Transcript Slide 1

Positronium in
Quartz:
Surface and
Bulk
Bernardo Barbiellini
Northeastern University
Boston, Massachusetts
Outline
• Positron surface states. Why they are
useful?
• Ps interaction with a Quartz surface: the
potential calculation by first-principles.
• The mechanism of the Ps2 production on
the Quartz surface.
• A new criteria for Ps formation.
PAS can probe surfaces
Low energy (~10ev) positron in.
Implantation, thermalization,
diffusion, encountering the surface
10-12 - 10-11 sec
Positron trapped in surface state
10-10 sec
Annihilation of surface state
positron with an electron
Experiments reveal surface states
The theory for positron surface states is still in its infancy.
We have recently solved the case for a quartz surface.
PAS a new probe for Nanoparticles
CdSe nanoparticles [Eijt et al., Nat. Mat. 5, 23 (2006) ]
The PAS provides a powerful tool
to determine the composition of
the surface region of NPs.
PAS has confirmed the Self-healing
mechanism in CdSe QDs
Cd: Blue
Se: Green
Puzder et al. ,
Phys. Rev. Lett. 92,
217401 (2004).
Theory: optical gap properties explained by Se atoms outward relaxation.
Positronium formation
at a surface of quartz
Positrons can pair up with electrons as Ps
at a surface of quartz and Ps can stick
to the surface.
Saniz, B. Barbiellini, P. M. Platzman, and
A. J. Freeman, PRL 99, 096101, (2007);
PRL 100, 019902, (2008).
Michael Schirber, Phys Rev. Focus 20, story 7
Ps-surface interaction potential
Repulsive
van der Waals
z
z0
0
vdW constant:
Where a(w) is Ps polarizability and e(w)
is the bulk dielectric function.
zVW = z0
Surface position
Bulk dielectric function e(w)
We deduce
C=8.43 eV bohr3
First-principles DFT for band structure:
Full-potential linearized augmented plane wave (FLAPW).
Charge density exponential
decay at the surface
z0=0.95 a.u.
1/l =2.06 a.u.
kc= 1/l
The repulsive part of the
potential is given by
Ps surface states
Ground state : -0.112 eV
Excited state: -0.005 eV
Molecular Ps Formation
Ps + Ps
Ps2
D.B. Cassidy and A.P. Mills Jr.,
Nature 449, 195 (2007).
Gas phase reaction - inefficient
More efficient channel on surfaces
Once two positroniums are
trapped on a surface, they can
easily combine to form a
dipositronium molecule.
The mechanism is analogous
to H2 formation on dust grain
surfaces in space.
Langmuir-Hishelwood reaction
•2 Ps atoms bound to a surface
•Effective Lennard-Jones potential
•Collision → surface assisted recombination
•Desorption
Energy balance:
Ps2 binding energy: Eb=-0.44 eV
2×EPs > Eb =>
Ps + Ps → Ps2 + EK
Nature of the Ps at the surface
• At the surface the Ps has two well defined
spin states.
• Para-Ps (S=0) with t~125 (ps)
• Ortho-Ps (S=1) with t~10 (ns)
• In which conditions there is a transition
from a spin mixture state with only one
lifetime component to well defined spin
states having two markedly different
lifetimes components ?
Total Spin
2D-ACAR in bulk quartz
These peaks are a manifestation of Ps delocalzation (Bloch wave).
Ps in Bulk quartz
Saito & Hyodo,
PRL 90, 193401 (2003)
The self annihilation parameter k can
be seen as an order parameter
associate to positron formation.
The ortho-Ps lifetime is about 300 ps much shorter that the corresponding lifetime
at the surface: important pickoff effect due to high electron density.
Ps wavefunction
The existence coherent state catacterized parameter l
different from 0 could be used a criteria for Ps formation.
The parameter l is connected to the self annihilation
parameter k by a trigonometric formula.
k
Conclusion
• The PAS has recently provided a powerful
technique to determine the composition of the
surface region of nanoparticles (solar cells).
• We are still exploring the fascinating theory of
positrons and Ps states at surfaces and in the
bulk.
• Could the Ps formation and in particular the selfannihilation parameter k described by a
coherent state?
Barbiellini Theory effort
DFT
QMC
Hsin Lin
Ray Wang
Dan Nissenbaum
Spectroscopy
RIXS
Wael Al-Sawai
X-ray
Compton
Susmita Basak
Collaborators: A. Bansil and R.S. Markiewicz
Positron
Annihilation
Peter Mijnarends