Enhanced localization, energy anomalous diffusion and resonant mode in harmonic chains with correlated mass-spring disorder

In this work, we study the vibrational modes and energy spreading in a harmonic chain model with diluted second-neighbors couplings and correlated mass-spring disorder. While all nearest neighbor masses are coupled by an elastic spring, second neighbors springs are introduced with a probability p(D). The masses are randomly distributed according to the site connectivity m(i) = m(0) (1+1/n(i)(alpha)), where n(i) is the connectivity of the site i and alpha is a tunable exponent. We show that maximum localization of the vibrational modes is achieved for alpha similar or equal to 3/4. The time-evolution of the energy wave-packet is followed after an initial localized excitation. While the participation number remains finite, the energy spread is shown to be sub-diffusive after a displacement and super-diffusive after an impulse excitation. These features are related to the development of a power-law tail in the wave-packet distribution. Further, we unveil that the spring dilution leads to the emergence of a resonant localized state which is signaled by a van Hove singularity in the density of states.