Typical-medium multiple-scattering theory for disordered systems with Anderson localization

Abstract

The typical medium dynamical cluster approximation (TMDCA) is reformulated in the language of multiple scattering theory to make possible first principles calculations of the electronic structure of substitutionally disordered alloys including the effect of Anderson localization. The TMDCA allows for a systematic inclusion of non-local multi-site correlations and at same time provides an order parameter, the typical density of states, for the Anderson localization transition. The relation between the dynamical cluster approximation and the multiple scattering theory is analyzed, and is illustrated for a tight-binding model.

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

“…This will be relevant, for example, to unraveling the role of disorder in topological materials [75,97]. Another interesting topic is to combine this approach with the multiple scattering theory [58], and the locally selfconsistent multiple scattering method [66] for the study of materials with random disorder. both local and non-local ansatzes.…”

“…The TMDCA overcomes the shortcomings of the local single site TMT and accurately predicts the critical disorder strength of the Anderson localization transition in a single-band Anderson model. For model Hamiltonian systems, the TMDCA has been applied to non-interacting and weakly interacting disordered three-dimensional systems [52,53,57,58], systems with off-diagonal disorder [59], phonon localization [60,61], and multi-orbital models [62]. Some of the methods inspired by the typical medium theories have been combined with first-principles calculations [63][64][65].…”

Correlated electronic structure with uncorrelated disorder

“…This would allow to compute disordered strongly correlated system without any bias. Another interesting venue is to change the arithmetic configuration average used in the CPA to the geometric average used in typical medium methods 86,87 . This will allow one to investigate the effects of Anderson localization 43 in realistic materials.…”

“…In the next step the many-body problem is solved using the DMFT methodology: the DMFT bath Green's function is constructed as: (20) are equivalent as they provide the alloy components computed using the Dyson equation. In our recent paper 86 we have extensively discussed several self-consistent loop algorithms for the disorder problem. These include cluster extensions and alternative effective medium theories beyond the CPA.…”

Real Space Quantum Cluster Formulation for the Typical Medium Theory of Anderson Localization

“…The TMDCA overcomes the shortcomings of the local single site TMT, and accurately predicts the critical disorder strength of the Anderson localization transition in a single-band Anderson model. For model Hamiltonian systems, the TMDCA has been applied to non-interacting and weakly interacting disordered three dimensional systems 26,27,31,32 , systems with off-diagonal disorder 33 , phonon localization 34,35 and multi-orbital models 36 . Some of the methods inspired by the typical medium theories have been combined with the first-principles calculations [37][38][39] .…”