Unusual localisation effects in quantum percolation

Abstract

We present a detailed study of the quantum site percolation problem on simple cubic lattices, thereby focussing on the statistics of the local density of states and the spatial structure of the single particle wavefunctions. Using the Kernel Polynomial Method we refine previous studies of the metal-insulator transition and demonstrate the non-monotonic energy dependence of the quantum percolation threshold. Remarkably, the data indicates a ``fragmentation'' of the spectrum into extended and localised states. In addition, the observation of a chequerboard-like structure of the wavefunctions at the band centre can be interpreted as anomalous localisation.

5 pages, 7 figures

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Cited by in corpus (22)

• The Kernel Polynomial Method
• A many body localization proximity effect
• Localization in random fractal lattices
• Mott-Hubbard and Anderson metal-insulator transitions in correlated lattice fermions with binary disorder
• Study of off-diagonal disorder using the typical medium dynamical cluster approximation
• The geometrically-averaged density of states as a measure of localization
• Dynamical Aspects of 2D Quantum Percolation
• Local distribution approach to disordered binary alloys
• Study of multiband disordered systems using the typical medium dynamical cluster approximation
• Localization-delocalization transitions in a two-dimensional quantum percolation model: von Neumann entropy studies
• Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
• High-resolution real-space evaluation of the self-energy operator of disordered lattices: Gade singularity, spin-orbit effects and p-wave superconductivity
• Dulmage-Mendelsohn percolation: Geometry of maximally-packed dimer models and topologically-protected zero modes on site-diluted bipartite lattices
• Characterisation of Anderson localisation using distributions
• Hölder mean applied to Anderson localization
• Metal - Insulator Transition in 3D Quantum Percolation
• Transport in tight-binding bond percolation models
• Anderson localization on Falicov-Kimball model with next-nearest-neighbor hopping and long-range correlated disorder
• Diffusion and localization in quantum random resistor networks
• Quantum $k$-core conduction on the Bethe lattice
• Anderson Transition in Disordered Bilayer Graphene
• Level statistics for quantum $k$-core percolation