Unconventional delocalization in a family of 3D Lieb lattices

Abstract

Uncorrelated disorder in generalized 3D Lieb models gives rise to the existence of bounded mobility edges, destroys the macroscopic degeneracy of the flat bands and breaks their compactly-localized states. We now introduce a mix of order and disorder such that this degeneracy remains and the compactly-localized states are preserved. We obtain the energy-disorder phase diagrams and identify mobility edges. Intriguingly, for large disorder the survival of the compactly-localized states induces the existence of delocalized eigenstates close to the original flat band energies -- yielding seemingly divergent mobility edges. For small disorder, however, a change from extended to localized behavior can be found upon decreasing disorder -- leading to an unconventional ``inverse Anderson" behavior. We show that transfer matrix methods, computing the localization lengths, as well as sparse-matrix diagonalization, using spectral gap-ratio energy-level statistics, are in excellent quantitative agreement. The preservation of the compactly-localized states even in the presence of this disorder might be useful for envisaged storage applications.

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Cited by in corpus (8)

• Kaleidoscopes of Hofstadter Butterflies and Aharonov-Bohm caging from $2^n$-root topology in decorated square lattices
• A tale of two localizations: coexistence of flat bands and Anderson localization in a photonics-inspired amorphous system
• Symmetry-enforced double Weyl points, multiband quantum geometry, and singular flat bands of doping-induced states at the Fermi level
• Electronic structure and transport in materials with flat bands: 2D materials and quasicrystals
• Non-perturbative dynamics of flat-band systems with correlated disorder
• Quantum engineering for compactly localized states in disordered Lieb lattices
• Localization and Flat Bands in Bond-Inflated Lattices
• Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping