Localization properties in Lieb lattices and their extensions

  title={Localization properties in Lieb lattices and their extensions},
  author={Jie Liu and Xiaoyu Mao and Jian-Cheng Zhong and Rudolf A. R{\"o}mer},
We study the localization properties of generalized, twoand three-dimensional Lieb lattices, L2(n) and L3(n), n = 1, 2, 3 and 4, at energies corresponding to flat and dispersive bands using the transfer matrix method (TMM) and finite size scaling (FSS). We find that the scaling properties of the flat bands are different from scaling in dispersive bands for all Ld(n). For the d = 3 dimensional case, states are extended for disorders W down to W = 0.01t at the flat bands, indicating that the… 

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