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Systematic Quantum Cluster Typical Medium Method for the Study of Localization in Strongly Disordered Electronic Systems. APPLIED SCIENCES-BASEL 2018. [DOI: 10.3390/app8122401] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
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 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.
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Drchal V, Kudrnovský J, Pasturel A, Turek I, Weinberger P, Gonis A, Turchi PEA. Effective Interatomic Interactions VIA The TB-LMTO Method. ACTA ACUST UNITED AC 2011. [DOI: 10.1557/proc-491-65] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/13/2022]
Abstract
ABSTRACTThe energetics of metallic alloys, their surfaces or interfaces, and magnetic multilayers is studied in terms of effective interatomic (or interlayer) interactions that are determined from ab initio electronic structure calculations using the TB-LMTO method combined with the coherent potential approximation and the method of surface Green functions. First the theoretical background (force theorem, Lloyd formula, generalized perturbation method for bulk and surfaces, vertex cancellation theorem, method of infinitesimal rotations) is discussed, and then the applications to the phase stability of bulk alloys, surface segregation in disordered alloys, magnetism-induced ordering in two- and three-dimensional systems, phase diagram of two-dimensional alloys, interlayer exchange coupling in metallic multilayers, and the construction of Heisenberg-like Hamiltonians for magnetic systems are presented.
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Exchange Interactions in the Bcc Fe/TaW(001) System. E-JOURNAL OF SURFACE SCIENCE AND NANOTECHNOLOGY 2010. [DOI: 10.1380/ejssnt.2010.157] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Disorder-Induced Antiferromagnetic to Ferromagnetic Transition in Magnetic Overlayers: (Fe,Mn)/W(001) as a Case Study. E-JOURNAL OF SURFACE SCIENCE AND NANOTECHNOLOGY 2010. [DOI: 10.1380/ejssnt.2010.184] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Ganduglia-Pirovano MV, Natoli V, Cohen MH, Kudrnovsk J, Turek I. Potential, core-level, and d band shifts at transition-metal surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8892-8898. [PMID: 9984570 DOI: 10.1103/physrevb.54.8892] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Drchal V, Kudrnovsk J, Pasturel A, Turek I, Weinberger P. Ab initio theory of surface segregation: Self-consistent determination of the concentration profile. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 54:8202-8212. [PMID: 9984503 DOI: 10.1103/physrevb.54.8202] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Drchal V, Kudrnovsk J, Turek I, Weinberger P. Interlayer magnetic coupling: The torque method. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:15036-15044. [PMID: 9983300 DOI: 10.1103/physrevb.53.15036] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kudrnovsk J, Drchal V, Turek I, Sob M, Weinberger P. Interlayer magnetic coupling: Effect of interface roughness. PHYSICAL REVIEW. B, CONDENSED MATTER 1996; 53:5125-5128. [PMID: 9984107 DOI: 10.1103/physrevb.53.5125] [Citation(s) in RCA: 27] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Tétot R, Kudrnovsk J, Pasturel A, Drchal V, Weinberger P. Phase diagram of the Cu-Pd surface alloy: A first-principles calculation. PHYSICAL REVIEW. B, CONDENSED MATTER 1995; 51:17910-17915. [PMID: 9978825 DOI: 10.1103/physrevb.51.17910] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kudrnovsk J, Drchal V, Turek I, Weinberger P. Magnetic coupling of interfaces: A surface-Green's-function approach. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:16105-16108. [PMID: 9975990 DOI: 10.1103/physrevb.50.16105] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ganduglia-Pirovano MV, Cohen MH, Kudrnovsk J. Interference, resonances, and bound states at the Pd(001) and Rh(001) surfaces. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:11142-11145. [PMID: 9975225 DOI: 10.1103/physrevb.50.11142] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kudrnovsk J, Turek I, Pasturel A, Tetot R, Drchal V, Weinberger P. Magnetism-induced ordering in two and three dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:9603-9606. [PMID: 9975021 DOI: 10.1103/physrevb.50.9603] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Drchal V, Kudrnovsk J, Weinberger P. Relativistic electronic structure of random alloys and their surfaces by linear band-structure methods. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:7903-7914. [PMID: 9974780 DOI: 10.1103/physrevb.50.7903] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Aldén M, Abrikosov IA, Johansson B, Rosengaard NM, Skriver HL. Self-consistent Green's-function technique for bulk and surface impurity calculations: Surface core-level shifts by complete screening. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 50:5131-5146. [PMID: 9976851 DOI: 10.1103/physrevb.50.5131] [Citation(s) in RCA: 29] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Cohen MH, Ganduglia-Pirovano MV, Kudrnovský J. Orbital symmetry, reactivity, and transition metal surface chemistry. PHYSICAL REVIEW LETTERS 1994; 72:3222-3225. [PMID: 10056138 DOI: 10.1103/physrevlett.72.3222] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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Ruban AV, Abrikosov IA, Kats DY, Gorelikov D, Jacobsen KW, Skriver HL. Self-consistent electronic structure and segregation profiles of the Cu-Ni (001) random-alloy surface. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:11383-11396. [PMID: 10009991 DOI: 10.1103/physrevb.49.11383] [Citation(s) in RCA: 33] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Turek I, Kudrnovsk J, Drchal V, Weinberger P. Itinerant magnetism of disordered Fe-Co and Ni-Cu alloys in two and three dimensions. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:3352-3362. [PMID: 10011197 DOI: 10.1103/physrevb.49.3352] [Citation(s) in RCA: 34] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Ganduglia-Pirovano MV, Kudrnovsk J, Turek I, Drchal V, Cohen MH. Electronic structure of random Ag-Pd and Ag-vacancy overlayers on an fcc Pd(001) substrate. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:1870-1876. [PMID: 10008553 DOI: 10.1103/physrevb.48.1870] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Kudrnovsk J, Turek I, Drchal V, Weinberger P, Bose SK, Pasturel A. Self-consistent Green's-function method for surfaces of random alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:16525-16531. [PMID: 10006089 DOI: 10.1103/physrevb.47.16525] [Citation(s) in RCA: 29] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Abrikosov IA, Skriver HL. Self-consistent linear-muffin-tin-orbitals coherent-potential technique for bulk and surface calculations: Cu-Ni, Ag-Pd, and Au-Pt random alloys. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 47:16532-16541. [PMID: 10006090 DOI: 10.1103/physrevb.47.16532] [Citation(s) in RCA: 64] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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