephmat and plot the results (see the Perturbopy tutorials). You will find a 3-band electronic structure characteristic of t-2g orbitals with a band width of ~2.5 eV, and phonons with a number of optical modes with strong e-ph coupling and energies of 50-90 meV.

  • Then run the Perturbo calculations in pert-setup, pert-imsigma, and pert-trans-RTA.

Hint: you can run all calculations with a job script like:

PT="$PATH_TO_QE/qe-***/perturbo/bin/perturbo.x"
RUN="srun -n $mpi_tot $PT -npools $mpi_tot"

cd pert-bands
$RUN -i pert.in > pert.out
cd ../pert-phdisp
$RUN -i pert.in > pert.out
cd ../pert-ephmat
$RUN -i pert.in > pert.out
cd ../pert-setup
$RUN -i pert.in > pert.out
cd ../pert-imsigma
cp ../pert-setup/svo_tet.* ./
$RUN -i pert.in > pert.out
cd ../pert-trans-RTA
cp ../pert-imsigma/svo.imsigma ./
cp ../pert-setup/svo_tet.* ./
$RUN -i pert.in > pert.out
  • Check the outputs of in pert-trans-RTA. In the svo.trans_coef output file, you should get values of the conductivity (1/Ohm/m) of approximately
#  T (K)   E_f(eV)   n_c (cm^-3)      sigma_xx       sigma_xy       sigma_yy       sigma_xz       sigma_yz       sigma_zz
  100.00  12.48930   0.51237E+22    0.537733E+08  -0.107585E+07   0.537733E+08  -0.107585E+07  -0.107585E+07   0.537733E+08
  200.00  12.48930   0.51336E+22    0.141496E+08  -0.837104E+05   0.141496E+08  -0.837104E+05  -0.837104E+05   0.141496E+08
  300.00  12.48930   0.51501E+22    0.733779E+07  -0.146515E+05   0.733779E+07  -0.146515E+05  -0.146515E+05   0.733779E+07
  • Consider running the calculations with different values of the Hubbard U parameter between 0 and 3 eV. You will notice that the Hubbard parameter has essentially no effect on the bands and a minor effect of phonon dispersion, but that the e-ph coupling of some phonon modes and the resistivity significantly increase with increasing U. The value U = 2 eV used in this tutorial is probably too low, but improves the convergence of the Quantum Espresso phonon calculations.