Figure - available from: Journal of Physics: Condensed Matter
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Fractal dimension Γ of eigenstates as functions of corresponding eigenvalues E and quasiperiodic potential strength λ, for a fixed sample size L = 200. (a) Non-mosaic with κ = 1. (b) Mosaic with κ = 2.
Source publication
A one-dimensional lattice model with mosaic quasiperiodic potential is found to exhibit interesting localization properties, e.g., clear mobility edges [Y. Wang et al., Phys. Rev. Lett. \textbf{125}, 196604 (2020)]. We generalize this mosaic quasiperiodic model to a two-dimensional version, and numerically investigate its localization properties: t...
Citations
... When G is small (strong disorder) and/or M c is large (large size), G I ≈ G . This intrinsic conductance ( N x × N x ) has been widely employed to investigate the occurrence, scaling and critical properties of the MIT in 2D and 3D systems [53][54][55][56][57] . For example, it can be used to evaluate the standard scaling function β = d�ln G I � d ln N x 2,3,65 of MIT, where �· · · � still stands for averaging over the disorder ensemble. ...
... In Fig. 6d, we fix the fermi energy at E = 0 and display the development of the size scaling with increasing the disorder strength W. From the first glance, it seems to be a scaling pattern for the MIT, where the conductance is increasing ( β > 0 ) or decreasing ( β < 0 ) with N x on two ends of the W axis, respectively 53,54,56,57 . However a careful scrutinize can reveal several distinct differences from the scaling pattern of the standard MIT. ...
Abstract We investigate the effects of disorder and shielding on quantum transports in a two dimensional system with all-to-all long range hopping. In the weak disorder, cooperative shielding manifests itself as perfect conducting channels identical to those of the short range model, as if the long range hopping does not exist. With increasing disorder, the average and fluctuation of conductance are larger than those in the short range model, since the shielding is effectively broken and therefore long range hopping starts to take effect. Over several orders of disorder strength (until $$\sim 10^4$$ ∼ 10 4 times of nearest hopping), although the wavefunctions are not fully extended, they are also robustly prevented from being completely localized into a single site. Each wavefunction has several localization centers around the whole sample, thus leading to a fractal dimension remarkably smaller than 2 and also remarkably larger than 0, exhibiting a hybrid feature of localization and delocalization. The size scaling shows that for sufficiently large size and disorder strength, the conductance tends to saturate to a fixed value with the scaling function $$\beta \sim 0$$ β ∼ 0 , which is also a marginal phase between the typical metal ( $$\beta >0$$ β > 0 ) and insulating phase ( $$\beta
