Title: Localization, phases and transitions in the three-dimensional extended Lieb lattices

Abstract: We study the localization properties and the Anderson transition in the 3D Lieb lattice 3(1)and its extensions 3(2) in the presence of disorder. We compute the positions of the flat bands, the disorder- broadened density of states and the energy-disorder phase diagrams for up to 4 different such Lieb lattices. Via nite-size scaling, we obtain the critical properties such as critical disorders and energies as well as the universal localization lengths exponent. We find that the critical disorder Wc decreases from 16.5 for the cubic lattice, to 8.6 for 3(1) 5.9 for 3(2) and 4.8 for 3(3). Nevertheless, the value of the critical exponent for all Lieb lattices studied here and across disorder and energy transitions agrees within error bars with the generally accepted universal value= 1.590(1.579, 1.602).

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