phonon assisted absorption
Posted: Sat Jun 15, 2019 2:35 pm
Hello,
For the phonon assisted absorption calculations, in the PRL paper (Phys. Rev Lett. 108, 167402 (2012)), the generalized optical matrix elements are:
S1(k,q) = Sum_m v_im(k)*g_mj,nu(k,q) / (e_mk - e_ik - hbar*omega + i*eta)
S2(k,q) = Sum_m g_im,nu(k,q)*v_mj(k+q) / (e_mk+q - e_ik +/- hbar*omega_nu,q + i*eta)
the plus and minus signs in the above equation are for phonon emission and absorption.
As of the implementation, in the source indabs.f90 file, the matrix elements are:
s1a(:) = s1a(:) + epf(mbnd, jbnd,imode) * 0.5 * vkk(:,ibnd, mbnd) / ( ekmk - ekq + wq(imode) + ci * eta(m) )
s1e(:) = s1e(:) + epf(mbnd, jbnd,imode) * 0.5 * vkk(:,ibnd, mbnd) / ( ekmk - ekq - wq(imode) + ci * eta(m) )
s2a(:) = s2a(:) + epf(ibnd, mbnd,imode) * 0.5 * vkq(:,mbnd, jbnd) / ( ekmq - ekk - wq(imode)+ ci * eta(m))
s2e(:) = s2e(:) + epf(ibnd, mbnd,imode) * 0.5 * vkq(:,mbnd, jbnd) / ( ekmq - ekk + wq(imode)+ ci * eta(m))
As we can see, the S2 agrees with each other, however, S1a and S1e are not the S1 in the PRL paper. Discrepancy can also be found for the carrier and phonon statistic function P = (n_nu,q + 1/2 +/- 1/2)(f_ik - f_jk+q) in the paper. For the implementation, it is however:
pfac = nqv(imode) * wgkk *(one- wgkq ) - (nqv(imode)+one)*(one-wgkk) * wgkq
pface = (nqv(imode)+one) * wgkk *(one- wgkq ) - nqv(imode) *(one-wgkk) * wgkq
for phonon absorption and emission, respectively. I really appreciate if anyone could give some comments and suggestions.
Best,
Xiaoming Wang
For the phonon assisted absorption calculations, in the PRL paper (Phys. Rev Lett. 108, 167402 (2012)), the generalized optical matrix elements are:
S1(k,q) = Sum_m v_im(k)*g_mj,nu(k,q) / (e_mk - e_ik - hbar*omega + i*eta)
S2(k,q) = Sum_m g_im,nu(k,q)*v_mj(k+q) / (e_mk+q - e_ik +/- hbar*omega_nu,q + i*eta)
the plus and minus signs in the above equation are for phonon emission and absorption.
As of the implementation, in the source indabs.f90 file, the matrix elements are:
s1a(:) = s1a(:) + epf(mbnd, jbnd,imode) * 0.5 * vkk(:,ibnd, mbnd) / ( ekmk - ekq + wq(imode) + ci * eta(m) )
s1e(:) = s1e(:) + epf(mbnd, jbnd,imode) * 0.5 * vkk(:,ibnd, mbnd) / ( ekmk - ekq - wq(imode) + ci * eta(m) )
s2a(:) = s2a(:) + epf(ibnd, mbnd,imode) * 0.5 * vkq(:,mbnd, jbnd) / ( ekmq - ekk - wq(imode)+ ci * eta(m))
s2e(:) = s2e(:) + epf(ibnd, mbnd,imode) * 0.5 * vkq(:,mbnd, jbnd) / ( ekmq - ekk + wq(imode)+ ci * eta(m))
As we can see, the S2 agrees with each other, however, S1a and S1e are not the S1 in the PRL paper. Discrepancy can also be found for the carrier and phonon statistic function P = (n_nu,q + 1/2 +/- 1/2)(f_ik - f_jk+q) in the paper. For the implementation, it is however:
pfac = nqv(imode) * wgkk *(one- wgkq ) - (nqv(imode)+one)*(one-wgkk) * wgkq
pface = (nqv(imode)+one) * wgkk *(one- wgkq ) - nqv(imode) *(one-wgkk) * wgkq
for phonon absorption and emission, respectively. I really appreciate if anyone could give some comments and suggestions.
Best,
Xiaoming Wang