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Title: Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems

Abstract

Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical reviewmore » of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.« less

Authors:
 [1];  [2];  [2];  [3]; ORCiD logo [4];  [5];  [2]
+ Show Author Affiliations
  1. Middle Tennessee State Univ., Murfreesboro, TN (United States). Dept. of Physics and Astronomy. Computational Science Program
  2. Louisiana State Univ., Baton Rouge, LA (United States). Dept. of Physics and Astronomy. Center for Computation and Technology
  3. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Center for Nanophase Materials Sciences. Computer Science and Mathematics Division
  4. Univ. of Augsburg (Germany). Augsburg Center for Innovative Technologies. Theoretical Physics III. Center for Electronic Correlations and Magnetism. Inst. of Physics
  5. Jawaharlal Nehru Centre for Advanced Scientific Research, Bengaluru (India). Theoretical Sciences Unit
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Louisiana State Univ., Baton Rouge, LA (United States); Middle Tennessee State Univ., Murfreesboro, TN (United States); Univ. of Augsburg (Germany)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF); Louisiana Board of Regents (United States); German Research Foundation (DFG)
OSTI Identifier:
1484098
Alternate Identifier(s):
OSTI ID: 1658620
Grant/Contract Number:  
AC05-00OR22725; SC0017861; EPS-1003897; DMR1728457; TRR80/F6
Resource Type:
Accepted Manuscript
Journal Name:
Applied Sciences
Additional Journal Information:
Journal Volume: 8; Journal Issue: 12; Journal ID: ISSN 2076-3417
Publisher:
MDPI
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; disordered electrons; Anderson localization; metal-insulator transition; coarse-graining; typical medium; quantum cluster methods; first principles

Citation Formats

Terletska, Hanna, Zhang, Yi, Tam, Ka -Ming, Berlijn, Tom, Chioncel, Liviu, Vidhyadhiraja, N., and Jarrell, Mark. Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems. United States: N. p., 2018. Web. doi:10.3390/app8122401.
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Terletska, Hanna, Zhang, Yi, Tam, Ka -Ming, Berlijn, Tom, Chioncel, Liviu, Vidhyadhiraja, N., & Jarrell, Mark. Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems. United States. https://doi.org/10.3390/app8122401
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Terletska, Hanna, Zhang, Yi, Tam, Ka -Ming, Berlijn, Tom, Chioncel, Liviu, Vidhyadhiraja, N., and Jarrell, Mark. Mon . "Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems". United States. https://doi.org/10.3390/app8122401. https://www.osti.gov/servlets/purl/1484098.
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@article{osti_1484098,
title = {Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems},
author = {Terletska, Hanna and Zhang, Yi and Tam, Ka -Ming and Berlijn, Tom and Chioncel, Liviu and Vidhyadhiraja, N. and Jarrell, Mark},
abstractNote = {Great progress has been made in recent years towards understanding the properties of disordered electronic systems. In part, this is made possible by recent advances in quantum effective medium methods which enable the study of disorder and electron-electronic interactions on equal footing. They include dynamical mean-field theory and the Coherent Potential Approximation, and their cluster extension, the dynamical cluster approximation. Despite their successes, these methods do not enable the first-principles study of the strongly disordered regime, including the effects of electronic localization. The main focus of this review is the recently developed typical medium dynamical cluster approximation for disordered electronic systems. This method has been constructed to capture disorder-induced localization and is based on a mapping of a lattice onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Unlike the average effective medium-based methods mentioned above, typical medium-based methods properly capture the states localized by disorder. The typical medium dynamical cluster approximation not only provides the proper order parameter for Anderson localized states, but it can also incorporate the full complexity of Density-Functional Theory (DFT)-derived potentials into the analysis, including the effect of multiple bands, non-local disorder, and electron-electron interactions. After a brief historical review of other numerical methods for disordered systems, we discuss coarse-graining as a unifying principle for the development of translationally invariant quantum cluster methods. Together, the Coherent Potential Approximation, the Dynamical Mean-Field Theory and the Dynamical Cluster Approximation may be viewed as a single class of approximations with a much-needed small parameter of the inverse cluster size which may be used to control the approximation. We then present an overview of various recent applications of the typical medium dynamical cluster approximation to a variety of models and systems, including single and multiband Anderson model, and models with local and off-diagonal disorder. We then present the application of the method to realistic systems in the framework of the DFT and demonstrate that the resulting method can provide a systematic first-principles method validated by experiment and capable of making experimentally relevant predictions. We also discuss the application of the typical medium dynamical cluster approximation to systems with disorder and electron-electron interactions. Most significantly, we show that in the limits of strong disorder and weak interactions treated perturbatively, that the phenomena of 3D localization, including a mobility edge, remains intact. However, the metal-insulator transition is pushed to larger disorder values by the local interactions. We also study the limits of strong disorder and strong interactions capable of producing moment formation and screening, with a non-perturbative local approximation. Here, we find that the Anderson localization quantum phase transition is accompanied by a quantum-critical fan in the energy-disorder phase diagram.},
doi = {10.3390/app8122401},
journal = {Applied Sciences},
number = 12,
volume = 8,
place = {United States},
year = {Mon Nov 26 00:00:00 EST 2018},
month = {Mon Nov 26 00:00:00 EST 2018}
}
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Study of off-diagonal disorder using the typical medium dynamical cluster approximation
journal, September 2014

Chebyshev expansion approach to the AC conductivity of the Anderson model
journal, August 2004

Real-Space Calculation of the Conductivity Tensor for Disordered Topological Matter
journal, March 2015

Disorder Screening in Strongly Correlated Systems
journal, August 2003

Superconductivity in the iron selenide K x Fe 2 Se 2 ( 0 ≤ x ≤ 1.0 )
journal, November 2010

A Novel Large Moment Antiferromagnetic Order in K 0.8 Fe 1.6 Se 2 Superconductor
journal, August 2011

Theory of ferromagnetic (III,Mn)V semiconductors
journal, August 2006

Hole-mediated ferromagnetism in tetrahedrally coordinated semiconductors
journal, April 2001

Paramagnetism and antiferromagnetic d–d coupling in GaMnN magnetic semiconductor
journal, October 2001

  • Zając, M.; Gosk, J.; Kamińska, M.
  • Applied Physics Letters, Vol. 79, Issue 15
  • DOI: 10.1063/1.1406558

Observation of spin-glass behavior in homogeneous (Ga,Mn)N layers grown by reactive molecular-beam epitaxy
journal, April 2003

Indication of ferromagnetism in molecular-beam-epitaxy-derived N-type GaMnN
journal, August 2001

  • Overberg, Mark E.; Abernathy, Cammy R.; Pearton, Stephen J.
  • Applied Physics Letters, Vol. 79, Issue 9
  • DOI: 10.1063/1.1397763

Phase diagram and critical behavior of the random ferromagnet Ga 1 − x Mn x N
journal, August 2013

Magnetic and transport characteristics on high Curie temperature ferromagnet of Mn-doped GaN
journal, January 2002

  • Sasaki, Takahiko; Sonoda, Saki; Yamamoto, Yoshiyuki
  • Journal of Applied Physics, Vol. 91, Issue 10
  • DOI: 10.1063/1.1451879

Topological Anderson Insulator
journal, April 2009

Topological Anderson Insulator in Three Dimensions
journal, November 2010

Correlated Lattice Fermions in d = ∞ Dimensions
journal, February 1989

Metal-insulator transitions
journal, June 1991

Gate-defined Josephson junctions in magic-angle twisted bilayer graphene
journal, May 2021

Disordered Electronic Systems
journal, December 1988

  • Al'tshuler, Boris L.; Lee, Patrick A.
  • Physics Today, Vol. 41, Issue 12
  • DOI: 10.1063/1.881139

Quantum cluster theories
text, January 2005

Cellular Dynamical Mean Field Approach to Strongly Correlated Systems
text, January 2001

  • Biroli, Giulio; Kotliar, Gabriel; Pálsson, Gunnar
  • The American Physical Society
  • DOI: 10.17877/de290r-11153

Anderson transitions
text, January 2008

Anisotropic Lattice Distortions in Random Alloys from First-Principles Theory
text, January 2001

Anderson Transitions
text, January 2007

Classification of topological insulators and superconductors in three spatial dimensions
text, January 2008

Topological Anderson Insulator
text, January 2008

Experimental probing of the interplay between ferromagnetism and localisation in (Ga,Mn)As
text, January 2009

Correlated electrons in the presence of disorder
text, January 2010

Do Transition Metal Substitutions Dope Carriers in Iron Based Superconductors?
text, January 2011

Real-space calculation of the conductivity tensor for disordered topological matter
text, January 2014

Two-Channel Kondo Lattice: An Incoherent Metal
text, January 1996

Scaling theory of two-dimensional metal-insulator transitions
text, January 1997

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    Ab initio typical medium theory of substitutional disorder
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    Phonon localization in binary alloys with diagonal and off-diagonal disorder: A cluster Green's function approach
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