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Effective cluster typical medium theory for the diagonal Anderson disorder model in one- and two-dimensions
Chinedu E Ekuma1, Hanna Terletska, Zi Yang Meng
1Department 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.
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.
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