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 Ps 2 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 z

0 0 vdW constant:

Where

a(w)

is Ps polarizability and

e(w)

is the bulk dielectric function.

z VW = z 0 Surface position

Bulk dielectric function

e(w) We deduce C=8.43 eV bohr 3

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

Charge density exponential decay at the surface

z 0 =0.95 a.u.

1/ l =2.06 a.u.

k c = 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 Ps 2 Gas phase reaction - inefficient More efficient channel on surfaces D.B. Cassidy and A.P. Mills Jr., Nature 449, 195 (2007).

Once two positroniums are trapped on a surface, they can easily combine to form a dipositronium molecule.

The mechanism is analogous to H 2 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: Ps 2 binding energy: E b =-0.44 eV 2× E Ps > E b => Ps + Ps → Ps 2 + E K

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 be seen as an order parameter associate to positron formation.

k can 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 The parameter l l different from 0 could be used a criteria for Ps formation. 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 self annihilation parameter k described by a coherent state?

Barbiellini Theory effort

DFT QMC Hsin Lin Ray Wang Dan Nissenbaum Spectroscopy

RIXS X-ray Compton

Wael Al-Sawai Susmita Basak Collaborators: A. Bansil and R.S. Markiewicz

Positron Annihilation

Peter Mijnarends