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

Abstract

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Localization properties in Lieb lattices and their extensions

“…For the d = 3 dimensional case, states are extended for disorders W down to W = 0.01t at the flat bands, indicating that the disorder can lift the degeneracy of the flat bands quickly. The phase diagram with periodic boundary condition for L 3 (1) looks similar to the one for hard boundaries [1]. We present the critical disorder W c at energy E = 0 and find a decreasing W c for increasing n for L 3 (n), up to n = 3.…”

“…In Ref. [1], we investigated the DOS, the localization properties and the phase diagrams for the 3D Lieb lattices L 3 (n), n = 1, 2, 3 and 4 as shown in Fig. 1.…”

“…1. Obviously, the main difference to the 2D case is the existence of an Anderson metal insulator transition (MIT) in 3D Lieb lattices [1]. Details of the TMM construction for L 3 (n) can also be found in Ref.…”

“…Details of the TMM construction for L 3 (n) can also be found in Ref. [1] along with finitesize scaling results for the universal critical exponent ν of the localization lengths. We found ν to be in good agreement with the currently accepted value of ν = 1.590(1.579, 1.602) [28,29] for the Anderson transition.…”

“…The phase diagrams given in Ref. [1] have been computed for the L 3 (n) lattices with hard wall boundaries. In Fig.…”