修改printing.f90中的subroutine print_gkk，输出复数形式的$g^{SE}_{mn\nu}(\textbf{k},\textbf{q})$
要求： 不需要根据简并特点求平均，为了得到能量量纲的电声耦合大小，输出的值为：$\sqrt{\frac{\hbar}{2m_0\omega_{qv}}}g_{mnv}(\textbf{k},\textbf{q})$
\[g_{mn\nu}(\textbf{k},\textbf{q})=\langle{m\textbf{k+q}}|\partial_{\textbf{q}\nu}V|n\textbf{k}\rangle\] \[g^{SE}_{mn\nu}(\textbf{k},\textbf{q})=\sqrt{\frac{\hbar}{2m_0\omega_{q\nu}}}g_{mn\nu}(\textbf{k},\textbf{q})\]其中$m_0$为一个任意的参考质量，只是为了方便数据处理，$m_0$一般选择为质子质量,用于消除文献：Electron-phonon interaction using Wannier functions中公式（12）、（13）、（15）、（17）中计算$\partial_{\textbf{q}\nu}V$时引入的$m_0$。
其中
$g^{SE}_{mn\nu}(\textbf{k},\textbf{q})$
具有能量量纲,
$g_{mn\nu}(\textbf{k},\textbf{q})$
具有能量除以长度量纲。
reference:Electron-phonon interaction using Wannier functions
在实际的EPW程序中，epf17的量纲是$\frac{E}{\sqrt{M}l}$,输出
\(g^{SE}_{mn\nu}(\textbf{k},\textbf{q})\)
时只需要乘以
\(\sqrt{\frac{\hbar}{2\omega_{qv}}}\)
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gamma = (ABS(epf17(jbnd, ibnd, nu, ik)))**two
IF (wq > 0.d0) THEN
gamma = gamma / (two * wq)
对printing.f90做如下修改：
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USE constants_epw, ONLY : ryd2mev, ryd2ev, two, zero, czero ! Line 32
complex(kind=dp),allocatable :: epc_cmp(:,:,:,:) ! Line 92
!! complex gmnvkq-vertex with out "SYMMETRIZE"
!! "SYMMETRIZE": actually we simply take the averages over
!! degenerate states, it is only a convention because g is gauge-dependent!
allocate(epc_cmp(nbndfst,nbndfst,nmodes,nktotf),STAT = ierr) ! Line 104
IF (ierr /= 0) CALL errore('print_gkk', 'Error allocating epc_cmp', 1)
epc_cmp(:,:,:,:) = czero ! Line 109
! First do the average over bands and modes for each pool
DO ik = 1, nkf
ikk = 2 * ik - 1
ikq = ikk + 1
!
DO nu = 1, nmodes
wq = wf(nu, iq)
DO ibnd = 1, nbndfst
DO jbnd = 1, nbndfst
gamma = (ABS(epf17(jbnd, ibnd, nu, ik)))**two
IF (wq > 0.d0) THEN
gamma = gamma / (two * wq)
epc_cmp(ibnd, jbnd, nu, ik + lower_bnd - 1) = epf17(jbnd, ibnd, nu, ik)/sqrt(two * wq)
ELSE
gamma = 0.d0
epc_cmp(ibnd, jbnd, nu, ik + lower_bnd - 1) = czero
ENDIF
gamma = DSQRT(gamma)
! gamma = |g| [Ry]
epc(ibnd, jbnd, nu, ik + lower_bnd - 1) = gamma
ENDDO ! jbnd
ENDDO ! ibnd
ENDDO ! loop on modes
!
CALL mp_sum(epc_cmp, inter_pool_comm ) !Line 214
! Only master writes
IF (mpime == ionode_id) THEN
!
WRITE(stdout, '(5x, a)') ' Electron-phonon vertex |g| (meV)'
!
WRITE(stdout, '(/5x, "iq = ", i7, " coord.: ", 3f12.7)') iq, xqf(:, iq)
DO ik = 1, nktotf
!
ikk = 2 * ik - 1
ikq = ikk + 1
!
WRITE(stdout, '(5x, "ik = ", i7, " coord.: ", 3f12.7)') ik, xkf_all(:, ikk)
WRITE(stdout, '(5x, a)') ' ibnd jbnd imode enk[eV] enk+q[eV] &
& omega(q)[meV] |g|[meV] Re[gmnvkq][meV] Im[gmnvkq][meV]'
WRITE(stdout, '(5x, a)') REPEAT('-', 118)
!
DO ibnd = 1, nbndfst
ekk = etf_all(ibndmin - 1 + ibnd, ikk)
DO jbnd = 1, nbndfst
ekq = etf_all(ibndmin - 1 + jbnd, ikq)
DO nu = 1, nmodes
WRITE(stdout, '(3i9, 2f12.6, 1f20.10, 3e20.10)') ibndmin - 1 + ibnd, ibndmin - 1 + jbnd, &
nu, ryd2ev * ekk, ryd2ev * ekq, ryd2mev * wf(nu, iq), ryd2mev * epc(ibnd, jbnd, nu, ik), &
ryd2mev*epc_cmp(ibnd, jbnd, nu, ik)
ENDDO
ENDDO
!
ENDDO
WRITE(stdout, '(5x, a/)') REPEAT('-', 118)
!
ENDDO
ENDIF ! master node
!
DEALLOCATE(epc, STAT = ierr)
IF (ierr /= 0) CALL errore('print_gkk', 'Error deallocating epc', 1)
DEALLOCATE(epc_sym, STAT = ierr)
IF (ierr /= 0) CALL errore('print_gkk', 'Error deallocating epc_sym', 1)
deallocate(epc_cmp,stat = ierr)
IF (ierr /= 0) CALL errore('print_gkk', 'Error deallocating epc_sym', 1)
!
修改后代码以及软件编译参考：QUANTUM ESPRESSO v7.1 修改版安装
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