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Title: 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 article, 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 reentrance 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 computational approach, which recovers the thermodynamic limit, is versatile and computationally inexpensive, to investigate lattice vibrations in disorderedmore » lattice systems.« less

Authors:
 [1];  [1];  [2];  [2]; ORCiD logo [3]
  1. Louisiana State Univ., Baton Rouge, LA (United States)
  2. Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore (India)
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1399529
Alternate Identifier(s):
OSTI ID: 1372131
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review B
Additional Journal Information:
Journal Volume: 96; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Jarrell, Mark, Moreno, Juana, Raja Mondal, Wasim, S. Vidhyadhiraja, N., and Berlijn, Tom. Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach. United States: N. p., 2017. Web. doi:10.1103/PhysRevB.96.014203.
Jarrell, Mark, Moreno, Juana, Raja Mondal, Wasim, S. Vidhyadhiraja, N., & Berlijn, Tom. Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach. United States. doi:10.1103/PhysRevB.96.014203.
Jarrell, Mark, Moreno, Juana, Raja Mondal, Wasim, S. Vidhyadhiraja, N., and Berlijn, Tom. Thu . "Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach". United States. doi:10.1103/PhysRevB.96.014203. https://www.osti.gov/servlets/purl/1399529.
@article{osti_1399529,
title = {Localization of phonons in mass-disordered alloys: A typical medium dynamical cluster approach},
author = {Jarrell, Mark and Moreno, Juana and Raja Mondal, Wasim and S. Vidhyadhiraja, N. and Berlijn, Tom},
abstractNote = {The effect of disorder on lattice vibrational modes has been a topic of interest for several decades. In this article, 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 reentrance 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 computational approach, which recovers the thermodynamic limit, is versatile and computationally inexpensive, to investigate lattice vibrations in disordered lattice systems.},
doi = {10.1103/PhysRevB.96.014203},
journal = {Physical Review B},
number = ,
volume = 96,
place = {United States},
year = {2017},
month = {7}
}

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