quantum-espresso/PW/c_phase_field.f90

591 lines
19 KiB
Fortran

!
! Copyright (C) 2001-2004 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 .
!
! this routine is used to calculate the electronic polarization
! when a finite electric field describe through the modern
! theory of the polarization is applied.
! is very close to the routine c_phase in bp_c_phase
! however the numbering of the k-points in the strings is different
#include "f_defs.h"
!======================================================================!
SUBROUTINE c_phase_field
!----------------------------------------------------------------------!
! Geometric phase calculation along a strip of nppstr k-points
! averaged over a 2D grid of nkort k-points ortogonal to nppstr
! --- Make use of the module with common information ---
USE kinds, ONLY : DP
USE parameters, ONLY : nbrx
USE io_global, ONLY : stdout
USE io_files, ONLY : iunwfc, nwordwfc
USE ions_base, ONLY : nat, ntyp => nsp, ityp, tau, zv, atm
USE cell_base, ONLY : at, alat, tpiba, omega, tpiba2
USE constants, ONLY : pi, tpi
USE gvect, ONLY : ngm, nr1, nr2, nr3, nrx1, nrx2, nrx3, &
ecutwfc, g, gcutm
USE uspp, ONLY : nkb, vkb, okvan
USE uspp_param, ONLY : lmaxq, nh, nhm, tvanp
USE lsda_mod, ONLY : nspin
USE klist, ONLY : nelec, degauss, nks, xk, wk
USE wvfct, ONLY : npwx, npw, nbnd
USE wavefunctions_module, ONLY : evc
USE bp
USE fixed_occ
! --- Make use of the module with common information ---
! --- Avoid implicit definitions ---
IMPLICIT NONE
! --- Internal definitions ---
INTEGER :: i
INTEGER :: igk1(npwx)
INTEGER :: igk0(npwx)
INTEGER :: ig
INTEGER :: ind1
INTEGER :: info
INTEGER :: is
INTEGER :: istring
INTEGER :: iv
INTEGER :: ivpt(nbnd)
INTEGER :: j
INTEGER :: jkb
INTEGER :: jkb_bp
INTEGER :: jkb1
INTEGER :: job
INTEGER :: jv
INTEGER :: kindex
INTEGER :: kort
INTEGER :: kpar
INTEGER :: kpoint
INTEGER :: kstart
INTEGER :: mb
INTEGER :: mk1
INTEGER :: mk2
INTEGER :: mk3
INTEGER , ALLOCATABLE :: mod_elec(:)
INTEGER :: mod_elec_dw
INTEGER :: mod_elec_tot
INTEGER :: mod_elec_up
INTEGER :: mod_ion(nat)
INTEGER :: mod_ion_dw
INTEGER :: mod_ion_tot
INTEGER :: mod_ion_up
INTEGER :: mod_tot
INTEGER :: n1
INTEGER :: n2
INTEGER :: n3
INTEGER :: na
INTEGER :: nb
INTEGER :: ng
INTEGER :: nhjkb
INTEGER :: nhjkbm
INTEGER :: nkbtona(nkb)
INTEGER :: nkbtonh(nkb)
INTEGER :: nkort
INTEGER :: np
INTEGER :: npw1
INTEGER :: npw0
INTEGER :: nstring
INTEGER :: nt
LOGICAL :: lodd
REAL(dp) :: dk(3)
REAL(dp) :: dkmod
REAL(dp) :: el_loc
REAL(dp) :: eps
REAL(dp) :: fac
REAL(dp) :: g2kin_bp(npwx)
REAL(dp) :: gpar(3)
REAL(dp) :: gtr(3)
REAL(dp) :: gvec
REAL(dp) :: ln(-nr1:nr1,-nr2:nr2,-nr3:nr3)
REAL(dp), ALLOCATABLE :: loc_k(:)
REAL(dp) , ALLOCATABLE :: pdl_elec(:)
REAL(dp) :: pdl_elec_dw
REAL(dp) :: pdl_elec_tot
REAL(dp) :: pdl_elec_up
REAL(dp) :: pdl_ion(nat)
REAL(dp) :: pdl_ion_dw
REAL(dp) :: pdl_ion_tot
REAL(dp) :: pdl_ion_up
REAL(dp) :: pdl_tot
REAL(dp) , ALLOCATABLE :: phik(:)
REAL(dp) :: phidw
REAL(dp) :: phiup
REAL(dp) :: rmod
REAL(dp) :: qrad_dk(nbrx,nbrx,lmaxq,ntyp)
REAL(dp) :: upol(3)
REAL(dp) :: weight
REAL(dp), ALLOCATABLE :: wstring(:)
REAL(dp) :: ylm_dk(lmaxq*lmaxq)
REAL(dp) :: zeta_mod
REAL(dp) :: chi
REAL(dp) :: pola, pola_ion
COMPLEX(dp) :: aux(ngm)
COMPLEX(dp) :: aux0(ngm)
COMPLEX(dp) :: becp0(nkb,nbnd)
COMPLEX(dp) :: becp_bp(nkb,nbnd)
COMPLEX(dp) :: cdet(2)
COMPLEX(dp) :: cdwork(nbnd)
COMPLEX(dp) :: cave
COMPLEX(dp) :: cave_dw
COMPLEX(dp) :: cave_up
COMPLEX(dp) , ALLOCATABLE :: cphik(:)
COMPLEX(dp) :: det
COMPLEX(dp) :: dtheta
COMPLEX(dp) :: mat(nbnd,nbnd)
COMPLEX(dp) :: pref
COMPLEX(dp) :: q_dk(nhm,nhm,ntyp)
COMPLEX(dp) :: struc(nat)
COMPLEX(dp) :: theta0
COMPLEX(dp) :: zdotc
COMPLEX(dp) :: zeta
COMPLEX(dp) :: psi(npwx,nbnd)
COMPLEX(dp) :: psi1(npwx,nbnd)
COMPLEX(dp) :: zeta_loc
INTEGER ipivi(nbnd,nbnd),ii
LOGICAL l_cal!flag for doing mat calculation
INTEGER, ALLOCATABLE :: map_g(:)
! ------------------------------------------------------------------------- !
! INITIALIZATIONS
! ------------------------------------------------------------------------- !
allocate(map_g(npwx))
pola=0.d0!set to 0 electronic polarization
! --- Check that we are working with an insulator with no empty bands ---
! IF ((degauss > 0.01) .OR. (nbnd /= nelec/2)) CALL errore('c_phase', &
! 'Polarization only for insulators and no empty bands',1)
IF ((degauss > 0.01) .OR. (nbnd /= nelec/2)) &
&write(stdout,*) 'PAY ATTENTION: EL FIELD AND OCCUPATIONS'
! --- Define a small number ---
eps=1.0E-6_dp
! --- Recalculate FFT correspondence (see ggen.f90) ---
DO ng=1,ngm
mk1=nint(g(1,ng)*at(1,1)+g(2,ng)*at(2,1)+g(3,ng)*at(3,1))
mk2=nint(g(1,ng)*at(1,2)+g(2,ng)*at(2,2)+g(3,ng)*at(3,2))
mk3=nint(g(1,ng)*at(1,3)+g(2,ng)*at(2,3)+g(3,ng)*at(3,3))
ln(mk1,mk2,mk3) = ng
END DO
if(okvan) then
! --- Initialize arrays ---
jkb_bp=0
DO nt=1,ntyp
DO na=1,nat
IF (ityp(na).eq.nt) THEN
DO i=1, nh(nt)
jkb_bp=jkb_bp+1
nkbtona(jkb_bp) = na
nkbtonh(jkb_bp) = i
END DO
END IF
END DO
END DO
endif
! --- Get the number of strings ---
nstring=nks/nppstr
nkort=nstring/(nspin)
! --- Allocate memory for arrays ---
ALLOCATE(phik(nstring))
ALLOCATE(loc_k(nstring))
ALLOCATE(cphik(nstring))
ALLOCATE(wstring(nstring))
ALLOCATE(pdl_elec(nstring))
ALLOCATE(mod_elec(nstring))
! ------------------------------------------------------------------------- !
! electronic polarization: set values for k-points strings !
! ------------------------------------------------------------------------- !
! --- Find vector along strings ---
if(nppstr .ne. 1) then
gpar(1)=(xk(1,nppstr)-xk(1,1))*DBLE(nppstr)/DBLE(nppstr-1)
gpar(2)=(xk(2,nppstr)-xk(2,1))*DBLE(nppstr)/DBLE(nppstr-1)
gpar(3)=(xk(3,nppstr)-xk(3,1))*DBLE(nppstr)/DBLE(nppstr-1)
gvec=dsqrt(gpar(1)**2+gpar(2)**2+gpar(3)**2)*tpiba
else
gpar(1)=0.
gpar(2)=0.
gpar(3)=0.
gpar(gdir)=1./at(gdir,gdir)!
gvec=tpiba/sqrt(at(gdir,1)**2.+at(gdir,2)**2.+at(gdir,3)**2.)
endif
! --- Find vector between consecutive points in strings ---
if(nppstr.ne.1) then
dk(1)=xk(1,2)-xk(1,1)
dk(2)=xk(2,2)-xk(2,1)
dk(3)=xk(3,2)-xk(3,1)
dkmod=SQRT(dk(1)**2+dk(2)**2+dk(3)**2)*tpiba!orthorombic cell
else!caso punto gamma, per adesso solo cella cubica
dk(1)=0.
dk(2)=0.
dk(3)=0.
dk(gdir)=1./at(gdir,gdir)
dkmod=tpiba/sqrt(at(gdir,1)**2.+at(gdir,2)**2.+at(gdir,3)**2.)
endif
! ------------------------------------------------------------------------- !
! electronic polarization: weight strings !
! ------------------------------------------------------------------------- !
! --- Calculate string weights, normalizing to 1 (no spin) or 1+1 (spin) ---
DO is=1,nspin
weight=0.0_dp
DO kort=1,nkort
istring=kort+(is-1)*nkort
wstring(istring)=wk(nppstr*istring)
weight=weight+wstring(istring)
END DO
DO kort=1,nkort
istring=kort+(is-1)*nkort
wstring(istring)=wstring(istring)/weight
END DO
END DO
! ------------------------------------------------------------------------- !
! electronic polarization: structure factor !
! ------------------------------------------------------------------------- !
! --- Calculate structure factor e^{-i dk*R} ---
DO na=1,nat
fac=(dk(1)*tau(1,na)+dk(2)*tau(2,na)+dk(3)*tau(3,na))*tpi
struc(na)=CMPLX(cos(fac),-sin(fac))
END DO
! ------------------------------------------------------------------------- !
! electronic polarization: form factor !
! ------------------------------------------------------------------------- !
if(okvan) then
! --- Calculate Bessel transform of Q_ij(|r|) at dk [Q_ij^L(|r|)] ---
CALL calc_btq(dkmod,qrad_dk,0)
! --- Calculate the q-space real spherical harmonics at dk [Y_LM] ---
CALL ylm_q(lmaxq*lmaxq,dk,dkmod,ylm_dk)!questa no funzia perche'??
! --- Form factor: 4 pi sum_LM c_ij^LM Y_LM(Omega) Q_ij^L(|r|) ---
! CALL setv(2*nhm*nhm*ntyp,0.d0,q_dk,1)
q_dk=(0.d0,0.d0)
DO np =1, ntyp
if(tvanp(np)) then
DO iv = 1, nh(np)
DO jv = iv, nh(np)
call qvan3(iv,jv,np,pref,ylm_dk,qrad_dk)
q_dk(iv,jv,np) = omega*pref
q_dk(jv,iv,np) = omega*pref
ENDDO
ENDDO
endif
ENDDO
endif
! ------------------------------------------------------------------------- !
! electronic polarization: strings phases !
! ------------------------------------------------------------------------- !
el_loc = 0.d0
kpoint=0
zeta=(1.d0,0.d0)
! --- Start loop over spin ---
DO is=1,nspin
! --- Start loop over orthogonal k-points ---
DO kort=1,nkort
zeta_loc=(1.d0,0.d0)
! --- Index for this string ---
istring=kort+(is-1)*nkort
! --- Initialize expectation value of the phase operator ---
zeta_mod = 1.d0
! --- Start loop over parallel k-points ---
DO kpar = 1,nppstr+1
! --- Set index of k-point ---
kpoint = kpoint + 1
! --- Calculate dot products between wavefunctions and betas ---
IF (kpar /= 1 ) THEN
! --- Dot wavefunctions and betas for PREVIOUS k-point ---
CALL gk_sort(xk(1,kpoint-1),ngm,g,ecutwfc/tpiba2, &
npw0,igk0,g2kin_bp)
CALL davcio(psi,nwordwfc,iunwfc,kpoint-1,-1)
if(okvan) then
CALL init_us_2 (npw0,igk0,xk(1,kpoint-1),vkb)
CALL ccalbec(nkb, npwx, npw0, nbnd, becp0, vkb, psi)
endif
! --- Dot wavefunctions and betas for CURRENT k-point ---
IF (kpar /= (nppstr+1)) THEN
CALL gk_sort(xk(1,kpoint),ngm,g,ecutwfc/tpiba2, &
npw1,igk1,g2kin_bp)
CALL davcio(psi1,nwordwfc,iunwfc,kpoint,-1)
if(okvan) then
CALL init_us_2 (npw1,igk1,xk(1,kpoint),vkb)
CALL ccalbec(nkb,npwx,npw1,nbnd,becp_bp,vkb,psi1)
endif
ELSE
kstart = kpoint-(nppstr+1)+1
CALL gk_sort(xk(1,kstart),ngm,g,ecutwfc/tpiba2, &
npw1,igk1,g2kin_bp)
CALL davcio(psi1,nwordwfc,iunwfc,kstart,-1)
if(okvan) then
CALL init_us_2 (npw1,igk1,xk(1,kstart),vkb)
CALL ccalbec(nkb,npwx,npw1,nbnd,becp_bp,vkb,psi1)
endif
ENDIF
! --- Matrix elements calculation ---
! CALL setv(2*nbnd*nbnd,0.d0,mat,1)
!
IF (kpar == (nppstr+1)) THEN
map_g(:) = 0
do ig=1,npw1
! --- If k'=k+G_o, the relation psi_k+G_o (G-G_o) ---
! --- = psi_k(G) is used, gpar=G_o, gtr = G-G_o ---
gtr(1)=g(1,igk1(ig)) - gpar(1)
gtr(2)=g(2,igk1(ig)) - gpar(2)
gtr(3)=g(3,igk1(ig)) - gpar(3)
! --- Find crystal coordinates of gtr, n1,n2,n3 ---
! --- and the position ng in the ngm array ---
IF (gtr(1)**2+gtr(2)**2+gtr(3)**2 <= gcutm) THEN
n1=NINT(gtr(1)*at(1,1)+gtr(2)*at(2,1) &
+gtr(3)*at(3,1))
n2=NINT(gtr(1)*at(1,2)+gtr(2)*at(2,2) &
+gtr(3)*at(3,2))
n3=NINT(gtr(1)*at(1,3)+gtr(2)*at(2,3) &
+gtr(3)*at(3,3))
ng=ln(n1,n2,n3)
IF ((ABS(g(1,ng)-gtr(1)) > eps) .OR. &
(ABS(g(2,ng)-gtr(2)) > eps) .OR. &
(ABS(g(3,ng)-gtr(3)) > eps)) THEN
WRITE(6,*) ' error: translated G=', &
gtr(1),gtr(2),gtr(3), &
& ' with crystal coordinates',n1,n2,n3, &
& ' corresponds to ng=',ng,' but G(ng)=', &
& g(1,ng),g(2,ng),g(3,ng)
WRITE(6,*) ' probably because G_par is NOT', &
& ' a reciprocal lattice vector '
WRITE(6,*) ' Possible choices as smallest ', &
' G_par:'
DO i=1,50
WRITE(6,*) ' i=',i,' G=', &
g(1,i),g(2,i),g(3,i)
ENDDO
STOP
ENDIF
ELSE
WRITE(6,*) ' |gtr| > gcutm for gtr=', &
gtr(1),gtr(2),gtr(3)
STOP
END IF
map_g(ig)=ng
enddo
ENDIF
mat=(0.d0,0.d0)
DO nb=1,nbnd
DO mb=1,nbnd
! CALL setv(2*ngm,0.d0,aux,1)
!
!added support for spin polarized case
l_cal=.true.
if( nspin==2 .and. tfixed_occ) then
if(f_inp(nb,is)==0.d0 .or. f_inp(mb,is)==0.d0) then
l_cal=.false.
if(nb==mb) then
mat(nb,mb)=1.d0
else
mat(nb,mb)=0.d0
endif
endif
endif
if(l_cal) then
! CALL setv(2*ngm,0.d0,aux0,1)
aux=(0.d0,0.d0)
aux0=(0.d0,0.d0)
DO ig=1,npw0
aux0(igk0(ig))=psi(ig,nb)
END DO
IF (kpar /= (nppstr+1)) THEN
do ig=1,npw1
aux(igk1(ig))=psi1(ig,mb)
enddo
ELSE
do ig=1,npw1
aux(map_g(ig))=psi1(ig,mb)
enddo
ENDIF
mat(nb,mb) = zdotc(ngm,aux0,1,aux,1)
call reduce(2,mat(nb,mb))
! --- Calculate the augmented part: ij=KB projectors, ---
! --- R=atom index: SUM_{ijR} q(ijR) <u_nk|beta_iR> ---
! --- <beta_jR|u_mk'> e^i(k-k')*R = ---
! --- also <u_nk|beta_iR>=<psi_nk|beta_iR> = becp^* ---
if(okvan) then
pref = (0.d0,0.d0)
DO jkb=1,nkb
nhjkb = nkbtonh(jkb)
na = nkbtona(jkb)
np = ityp(na)
nhjkbm = nh(np)
jkb1 = jkb - nhjkb
DO j = 1,nhjkbm
pref = pref+CONJG(becp0(jkb,nb))*becp_bp(jkb1+j,mb) &
*q_dk(nhjkb,j,np)*struc(na)
ENDDO
ENDDO
mat(nb,mb) = mat(nb,mb) + pref
endif
endif !on l_cal
ENDDO
ENDDO
! --- Calculate matrix determinant ---
! CALL zgefa(mat,nbnd,nbnd,ivpt,info)
! CALL errore('c_phase','error in zgefa',abs(info))
! job=10
! CALL zgedi(mat,nbnd,nbnd,ivpt,cdet,cdwork,job)
! det=cdet(1)*10.**cdet(2)
det=(1.,0.)
call zgetrf(nbnd,nbnd,mat,nbnd,ipivi,info)
CALL errore('c_phase','error in zgetrf',abs(info))
do ii=1,nbnd
if(ii.ne.ipivi(ii,1)) det=-det
enddo
do ii=1,nbnd
det = det*mat(ii,ii)
enddo
! write(6,*) "LogDet:", LOG(det)
! --- Multiply by the already calculated determinants ---
zeta=zeta*det
zeta_loc=zeta_loc*det
! --- End of dot products between wavefunctions and betas ---
ENDIF
! --- End loop over parallel k-points ---
END DO
pola=pola+wstring(istring)*aimag(log(zeta_loc))
kpoint=kpoint-1
! --- Calculate the phase for this string ---
phik(istring)=AIMAG(LOG(zeta))
cphik(istring)=COS(phik(istring))*(1.0_dp,0.0_dp) &
+SIN(phik(istring))*(0.0_dp,1.0_dp)
! --- Calculate the localization for current kort ---
zeta_mod= DBLE(CONJG(zeta)*zeta)
loc_k(istring)= - (nppstr-1) / gvec**2 / nbnd *log(zeta_mod)
! --- End loop over orthogonal k-points ---
END DO
! --- End loop over spin ---
END DO
!-----calculate polarization
!-----the factor 2. is because of spin
if(nspin==1) pola=pola*2.d0
pola=pola/(gpar(gdir)*tpiba)
!write output
write(stdout,*)
write(stdout,*) " Expectation value of exp(iGx):",zeta
write(stdout,*) " Electronic Dipole per cell (a.u.)",pola
! ------------------------------------------------------------------------- !
! ionic polarization !
! ------------------------------------------------------------------------- !
pola_ion=0.d0
DO na=1,nat
pola_ion=pola_ion+zv(ityp(na))*tau(gdir,na)
END DO
write(stdout,*) " Ionic Dipole per cell (a.u.)",pola_ion
write(stdout,*)
! ------------------------------------------------------------------------- !
! --- Free memory ---
DEALLOCATE(pdl_elec)
DEALLOCATE(mod_elec)
DEALLOCATE(wstring)
DEALLOCATE(loc_k)
DEALLOCATE(phik)
DEALLOCATE(cphik)
DEALLOCATE(map_g)
!------------------------------------------------------------------------------!
END SUBROUTINE c_phase_field
!==============================================================================!