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

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)∼1/k^α, α>0. The lattice supports a phase of extended states at the center of the band, provided α is larger than a critical value α_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. Díaz, F. Domínguez-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 α is large. We relate this exponential decay to the occurrence of the Wannier–Stark ladder in the exciton band.