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 ${\mathcal{L}}_3(1)$ and its extensions ${\mathcal{L}}_3(n)$ 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 $\nu$. We find that the critical disorder $W_c$ decreases from $\sim 16.5$ for the cubic lattice, to $\sim 8.6$ for ${\mathcal{L}}_3(1)$, $\sim 5.9$ for ${\mathcal{L}}_3(2)$ and $\sim 4.8$ for ${\mathcal{L}}_3(3)$. Nevertheless, the value of the critical exponent $\nu$ for all Lieb lattices studied here and across disorder and energy transitions agrees within error bars with the generally accepted universal value $\nu =1.590(1.579,1.602)$.

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• Localization properties in Lieb lattices and their extensions
• Persistent homology analysis of a generalized Aubry-André-Harper model
• Unconventional delocalization in a family of 3D Lieb lattices
• Compact localised states in magnonic Lieb lattices
• Complete escape from localization on a hierarchical lattice: A Koch fractal with all states extended
• Quantum percolation on Lieb Lattices
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Quantum engineering for compactly localized states in disordered Lieb lattices
• Numerical methods for localization
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping