"Ultra-fast carriers dynamics in semi-conductors: a first-principles
many-body approach"
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A first-principles implementation of the Kadanoff-Baym Equation (KBE)
for extended systems is presented. The KBE describes both the carriers
dynamics and the polarization dynamics by means of the
out-of-equilibrium Green’s function [1]. When the polarizarion is
considered, the inclusion of the static self-energy and the changes in
the time-dependent Hartree potentials
give, in the linear regime limit, the time dependent extension of the
well-known Bethe-Salpeter equation [2]. These effects also ensures a
correct coupling between the electronic system and the laser pulse,
that is between the field intensity and the number of electrons
injected in the conduction band. The terms describing the dynamical
correlation instead, also known as scattering terms, are the key
players in the relaxation process. In our approach they are included
within the out of equilibium extensions of the GW, for the
electron-electron interaction, and FAN, for the electron-phonon
interaction self-energy [3].
In particular we describe how equilibrium is restored in bulk Silicon,
when carriers are injected in the conduction band by an ultra-short
laser pulse. The excited electrons and holes relax towards two Fermi
distributions, within about one hundred femtoseconds. While the two
Fermi distributions are created the energy gained by the electronic
system is dissipated to the lattice. The whole process is completed on
the pico-seconds time-scale. The correct balance between the
electronic and the phononic scattering processes is obtained thanks to
a double grid sampling of the Brillouin zone. The results of the
simulations are also compared with recent pump-probe measurments with
femtosecond laser pulses [4–7]
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[1] H. W. J. Haug, and A.-P. Jauho, Quantum kinetics in transport and
optics of semiconductors, Springer series in solid-state science, 123,
Springer-Verlag Berlin Heidelberg 1997, 2nd edition(2008)
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[2] C. Attaccalite, M. Gruning, and A. Marini, Phys. Rev. B 84, 245110 (2011)
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[3] A. Marini, J. Phys.: Conf. Ser. 427, 012003 (2013)
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[4] D. Sangalli, and A. Marini, Ultra–fast degenerate L→L scattering
versus inter–valley L→X
scattering in bulk Silicon: a parameters free approach, manuscript in
preparation (2014)
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[5] D. Sangalli, and A. Marini, Ultra-fast carriers dynamics in
semi-conductors: a first-principles
many-body approach, manuscript in preparation (2014)
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[6] A. Marini, C. Hogan, M.Gruning, and D. Varsano, Comp. Phys. Comm.
180, 1392 (2009)
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[7] T. Ichibayashi, S. Tanaka, J. Kanasaki, and K. Tanimura, Phys.
Rev. B 84, 235210 (2011)