EXCITON LOCALIZATION IN STRUCTURALLY DISORDERED MATERIALS

Abstract

We study the localization of excitonic eigenstates in structurally disordered materials. For two-level systems the problem leads to the quantumpercolation model, of which the Anderson-localization is a special case. The general Hamiltonian admits both diagonal and off-diagonal randomness. Applications to the triplet excitons of naphthalene and anthracene mixed crystals involve mostly the diagonal disorder, on which we focus. As localization criterium we use the inverse participation ratios of the excitonic wave functions, and we monitor the localization properties of the protonated and deuterated species over the full range of mixing, As an extension of the procedure, the excitonic lineshapes are readily computed, The transition between localized and delocalized quantum states in disordered sys- terns is fundamental in the study of electron and energy transfer processes /1^3/. Applications range from molecular crystals to amorphous and polymeric materials/4,5/ Starting from an assembly of interacting two-level systems (TT£) one has as Hamiltonian in the local basis H = ZEjixil +.EVi.|i> . These have in the local basis the fonn k l$k> = C cili> , with i ]c:12=1 k 1 FL-m the coefficients c. the inverse participation ratio (IPR) associated w i t h the state I$k> is easily ob$ained $ obviously equals unity for an eigenstate localized on a single site, while it becLms snall, l/n, for a state evenly delocalized over n sites, We view the IPR as a god description of the properties of the wave function l$ >, and we have used it as criterium, obviously also bearing in mind the case with whch it may be calculated, after the state 1 $ > is known. However, for m s e s of averaging over many configurations, the dis&ibution of the is not readily pictured. we found it convenient to compute the density of the in the unit interval, n(L) and to use in graphical display the function /6,8/