The Calculation of Two-Particle Quantities in the Typical Medium Dynamical Cluster Approximation

Abstract

The mean-field theory for disordered electron systems without interaction is widely and successfully used to describe equilibrium properties of materials over the whole range of disorder strengths. However, it fails to take into account the effects of quantum coherence and information of localization. Vertex corrections due to multiple back-scatterings may drive the electrical conductivity to zero and make expansions around the mean field in strong disorder problematic. Here, we present a method for the calculation of two-particle quantities which enable us to characterize the metal-insulator transitions (MIT) in disordered electron systems by using the Typical Medium Dynamical Cluster Approximation (TMDCA). We show how to include vertex corrections and the information about the mobility edge to the typical mean-field theory. We successfully demonstrate the application of the developed method by showing that the conductivity formulated in this way properly characterizes the MIT in disordered systems.

arXiv comment7 pages, 5 figures

References in corpus (17)

• Quantum Cluster Theories
• The Kernel Polynomial Method
• Statistics and Scaling in Disordered Mesoscopic Electron Systems
• Mott--Hubbard transition vs. Anderson localization of correlated, disordered electrons
• A Quantum Monte Carlo algorithm for non-local corrections to the Dynamical Mean-Field Approximation
• Typical medium theory of Anderson localization: A local order parameter approach to strong disorder effects
• Systematic and Causal Corrections to the Coherent Potential Approximation
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Real-space calculation of the conductivity tensor for disordered topological matter
• Distribution of the local density of states as a criterion for Anderson localization: Numerically exact results for various lattices in two and three dimensions
• A Typical Medium Dynamical Cluster Approximation for the Study of Anderson Localization in Three Dimensions
• Chebyshev expansion approach to the AC conductivity of the Anderson model
• Universality of the metal-insulator transition in three-dimensional disordered systems
• Study of multiband disordered systems using the typical medium dynamical cluster approximation
• Generalized Multiband Typical Medium Dynamical Cluster Approximation: Application to (Ga,Mn)N
• Metal-Insulator-Transition in a Weakly interacting Disordered Electron System
• Dual Fermion Method for Disordered Electronic Systems

Cited by in corpus (4)

• Systematic Quantum Cluster Typical Medium Method For the Study of Localization in Strongly Disordered Electronic Systems
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• Theory of anisotropic elastoresistivity of two-dimensional extremely strongly correlated metals
• Two-particle excitations under coexisting electron interaction and disorder