Typical-Medium Theory of Mott-Anderson Localization

Abstract

The Mott and the Anderson routes to localization have long been recognized as the two basic processes that can drive the metal-insulator transition (MIT). Theories separately describing each of these mechanisms were discussed long ago, but an accepted approach that can include both has remained elusive. The lack of any obvious static symmetry distinguishing the metal from the insulator poses another fundamental problem, since an appropriate static order parameter cannot be easily found. More recent work, however, has revisited the original arguments of Anderson and Mott, which stressed that the key diference between the metal end the insulator lies in the dynamics of the electron. This physical picture has suggested that the "typical" (geometrically averaged) escape rate from a given lattice site should be regarded as the proper dynamical order parameter for the MIT, one that can naturally describe both the Anderson and the Mott mechanism for localization. This article provides an overview of the recent results obtained from the corresponding Typical-Medium Theory, which provided new insight into the the two-fluid character of the Mott-Anderson transition.

to be published in "Fifty Years of Anderson localization", edited by E. Abrahams (World Scientific, Singapore, 2010); 29 pages, 22 figures.

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Cited by in corpus (14)

• Anderson-Hubbard model with box disorder: Statistical dynamical mean-field theory investigation
• Systematic Quantum Cluster Typical Medium Method For the Study of Localization in Strongly Disordered Electronic Systems
• Universal quantum criticality at the Mott-Anderson transition
• The two-dimensional disordered Mott metal-insulator transition
• Interaction-induced metallicity in a two-dimensional disordered non-Fermi liquid
• Localization of correlated fermions in optical lattices with speckle disorder
• Typical-medium, multiple-scattering theory for disordered systems with Anderson localization
• Ab initio typical medium theory of substitutional disorder
• Chiral condensate and Mott-Anderson freeze-out
• Quantum criticality at the Anderson transition: a TMT perspective
• Superconducting transition temperatures of pure vanadium and vanadium-titanium alloys in the presence of dynamical electronic correlations
• Non-local corrections to the typical medium theory of Anderson localization
• Coherent cellular dynamical mean-field theory: a real-space quantum embedding approach to disorder in strongly correlated electron systems
• Electronic correlations and Fermi liquid behavior of intermediate-band states in titanium-doped silicon