Quantum cluster typical medium methods for the study of localization in strongly disordered electronic systems.

Disorder is a common feature of many materials and often plays a key role in changing and controlling their mechanical, electronic and other functional properties. Anderson localization is one of the fascinating effects of disorder in materials, which is often hard to capture numerically. There has been great progress made in the last several years towards understanding the properties of disordered electronic systems and electron localization, in particular, based on the effective medium methods. We have recently developed the Typical Medium Dynamical Cluster Approximation (TMDCA) for disordered electronic systems [1, 2]. The TMDCA enables quantitative analysis of electron localized states in disordered electron systems. The method is an effective medium approach that maps a given disorder lattice problem onto a quantum cluster embedded in an effective typical medium, which is determined self-consistently. Following the ideas of Dobrosavljevic et al. [3], the TMDCA employs the cluster typical (geometrically averaged) density of states as an order parameter to detect the localized electrons states. It has been shown that TMDCA not only correctly captures non-local effects but also recovers exact analytical results in simple disorder models [1]. In this talk, I will provide an overview of various recent applications of the TMDCA to a variety of models and systems, including application of the method to interacting disordered electrons as well as realistic systems in the framework of the ab-initio methods.
[1] Hanna Terletska, Yi Zhang, Ka Ming Tam, Tom Berlijn, Liviu Chioncel, N.S. Vidhyadhiraja, Mark
Jarrell, Review: App. Sci. 8, 12 (2018).
[2] C. E. Ekuma, H. Terletska, Z. Y. Meng, K. M. Tam, J. Moreno, and M. Jarrell, Phys. Rev. B 89, 081107(R) (2014).
[3] V. Dobrosavljevic, A. A. Pastor, B. K. Nikolic, Europhys. Lett. 62, 76 (2003).