quantum-espresso/PH/elphon.f90

494 lines
15 KiB
Fortran

!
! Copyright (C) 2001-2003 PWSCF group
! This file is distributed under the terms of the
! GNU General Public License. See the file `License'
! in the root directory of the present distribution,
! or http://www.gnu.org/copyleft/gpl.txt .
!
#include "f_defs.h"
!
!-----------------------------------------------------------------------
SUBROUTINE elphon()
!-----------------------------------------------------------------------
!
! Electron-phonon calculation from data saved in fildvscf
!
USE ions_base, ONLY : nat, ntyp => nsp, ityp, tau
USE pwcom
USE kinds, ONLY : DP
USE phcom
USE el_phon
!
IMPLICIT NONE
!
INTEGER :: irr, imode0, ipert, is
! counter on the representations
! counter on the modes
! the change of Vscf due to perturbations
COMPLEX(kind=DP), POINTER :: dvscfin(:,:,:), dvscfins (:,:,:)
CALL start_clock ('elphon')
!
! read Delta Vscf and calculate electron-phonon coefficients
!
!!! rewind (iudvscf)
imode0 = 0
DO irr = 1, nirr
ALLOCATE (dvscfin ( nrxx , nspin , npert(irr)) )
!!! read (iudvscf) dvscfin
DO ipert = 1, npert (irr)
CALL davcio_drho ( dvscfin(1,1,ipert), lrdrho, iudvscf, &
imode0 + ipert, -1 )
END DO
IF (doublegrid) THEN
ALLOCATE (dvscfins ( nrxxs , nspin , npert(irr)) )
DO is = 1, nspin
DO ipert = 1, npert(irr)
CALL cinterpolate (dvscfin(1,is,ipert),dvscfins(1,is,ipert),-1)
ENDDO
ENDDO
ELSE
dvscfins => dvscfin
ENDIF
CALL newdq (dvscfin, npert(irr))
CALL elphel (npert (irr), imode0, dvscfins)
!
imode0 = imode0 + npert (irr)
IF (doublegrid) DEALLOCATE (dvscfins)
DEALLOCATE (dvscfin)
ENDDO
!
! now read the eigenvalues and eigenvectors of the dynamical matrix
! calculated in a previous run
!
IF (.NOT.trans) CALL readmat (iudyn, ibrav, celldm, nat, ntyp, &
ityp, omega, amass, tau, xq, w2, dyn)
!
CALL stop_clock ('elphon')
RETURN
END SUBROUTINE elphon
!
!-----------------------------------------------------------------------
SUBROUTINE readmat (iudyn, ibrav, celldm, nat, ntyp, ityp, omega, &
amass, tau, q, w2, dyn)
!-----------------------------------------------------------------------
!
USE kinds, ONLY : DP
IMPLICIT NONE
! Input
INTEGER :: iudyn, ibrav, nat, ntyp, ityp (nat)
REAL(kind=DP) :: celldm (6), amass (ntyp), tau (3, nat), q (3), &
omega
! output
REAL(kind=DP) :: w2 (3 * nat)
COMPLEX(kind=DP) :: dyn (3 * nat, 3 * nat)
! local (control variables)
INTEGER :: ntyp_, nat_, ibrav_, ityp_
REAL(kind=DP) :: celldm_ (6), amass_, tau_ (3), q_ (3)
! local
REAL(kind=DP) :: dynr (2, 3, nat, 3, nat)
CHARACTER(len=80) :: line
CHARACTER(len=3) :: atm
INTEGER :: nt, na, nb, naa, nbb, nu, mu, i, j
!
!
REWIND (iudyn)
READ (iudyn, '(a)') line
READ (iudyn, '(a)') line
READ (iudyn, * ) ntyp_, nat_, ibrav_, celldm_
IF (ntyp.NE.ntyp_.OR.nat.NE.nat_.OR.ibrav_.NE.ibrav.OR.ABS ( &
celldm_ (1) - celldm (1) ) .GT.1.0d-5) CALL errore ('readmat', &
'inconsistent data', 1)
DO nt = 1, ntyp
READ (iudyn, * ) i, atm, amass_
IF (nt.NE.i.OR.ABS (amass_ - amass (nt) ) .GT.1.0d-5) CALL errore ( &
'readmat', 'inconsistent data', 1 + nt)
ENDDO
DO na = 1, nat
READ (iudyn, * ) i, ityp_, tau_
IF (na.NE.i.OR.ityp_.NE.ityp (na) ) CALL errore ('readmat', &
'inconsistent data', 10 + na)
ENDDO
READ (iudyn, '(a)') line
READ (iudyn, '(a)') line
READ (iudyn, '(a)') line
READ (iudyn, '(a)') line
READ (line (11:80), * ) (q_ (i), i = 1, 3)
READ (iudyn, '(a)') line
DO na = 1, nat
DO nb = 1, nat
READ (iudyn, * ) naa, nbb
IF (na.NE.naa.OR.nb.NE.nbb) CALL errore ('readmat', 'error reading &
&file', nb)
READ (iudyn, * ) ( (dynr (1, i, na, j, nb), dynr (2, i, na, j, nb) &
, j = 1, 3), i = 1, 3)
ENDDO
ENDDO
!
! divide the dynamical matrix by the masses
!
DO nb = 1, nat
DO j = 1, 3
DO na = 1, nat
DO i = 1, 3
dynr (1, i, na, j, nb) = dynr (1, i, na, j, nb) / SQRT (amass ( &
ityp (na) ) * amass (ityp (nb) ) )
dynr (2, i, na, j, nb) = dynr (2, i, na, j, nb) / SQRT (amass ( &
ityp (na) ) * amass (ityp (nb) ) )
ENDDO
ENDDO
ENDDO
ENDDO
!
! solve the eigenvalue problem.
! NOTA BENE: eigenvectors are overwritten on dyn
!
CALL cdiagh (3 * nat, dynr, 3 * nat, w2, dyn)
!
! divide by sqrt(mass) to get displacements
!
DO nu = 1, 3 * nat
DO mu = 1, 3 * nat
na = (mu - 1) / 3 + 1
dyn (mu, nu) = dyn (mu, nu) / SQRT (amass (ityp (na) ) )
ENDDO
ENDDO
!
!
RETURN
END SUBROUTINE readmat
!
!-----------------------------------------------------------------------
SUBROUTINE elphel (npe, imode0, dvscfins)
!-----------------------------------------------------------------------
!
! Calculation of the electron-phonon matrix elements el_ph_mat
! <\psi(k+q)|dV_{SCF}/du^q_{i a}|\psi(k)>
! Original routine written by Francesco Mauri
!
USE pwcom
USE wavefunctions_module, ONLY: evc
USE kinds, ONLY : DP
USE io_files, ONLY: iunigk
USE phcom
USE el_phon
IMPLICIT NONE
!
INTEGER :: npe, imode0
COMPLEX(kind=DP) :: dvscfins (nrxxs, nspin, npe)
! LOCAL variables
INTEGER :: ik, ikk, ikq, ipert, mode, nrec, ibnd, jbnd, ir, ig, &
ios
COMPLEX(kind=DP) , ALLOCATABLE :: aux1 (:), elphmat (:,:,:)
COMPLEX(kind=DP) :: ZDOTC
!
ALLOCATE (aux1 ( nrxxs))
ALLOCATE (elphmat ( nbnd , nbnd , npe))
!
! Start the loops over the k-points
!
IF (nksq.GT.1) REWIND (unit = iunigk)
DO ik = 1, nksq
IF (nksq.GT.1) THEN
READ (iunigk, err = 100, iostat = ios) npw, igk
100 CALL errore ('elphel', 'reading igk', ABS (ios) )
ENDIF
!
! ik = counter of k-points with vector k
! ikk= index of k-point with vector k
! ikq= index of k-point with vector k+q
! k and k+q are alternated if q!=0, are the same if q=0
!
IF (lgamma) THEN
ikk = ik
ikq = ik
npwq = npw
ELSE
ikk = 2 * ik - 1
ikq = ikk + 1
ENDIF
IF (lsda) current_spin = isk (ikk)
IF (.NOT.lgamma.AND.nksq.GT.1) THEN
READ (iunigk, err = 200, iostat = ios) npwq, igkq
200 CALL errore ('elphel', 'reading igkq', ABS (ios) )
ENDIF
!
CALL init_us_2 (npwq, igkq, xk (1, ikq), vkb)
!
! read unperturbed wavefuctions psi(k) and psi(k+q)
!
IF (nksq.GT.1) THEN
IF (lgamma) THEN
CALL davcio (evc, lrwfc, iuwfc, ikk, - 1)
ELSE
CALL davcio (evc, lrwfc, iuwfc, ikk, - 1)
CALL davcio (evq, lrwfc, iuwfc, ikq, - 1)
ENDIF
ENDIF
!
DO ipert = 1, npe
nrec = (ipert - 1) * nksq + ik
!
! dvbare_q*psi_kpoint is read from file (if available) or recalculated
!
IF (trans) THEN
CALL davcio (dvpsi, lrbar, iubar, nrec, - 1)
ELSE
mode = imode0 + ipert
! TODO : .false. or .true. ???
CALL dvqpsi_us (ik, mode, u (1, mode), .FALSE. )
ENDIF
!
! calculate dvscf_q*psi_k
!
DO ibnd = 1, nbnd
aux1(:) = (0.d0, 0.d0)
DO ig = 1, npw
aux1 (nls (igk (ig) ) ) = evc (ig, ibnd)
ENDDO
CALL cft3s (aux1, nr1s, nr2s, nr3s, nrx1s, nrx2s, nrx3s, + 2)
DO ir = 1, nrxxs
aux1 (ir) = aux1 (ir) * dvscfins (ir, current_spin, ipert)
ENDDO
CALL cft3s (aux1, nr1s, nr2s, nr3s, nrx1s, nrx2s, nrx3s, - 2)
DO ig = 1, npwq
dvpsi (ig, ibnd) = dvpsi (ig, ibnd) + aux1 (nls (igkq (ig) ) )
ENDDO
END DO
CALL adddvscf (ipert, ik)
!
! calculate elphmat(j,i)=<psi_{k+q,j}|dvscf_q*psi_{k,i}> for this pertur
!
DO ibnd =1, nbnd
DO jbnd = 1, nbnd
elphmat (jbnd, ibnd, ipert) = ZDOTC (npwq, evq (1, jbnd), 1, &
dvpsi (1, ibnd), 1)
ENDDO
!
ENDDO
ENDDO
!
CALL reduce (2 * nbnd * nbnd * npe, elphmat)
!
! save all e-ph matrix elements into el_ph_mat
!
DO ipert = 1, npe
DO jbnd = 1, nbnd
DO ibnd = 1, nbnd
el_ph_mat (ibnd, jbnd, ik, ipert + imode0) = elphmat (ibnd, jbnd, ipert)
ENDDO
ENDDO
ENDDO
ENDDO
!
DEALLOCATE (elphmat)
DEALLOCATE (aux1)
!
RETURN
END SUBROUTINE elphel
!
!-----------------------------------------------------------------------
SUBROUTINE elphsum
!-----------------------------------------------------------------------
!
! Sum over BZ of the electron-phonon matrix elements el_ph_mat
! Original routine written by Francesco Mauri
!
USE ions_base, ONLY : nat
USE pwcom
USE kinds, ONLY : DP
USE phcom
USE el_phon
USE mp_global, ONLY : me_pool, root_pool
!
IMPLICIT NONE
! eps = 20 cm^-1, in Ry
REAL(kind=DP) :: eps
PARAMETER (eps = 20.d0 / 13.6058d0 / 8065.5d0)
!
INTEGER :: ik, ikk, ikq, isig, ibnd, jbnd, ipert, jpert, nu, mu, &
vu, ngauss1, nsig, iuelph, ios
REAL(kind=DP) :: weight, w0g1, w0g2, w0gauss, degauss1, dosef, dos_ef, &
ef1, phase_space, lambda, gamma
EXTERNAL dos_ef
!
COMPLEX(kind=DP) :: el_ph_sum (3*nat,3*nat)
!
WRITE (6, '(5x,"electron-phonon interaction ..."/)')
ngauss1 = 1
nsig = 10
IF (filelph.NE.' ') THEN
! parallel case: only first node writes
IF ( me_pool /= root_pool ) THEN
iuelph = 0
ELSE
!
iuelph = 4
OPEN (unit = iuelph, file = filelph, status = 'unknown', err = &
100, iostat = ios)
100 CALL errore ('elphon', 'opening file'//filelph, ABS (ios) )
REWIND (iuelph)
WRITE (iuelph, '(3f15.8,2i8)') xq, nsig, 3 * nat
WRITE (iuelph, '(6e14.6)') (w2 (nu) , nu = 1, nmodes)
!
END IF
!
ELSE
iuelph = 0
ENDIF
!
!
DO isig = 1, nsig
degauss1 = 0.01 * isig
el_ph_sum(:,:) = (0.d0, 0.d0)
phase_space = 0.d0
!
! Recalculate the Fermi energy Ef=ef1 and the DOS at Ef, dosef = N(Ef)
! for this gaussian broadening
!
! Note that the weights of k+q points must be set to zero for the
! following call to yield correct results
!
CALL efermig (et, nbnd, nks, nelec, wk, degauss1, ngauss1, ef1, 0, isk)
dosef = dos_ef (ngauss1, degauss1, ef1, et, wk, nks, nbnd)
! N(Ef) is the DOS per spin, not summed over spin
dosef = dosef / 2.d0
!
! Sum over bands with gaussian weights
!
DO ik = 1, nksq
!
! see subroutine elphel for the logic of indices
!
IF (lgamma) THEN
ikk = ik
ikq = ik
ELSE
ikk = 2 * ik - 1
ikq = ikk + 1
ENDIF
DO ibnd = 1, nbnd
w0g1 = w0gauss ( (ef1 - et (ibnd, ikk) ) / degauss1, ngauss1) &
/ degauss1
DO jbnd = 1, nbnd
w0g2 = w0gauss ( (ef1 - et (jbnd, ikq) ) / degauss1, ngauss1) &
/ degauss1
! note that wk(ikq)=wk(ikk)
weight = wk (ikk) * w0g1 * w0g2
DO jpert = 1, 3 * nat
DO ipert = 1, 3 * nat
el_ph_sum (ipert, jpert) = el_ph_sum (ipert, jpert) + weight * &
CONJG (el_ph_mat (jbnd, ibnd, ik, ipert) ) * &
el_ph_mat (jbnd, ibnd, ik, jpert)
ENDDO
ENDDO
phase_space = phase_space+weight
ENDDO
ENDDO
ENDDO
!
! el_ph_sum(mu,nu)=\sum_k\sum_{i,j}[ <psi_{k+q,j}|dvscf_q(mu)*psi_{k,i}>
! x <psi_{k+q,j}|dvscf_q(nu)*psi_{k,i}>
! x \delta(e_{k,i}-Ef) \delta(e_{k+q,j}
!
! collect contributions from all pools (sum over k-points)
!
CALL poolreduce (2 * 3 * nat * 3 * nat, el_ph_sum)
CALL poolreduce (1, phase_space)
!
! symmetrize el_ph_sum(mu,nu) : it transforms as the dynamical matrix
!
CALL symdyn_munu (el_ph_sum, u, xq, s, invs, rtau, irt, irgq, at, &
bg, nsymq, nat, irotmq, minus_q)
!
WRITE (6, 9000) degauss1, ngauss1
WRITE (6, 9005) dosef, ef1 * 13.6058
WRITE (6, 9006) phase_space
IF (iuelph.NE.0) THEN
WRITE (iuelph, 9000) degauss1, ngauss1
WRITE (iuelph, 9005) dosef, ef1 * 13.6058
ENDIF
!
DO nu = 1, nmodes
gamma = 0.0
DO mu = 1, 3 * nat
DO vu = 1, 3 * nat
gamma = gamma + REAL (CONJG (dyn (mu, nu) ) * el_ph_sum (mu, vu) &
* dyn (vu, nu) )
ENDDO
ENDDO
gamma = 3.1415926 * gamma / 2.d0
!
! the factor 2 comes from the factor sqrt(hbar/2/M/omega) that appears
! in the definition of the electron-phonon matrix element g
! The sqrt(1/M) factor is actually hidden into the normal modes
!
! gamma = \pi \sum_k\sum_{i,j} \delta(e_{k,i}-Ef) \delta(e_{k+q,j}-Ef)
! | \sum_mu z(mu,nu) <psi_{k+q,j}|dvscf_q(mu)*psi_{k,i}> |^2
! where z(mu,nu) is the mu component of normal mode nu (z = dyn)
! gamma(nu) is the phonon linewidth of mode nu
!
! The factor N(Ef)^2 that appears in most formulations of el-ph interact
! is absent because we sum, not average, over the Fermi surface.
! The factor 2 is provided by the sum over spins
!
IF (SQRT (ABS (w2 (nu) ) ) .GT.eps) THEN
! lambda is the adimensional el-ph coupling for mode nu:
! lambda(nu)= gamma(nu)/(pi N(Ef) \omega_{q,nu}^2)
lambda = gamma / 3.1415926 / w2 (nu) / dosef
ELSE
lambda = 0.0
ENDIF
! 3.289828x10^6 is the conversion factor from Ry to GHz
WRITE (6, 9010) nu, lambda, gamma * 3.289828d6
IF (iuelph.NE.0) WRITE (iuelph, 9010) nu, lambda, gamma * &
3.289828d6
ENDDO
ENDDO
9000 FORMAT(5x,'Gaussian Broadening: ',f7.3,' Ry, ngauss=',i4)
9005 FORMAT(5x,'DOS =',f10.6,' states/spin/Ry/Unit Cell at Ef=', &
& f10.6,' eV')
9006 FORMAT(5x,'double delta at Ef =',f10.6)
9010 FORMAT(5x,'lambda(',i2,')=',f8.4,' gamma=',f8.2,' GHz')
!
!
IF (iuelph.NE.0) CLOSE (unit = iuelph)
RETURN
END SUBROUTINE elphsum
!
!-----------------------------------------------------------------------
FUNCTION dos_ef (ngauss, degauss, ef, et, wk, nks, nbnd)
!-----------------------------------------------------------------------
!
USE kinds, ONLY : DP
IMPLICIT NONE
REAL(kind=DP) :: dos_ef
INTEGER :: ngauss, nbnd, nks
REAL(kind=DP) :: et (nbnd, nks), wk (nks), ef, degauss
!
INTEGER :: ik, ibnd
REAL(kind=DP) :: w0gauss
!
! Compute DOS at E_F (states per Ry per unit cell)
!
dos_ef = 0.0
DO ik = 1, nks
DO ibnd = 1, nbnd
dos_ef = dos_ef + wk (ik) * w0gauss ( (et (ibnd, ik) - ef) &
/ degauss, ngauss) / degauss
ENDDO
ENDDO
!
! Collects partial sums on k-points from all pools
!
CALL poolreduce (1, dos_ef)
!
RETURN
END FUNCTION dos_ef