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 surfacesLow energy (~10ev) positron in.Implantation, thermalization, diffusion, encountering the surface

Positron trapped in surface state

Annihilation of surface state positron with an electron

10-12 - 10-11 sec

10-10 sec

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

Theory: optical gap properties explained by Se atoms outward relaxation.

Cd: BlueSe: Green

Puzder et al. ,Phys. Rev. Lett. 92, 217401 (2004).

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

0

z0

vdW constant:

Where is Ps polarizability and is the bulk dielectric function.

zVW = z0

Surface position

Bulk dielectric function

First-principles DFT for band structure: Full-potential linearized augmented plane wave (FLAPW).

We deduce

C=8.43 eV bohr3

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 eVExcited state: -0.005 eV

Molecular Ps FormationPs + Ps Ps2

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.

D.B. Cassidy and A.P. Mills Jr., Nature 449, 195 (2007).

Langmuir-Hishelwood reaction

•2 Ps atoms bound to a surface•Effective Lennard-Jones potential•Collision → surface assisted recombination•DesorptionEnergy 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 ~125 (ps)• Ortho-Ps (S=1) with ~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 annihilationparametercan 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 different from 0 could be used a criteria for Ps formation. The parameter is connected tothe self annihilation parameter by a trigonometric formula.

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 self-annihilation parameter described by a coherent state?

Barbiellini Theory effort

DFT

Spectroscopy

RIXS X-rayCompton

PositronAnnihilation

Hsin LinRay Wang

Peter MijnarendsWael Al-Sawai Susmita Basak

QMC

Dan Nissenbaum

Collaborators: A. Bansil and R.S. Markiewicz