Statistics of low energy levels of a one-dimensional weakly localized Frenkel exciton: A numerical study

Abstract

Numerical study of the one-dimensional Frenkel Hamiltonian with on-site randomness is carried out. We focus on the statistics of the energy levels near the lower exciton band edge, i.e., those determining optical response. We found that the distribution of the energy spacing between the states that are well localized at the same segment is characterized by a nonzero mean, i.e. these states undergo repulsion. This repulsion results in a local discrete energy structure of a localized Frenkel exciton. On the contrary, the energy spacing distribution for weakly overlapping local ground states ͑the states with no nodes within their localization segments͒ that are localized at different segments has zero mean and shows almost no repulsion. The typical width of the latter distribution is of the same order of magnitude as the typical spacing in the local discrete energy structure so that this local structure is hidden; it does not reveal itself either in the density of states or in the linear absorption spectra. However, this structure affects the two-exciton transitions involving the states of the same segment and can be observed by the pump-probe spectroscopy. We analyze also the disorder degree scaling of the first and second momenta of the distributions.

Scaling and Universality in the Optics of Disordered Exciton Chains

“…Using the relation / N p , the power E ÿ0:43 may be compared with the scaling of the typical localization length N . For the latter, previous studies yielded N / ÿ0:74 E [5] and N / ÿ0:8 E [15] (using different definitions for N ), which translates into values of E of ÿ0:37 and ÿ0:4, in good agreement with our findings. We also note that the values of E 1:44 and E ÿ0:43 comply well with the exchange narrowing argument (E / E = N p ), which implies that E 1 ÿ E .…”

“…The optically dominant states occur mostly in the DOS tail, below the lower bare band edge " b (" b ÿ2 and " b ÿ2:404 for NN and LR dipolar interactions, respectively). They are characterized by s-like wave functions that have no nodes on the main part of their localization segments [15]. The disorder imposes a typical localization size, N , for these states, which determines the typical transition dipole moment / N p (see, e.g., Ref.…”

Selection of dominant multi-exciton transitions in disordered linear J-aggregates

“…[12], | n ϕ νn |ϕ νn || ≥ C 0 . For a disorder-free the lowest state contains 81% of the total oscillator strength between the ground state and the one-exciton band [14].…”

“…These so-called p states may be identified as the second one-exciton state on a localization segment [11,12].…”

“…[7] that the three-state picture still holds to a good approximation, provided that one replaces the chain length by the typical exciton localization length. The existence of the so-called hidden structure of the Lifshits tail of the density of states (DOS) justifies this approach [11,12].…”