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 »
- Authors:
-
[3]
- Louisiana State Univ., Baton Rouge, LA (United States)
- Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore (India)
- 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. https://doi.org/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. https://doi.org/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 = {Thu Jul 20 00:00:00 EDT 2017},
month = {Thu Jul 20 00:00:00 EDT 2017}
}
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