Localization properties of harmonic chains with correlated mass and spring disorder: Analytical approach

Abstract

We study the localization properties of normal modes in harmonic chains with mass and spring weak disorder. Using a perturbative approach, an expression for the localization length is obtained, which is valid for arbitrary correlations of the disorder, and for practically the whole frequency band. In addition, we show how to generate effective mobility edges by the use of disorder with long range self-correlations and cross-correlations. Finally, the transport of phonons is also analyzed showing effective transparent windows that can be manipulated through the disorder correlations even for relative short chain sizes. Our results may have applications in modulating thermal transport, particularly in the design of thermal filters or in manufacturing high-thermal-conductivity materials.

10 pages, 6 figures

References in corpus (8)

• Heat Transport in low-dimensional systems
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• Heat transport in ordered harmonic lattices
• Role of pinning potentials in heat transport through disordered harmonic chain
• Localization in one-dimensional chains with Lévy-type disorder
• Anomalous thermal properties of a harmonic chain with correlated isotopic disorder
• Aspects of the disordered harmonic chain
• Thermal transport in disordered harmonic chains revisited: Formulation of thermal conductivity and local temperatures

Cited by in corpus (2)

• Tunable phononic transparency and opacity with isotopic defects
• Disordered harmonic chain with random masses and springs: a combinatorial approach