Download First Principle Calculations of Positron

First Principle Calculations of
Positron Annihilation in CdSe
Quantum Dots
B. Barbiellini, A. Bansil
(Northeastern University, Boston, MA 02115),
P. Mijnarends
(Delft University of Technology,Delft, The Netherlands),
R. Saniz
(UCB, Cochabamba, Bolivia),
P. Sterne
(Lawrence Livermore National Laboratory),
M. Weber, K. Lynn
(Washington State University, Pullman WA 99164),
A. Denison
(INEEL, Idaho Falls, ID 83415 and
Lawrence Livermore National Laboratory)
Theory I
The Density Functional Theory (DFT) is generalized
to positron-electron systems by including electron and
positron density(
The ground-state value of any operator is a functional
of the electron and positron densities and be calculated
via the Hellmann-Feynman theorem:
: Coupling constant
Theory II
The Local Density Approximation (LDA) was the first
implementation. It provides an explicit formula for
the Exchange-Correlation Energy
The Generalized Gradient Approximation (GGA)
reduces the LDA electron-positron correlation.
The GGA is very successful for positron lifetimes,
energetics, and momentum distributions of the
annihilating pairs.
Positron lifetime in bulk CdSe
An experimental lifetime of 275 ps was found in agreement
with the theoretical value of 279 ps based on the DFT GGA.
A highly accurate description of the electron-positron
correlation effects is needed to find such a good agreement.
Such agreement indicates also that our bulk sample is of
good quality (without any significant concentration of
atomic point defects).
Positron state in a CdSe Qdot
• The state of the positron can be explained in terms
of the positron Affinity (calculated by DFT GGA)
between the Qdot and the matrix.
• Potential well is about 2 eV therefore positrons are
trapped in the CdSe Qdots.
• Using an LMTO basis set we find that almost 80%
of the positron wave function is confined to the
interstitial region between the atoms thus limiting
the fraction that could extend beyond the quantum
dot volume.
MOMENTUM DENSITY I
DOS
The variation of the gap is proportional to the variation of the
momentum density smearing width (Peter & Friedel model).
Momentum density II
Gap: ZnSe>CdSe>CdTe
P (2pi/a)
Mometum smearing:
width of -dn(p)/dp
Smearing
= width
P (2pi/a)
Spectral
functions
From the H atom to the
H chain: the momentum
cutoff gets shaper
Momentum density
Orbitals of the H chain
Conclusion
The scheme based on measuring and calculating positron lifetime and
momentum distributions is a reliable tool to analyze materials properties.
The study (Lifetime and Doppler profile) of bulk CdSe gives credence to
use the DFT GGA scheme.
The localized positron states at Qdots have also been found well
described by the DFT GGA (Affinity).
The Doppler profile shows a smearing at the boundary of the Jones zone
proportional to the widening of the band gap that may occur due to a
reduction in the size of the quantum dots.