Localization of phonons in mass disordered alloys - A typical medium dynamical cluster approach

Abstract

The effect of disorder on lattice vibrational modes has been a topic of interest for several decades. In this work, we employ a Green's function based approach, namely the dynamical cluster approximation (DCA), to investigate phonons in mass disordered systems. Detailed benchmarks with previous exact calculations are used to validate the method in a wide parameter space. An extension of the method, namely the typical medium DCA (TMDCA), is used to study Anderson localization of phonons in three dimensions. We show that, for binary isotopic disorder, lighter impurities induce localized modes beyond the bandwidth of the host system, while heavier impurities lead to a partial localization of the low-frequency acoustic modes. For a uniform (box) distribution of masses, the physical spectrum is shown to develop long tails comprising mostly localized modes. The mobility edge separating extended and localized modes, obtained through the TMDCA, agrees well with results from the transfer matrix method. A re-entrance behavior of the mobility edge with increasing disorder is found that is similar to, but somewhat more pronounced than, the behavior in disordered electronic systems. Our work establishes a new computational approach, which recovers the thermodynamic limit, is versatile and computationally inexpensive, to investigate lattice vibrations in disordered lattice systems.

arXiv comment14 pages, 10 figures

References in corpus (18)

• Quantum Cluster Theories
• Localization of ultrasound in a three-dimensional elastic network
• Statistical Signatures of Photon Localization
• Measurement of the mobility edge for 3D Anderson localization
• Remarkable Reduction of Thermal Conductivity in Silicon Nanotubes
• Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects
• Calculation of Densities of States and Spectral Functions by Chebyshev Recursion and Maximum Entropy
• Systematic and Causal Corrections to the Coherent Potential Approximation
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Isotopic effects on the thermal conductivity of graphene nanoribbons: localization mechanism
• Phonons in random alloys: the itinerant coherent-potential approximation
• A Typical Medium Dynamical Cluster Approximation for the Study of Anderson Localization in Three Dimensions
• Multiple-beam Propagation in an Anderson Localized Optical Fiber
• Anderson localization of phonons in dimension $d=1,2,3$ : finite-size properties of the Inverse Participation Ratios of eigenstates
• Study of off-diagonal disorder using the typical medium dynamical cluster approximation
• Finite Size Scaling Analysis of the Anderson Transition
• Anderson universality in a model of disordered phonons
• Generalized Multiband Typical Medium Dynamical Cluster Approximation: Application to (Ga,Mn)N

Cited by in corpus (6)

• Unraveling the role of V-V dimer on the vibrational properties of VO${}_2$ by first-principles simulations and Raman spectroscopic analysis
• Mode Localization and Suppressed Heat Transport in Amorphous Alloys
• Phonon localization in binary alloys with diagonal and off-diagonal disorder: A cluster Green's function approach
• Effect of isotope disorder on the Raman spectra of cubic boron arsenide
• Success and breakdown of the T-matrix approximation for phonon-disorder scattering
• Elastic electron scattering and localization in a chain with isotopic disorder