Intraband exciton relaxation in a biased lattice with long-range correlated disorder

Abstract

We numerically study the intraband exciton relaxation in a one-dimensional lattice with a scale-free disorder in the presence of a linear bias. Exciton transport is the incoherent hopping over the eigenstates of the static lattice. The site potential of the unbiased lattice is long-range-correlated with a power-law spectral density S(k)similar to 1/k(alpha), alpha>0. The lattice supports a phase of extended states at the center of the band, provided alpha is larger than a critical value alpha(c) [F. A. B. F. de Moura and M. L. Lyra, Phys. Rev. Lett. 81, 3735 (1998)]. When the bias is applied, the absorption spectrum displays clear signatures of the Wannier-Stark ladder [E. Diaz, F. Dominguez-Adame, Yu. A. Kosevich, and V. A. Malyshev, Phys. Rev. B 73, 174210 (2006)]. We demonstrate that in unbiased lattices and in weakly correlated potentials, the decay law is nonexponential. However, the decay is purely exponential when the bias increases and alpha is large. We relate this exponential decay to the occurrence of the Wannier-Stark ladder in the exciton band.