Incoherent exciton trapping in self-similar aperiodic lattices

Abstract

Incoherent exciton dynamics in one-dimensional perfect lattices with traps at sites arranged according to aperiodic deterministic sequences is studied. We focus our attention on Thue-Morse and Fibonacci systems as canonical examples of self-similar aperiodic systems. Solving numerically the corresponding master equation we evaluate the survival probability and the mean-square displacement of an exciton initially created at a single site. Results are compared to systems of the same size with the same concentration of traps randomly as well as periodically distributed over the whole lattice. Excitons progressively extend over the lattice on increasing time and, in this sense, they act as a probe of the particular arrangements of traps in each system considered. The analysis of the characteristic features of their time decay indicates that exciton dynamics in self-similar aperiodic arrangements of traps is quite close to that observed in periodic ones, but differs significantly from that corresponding to random lattices. We also report on characteristic features of exciton motion suggesting that Fibonacci and Thue-Morse orderings might be clearly observed by appropriate experimental measurements. In the conclusions we comment on the implications of our work on the way towards a unified theory of the ordering of matter.

Tuning quantum corrections to the conductance in Andreev quantum dots

“…19 Our particular choice of parametrization builds on a recent work on ferromagnetic-normalferromagnetic systems 20 which is tailor-made for diagrammatic calculations. This parametrization requires the definition of matrices combining the information of the contacts and separating its scattering properties according to the direction of propagation.…”

Fluorescence decay in aperiodic Frenkel lattices

“…[11] Moreover, using a model based on the Pauli master equa-tion, we have also studied motion and capture of incoherent excitons when traps are arranged according to aperiodic sequences. [12] As an interesting feature, amenable to experimental confirmation by means of luminescence studies at moderate temperature, we obtained that the decay of the survival fraction of incoherent excitons is simply exponential P (t) ∼ exp(−At) instead of the asymptotic stretched exponential P (t) ∼ exp(−At 1/2 ) appearing in one-dimensional random lattices. [13] It is well-known that the exponent of the stretched exponential varies when passing from trapping of classical (incoherent) to quantum (coherent) excitons in random lattices.…”

“…[3][4][5][6] Following a long term project regarding electronic and transport properties of aperiodic systems, [7][8][9][10] our group focused its attention on optical absorption spectra of Frenkel excitons in Fibonacci and Thue-Morse lattices. [11,12] Our main aim was to learn about the phenomenology of incoherent and coherent exciton dynamics in molecular aggregates and polymers exhibiting longrange correlations. We considered Fibonacci and Thue-Morse lattices as canonical aperiodic models that are neither periodic nor random.…”

Optical absorption in Fibonacci lattices at finite temperature

“…Several electronic properties of these systems can be inferred from optical measurements: In particular, optical absorption techniques are suitable for their characterization because cuasiperiodic order causes the occurrence of well-defined lines which do not arise in periodic or random systems [1]. In previous works [1][2][3][4] we have focused our attention on Frenkel excitons in Fibonacci lattices as typical examples of lowdimensional quasiperiodic systems. By solving numerically the equation of motion of Frenkel excitons on the lattice, in which on-site energies take on two values following the Fibonacci sequence, we found that the characteristic satellites observed in the high-energy side of the absorption spectra correspond to well-defined peaks of the Fourier transform of the lattice.…”