Quasiparticle bands and optical spectra of highly ionic crystals: AlN and NaCl
F. Bechstedt, K. Seino, P. H. Hahn, and W. G. Schmidt*
Institut für Festkörpertheorie und -optik, Friedrich-Schiller-Universität, Max-Wien-Platz 1, 07743 Jena, Germany
Received 12 August 2005; revised manuscript received 27 October 2005; published 21 December 2005
Based on the ab initio density functional theory we study the influence of many-body effects on the
quasiparticle QP band structures and optical absorption spectra of highly ionic crystals. Quasiparticle shifts
and electron-hole interaction are studied within the GW approximation. In addition to the electronic screening
the effect of the lattice polarizability is discussed in detail. Substantial effects are observed for QP bands of
AlN and NaCl that have large polaron constants of 1–2. The effect of electronic and lattice polarization on the
optical spectra is discussed in terms of dynamical screening and vertex corrections. The results are critically
discussed in the light of experimental data available. We find that measured peak positions can be reproduced
without lattice polarizability in the screening of the electron-hole interaction and a reduced lattice contribution
to the QP shifts.
DOI: 10.1103/PhysRevB.72.245114 PACS numbers: 71.20.-b, 71.15.Qe
I. INTRODUCTION
Single-particle and two-particle electronic excitations are
accompanied by the rearrangement of the remaining elec-
trons in a solid. This effect is known as screening of excited
electrons above the Fermi level and excited holes missing
electrons below the Fermi level. The calculation of such
electronic excitations has made substantial progress in the
last decades, in particular using the framework of the many-
body perturbation theory MPBT.
1
In the case of clusters
and molecular structures also the density-functional response
theory is applied.
2
The most common assumption in the
MBPT is the GW approximation GWA of Hedin
3,4
which
describes the response of the electrons by a dynamically
screened Coulomb potential W. In this approximation the
self-energy operator of an excited particle is given as a
product of the potential W and the Green’s function G. The
poles of the G function correspond to the energies of the
dressed particles, the quasiparticles. Electron-hole pair exci-
tations are described by a special two-particle Green’s func-
tion, the so-called irreducible polarization function P. It
obeys a Bethe-Salpeter equation BSE.
5,6
Apart from an
electron-hole exchange local-field effect term proportional
to the bare Coulomb potential v, its kernel is dominated by
the variational derivative / G and hence by the screened
potential W in random-phase approximation RPA which is
already used in GWA and describes the attractive interaction
of quasielectrons and quasiholes.
7
The quasiparticle QP band structures of semiconductors
and insulators are now well described by means of ab initio
methods based on the density-functional theory
8
DFT
within the local-density approximation LDA for exchange
and correlation XC.
9
For DFT-LDA bands with a correct
energetical order the QP effects can be included by means
first-order perturbation theory with respect to the difference
of the XC self-energy and the XC potential already used in
the Kohn-Sham equation of the DFT. Its numerical
implementation
10,11
usually yields single-particle excitation
energies in good agreement with an accuracy of about
0.1 eV with angle-resolved photoemission/inverse photo-
emission experiments.
12–14
Solutions of the BSE in an ab
initio framework also appeared in the literature in the past
few years. Optical spectra can now be calculated including
excitonic effects for semiconductors and insulators,
15–17
solid
surfaces,
18,19
and even molecules.
17,20,21
These effects can
also be included in nonlinear optical properties.
22
All these
calculations are based on computations of the dielectric ma-
trix within the independent-particle approximation or a
model dielectric function for the electronic system. The same
calculational scheme has been also applied to wide-gap in-
sulators, such as LiF and MgO,
23,24
and wide gap semicon-
ductors, e.g., AlN.
25
These materials possess a remarkable
ionic contribution to the total chemical bonding. The bond
ionicity on an ab initio scale is given by the charge asymme-
try coefficient g with values g = 0.794 AlN and g = 0.958
NaCl.
26
Polar materials are characterized by longitudinal-optical
LO phonons whose excitation induces large macroscopic
electric fields in the crystal.
27
These fields strongly couple to
the excited electrons and holes and modify their motion.
Therefore, the question arises whether or not the lattice po-
larizability contributes to the dressing of the quasiparticles
and the screening of the electron-hole attraction. Ionic crys-
tals with big dynamical ion charges should show strong lat-
tice polaron effects modifying the electronic states near the
band edges.
28
Such systems have small static dielectric con-
stants
0
and
and relatively large longitudinal optical pho-
non frequencies
LO
. Because the static lattice polarizability
0
-
is of the same order of magnitude as the static elec-
tronic dielectric polarizability
-1 at high frequencies
LO
, large polaron constants
p
= 1/
-1/
0
/2ma
B
2
LO
1/2
a
B
-Bohr radius result,
28
for instance
p
1.2 or 2.0 for binary systems such as AlN and NaCl,
respectively. They yield non-negligible polaron shifts
p
LO
of about 0.1– 0.4 eV if perturbation theory can be
applied to electron or hole states. However, it is not clear i
how the lattice polarization really influences the quasiparticle
bands and ii whether or not the lattice polarization plays a
role on the time scale of the formation of a Coulomb-
correlated electron-hole pair. There are several open ques-
tions concerning the theoretical description of excitations in
PHYSICAL REVIEW B 72, 245114 2005
1098-0121/2005/7224/24511412/$23.00 ©2005 The American Physical Society 245114-1