Self trapping of the triplet exciton in Sodium Chloride

One of the interesting unresolved issues in the exciton research is the mechanism and enegretics of its self-trapping into a small polaron state, and a decay into spatially separated defects.

The small polaron type defects in dielectric crystals is one of the strongest manifistations of the electron-phonon coupling. The formation of the polaron involves the localisation of the initially extended electronic excitation (electron, hole or electron-hole pair) in a polarised field created by the excitation itself. This process is associated in solids with strong local atomic distortions, which are both caused by the excitation and create the potential well localising it. This process is called self-trapping underlying the self-interaction of the electronic excitation with itself through the polarisable lattice.

We consider here the self-trapping of the triplet exciton (STE) in the crystalline NaCl, which is a typical example of a polaron of a small radius. Brief technical details of our ultra-soft pseudopotential plane wave DFT calculations can be seen here.

The left-side of the animated figure displays the (001) plane of the sodium chloride crystal whith ions (Na- blue, Cl - green) initially occupying their perfect lattice positions. The red circle also represents chlorine ion which initially is indistiguishible from the others. Next, we shift the red Cl ion along (110) crystallographic direction and adiabtically relax all the other ions. Thus, the atomic animation on the left represents the lowest energy trajectory of the moving (red) Cl ion. The right-side figure shows the simultaneous spin density map for the triplet state as it varies with atomic positions.

(100) view of the spin density change along the adiabatic surface

In the initial perfect lattice configuration, both spins, that of the hole and of the electron, are extended over the whole system, with the majority of spin density concentrated around anions. The spin density of the electron has also significant coontribution of the cation sublattice, but this is not seen on the present scale. As the atoms move, the electron and hole quickly localise and, due to the Pauli repulsion, separate. The hole component of the exciton forms the pi-sigma bond between the two (the red and the next green) Chlorine ions forming the quasi-molecule Cl₂^-. The electron component localises in the vacancy, which is left behind the red Chlorine ion. The further movement causes the gradual switch of the pi-sigma bond to the next pair of Cl ions along the (100) direction. This corresponds to the further electron-hole separation and to the decay of the exciton into the next neighbour Frenkel pair - H and F centers .

The process of the exciton's self trapping and decay can be also seen in the adiabatic surface representation, where we can see how the energy, and the net force on the moving atom is changing with the adiabatic coordinate, which is shown on the figure below. Also shown is the distance between the two red Cl ions reflecting the fomation of the Cl₂^- quasi-molecule.

The energy, force in the singlet and triplet state and the Cl(red)-Cl(green) distance in the Cl2- molecule changing along the calculated adiabatic surface. Zero corresponds to the perfect lattice and 8 - to the moving atom displaced into the nearest (110) site.

J.L. Gavartin, P.V. Sushko, and A.L. Shluger. Modeling charge self-trapping in wide-gap dielectrics: Localization problem in local density functionals. 2003, Phys. Rev. B 67 035108, cond-mat/0205218 .

Jacob Gavartin .