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

Jie Liu (1) , Xiaoyu Mao (1) , Jianxin Zhong (1) , Rudolf Römer (2, 3)

1 Department of Physics, Xiangtan University
2 Department of Physics - University of Warwick
3 LPTM - UMR 8089 - Laboratoire de Physique Théorique et Modélisation

We study the localization properties and the Anderson transition in the 3D Lieb lattice L3(1) and its extensions L3(n) 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 finite-size scaling, we obtain the critical properties such as critical disorders and energies as well as the universal localization lengths exponent ν. We find that the critical disorder Wc decreases from ∼ 16.5 for the cubic lattice, to ∼ 8.6 for L3(1), ∼ 5.9 for L3(2) and ∼ 4.8 for L3(3). Nevertheless, the value of the critical exponent ν for all Lieb lattices studied here and across disorder and energy transitions agrees within error bars with the generally accepted universal value ν = 1.590(1.579, 1.602).

Domains: Physics [physics]; Condensed Matter [cond-mat]; Disordered Systems and Neural Networks [cond-mat.dis-nn]

Jie Liu, Xiaoyu Mao, Jianxin Zhong, Rudolf Römer. Localization, phases, and transitions in three-dimensional extended Lieb lattices. Physical Review B, 2020, 102 (17), pp.174207. ⟨10.1103/PhysRevB.102.174207⟩. ⟨hal-03636458⟩