title: Effective cluster typical medium theory for the diagonal Anderson disorder model in one- and two-dimensions.
abstract: We develop a cluster typical medium theory to study localization in disordered electronic systems. Our formalism is able to incorporate non-local correlations beyond the local typical medium theory in a systematic way. The cluster typical medium theory utilizes the momentum-resolved typical density of states and hybridization function to characterize the localization transition. We apply the formalism to the Anderson model of localization in one- and two-dimensions. In one-dimension, we find that the critical disorder strength scales inversely with the linear cluster size with a power law, Wc ∼ (1/Lc)(1/ν), whereas in two-dimensions, the critical disorder strength decreases logarithmically with the linear cluster size. Our results are consistent with previous numerical work and are in agreement with the one-parameter scaling theory.
authors.affiliation: Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803, USA. Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA.
authors.forename: Chinedu E
authors.initials: CE
authors.lastname: Ekuma
authors.forename: Hanna
authors.initials: H
authors.lastname: Terletska
authors.forename: Zi Yang
authors.initials: ZY
authors.lastname: Meng
authors.forename: Juana
authors.initials: J
authors.lastname: Moreno
authors.forename: Mark
authors.initials: M
authors.lastname: Jarrell
authors.forename: Samiyeh
authors.initials: S
authors.lastname: Mahmoudian
authors.forename: Vladimir
authors.initials: V
authors.lastname: Dobrosavljević
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004574:Electromagnetic Fields; D008956:Models, Chemical; D015233:Models, Statistical