Localization in random fractal lattices

Kosior, Arkadiusz; Sacha, Krzysztof

doi:10.1103/physrevb.95.104206

Cited by 31 publications

(22 citation statements)

References 61 publications

(87 reference statements)

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“…[47] but it avoids vacancies in the interior of the dots. Instead of keeping the fractional Hausdorff dimension fixed [47], in modeling the edge disorder it is more important to make sure the distribution of the vacancies and additional atoms at the structure edge avoids dis-order in the interior. This problem is similar to that of modeling coastlines in geophysics [48].…”

Section: Structures Classificationmentioning

confidence: 99%

Electro-optical properties of phosphorene quantum dots

et al. 2017

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We study electronic and optical properties of single layer phosphorene quantum dots with various shapes, sizes, and edge types (including disordered edges) subjected to an external electric field normal to the structure plane. Compared to graphene quantum dots, in phosphorene clusters of similar shape and size there is a set of edge states with energies dispersed at around the Fermi level. These states make the majority of phosphorene quantum dots metallic and enrich the phosphorene absorption gap with low-energy absorption peaks tunable by the electric field. The presence of the edge states dispersed at around the Fermi level is a characteristic feature that is independent of the edge morphology and roughness.

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Section: Structures Classificationmentioning

confidence: 99%

Electro-optical properties of phosphorene quantum dots

et al. 2017

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“…The demonstrated levels of local and time-dependent control over tunnelling elements and site energies in our synthetic momentum-space lattice have allowed us to perform explorations of annealed disorder in an atomic system. Such an approach based on synthetic dimensions should enable myriad future explorations of engineered Floquet dynamics 51 – 54 and unconventional disordered lattices 55 , 56 . Furthermore, the realisation of designer disorder in a system that supports nonlinear atomic interactions 57 , 58 should permit us to explore aspects of many-body localisation 59 .…”

Section: Discussionmentioning

confidence: 99%

Diffusive and arrested transport of atoms under tailored disorder

An¹,

Meier²,

Gadway³

2017

Nat Commun

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Ultracold atoms in optical lattices offer a unique platform for investigating disorder-driven phenomena. While static disordered site potentials have been explored in a number of experiments, a more general, dynamical control over site-energy and off-diagonal tunnelling disorder has been lacking. The use of atomic quantum states as synthetic dimensions has introduced the spectroscopic, site-resolved control necessary to engineer more tailored realisations of disorder. Here, we present explorations of dynamical and tunneling disorder in an atomic system by controlling laser-driven dynamics of atomic population in a momentum-space lattice. By applying static tunnelling phase disorder to a one-dimensional lattice, we observe ballistic quantum spreading. When the applied disorder fluctuates on time scales comparable to intersite tunnelling, we instead observe diffusive atomic transport, signalling a crossover from quantum to classical expansion dynamics. We compare these observations to the case of static site-energy disorder, where we directly observe quantum localisation.

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“…A fractal, with non-integer Hausdorff dimension d H [1][2][3][4], has a hierarchically self-similar structure. The intrinsic features from this, including electronic energy spectrum statistics and transport [5][6][7][8][9][10][11][12][13][14], quantum Hall effect [15,16], plasmon [17], flat bands [18][19][20][21], and topological properties [22][23][24][25][26] have attracted dense interest. For example, d H determines the box-counting dimension of quantum conductance fluctuations in Sierpinski carpet geometry with infinite ramification number [2,10], and there are sharp peaks in the optical spectrum due to the specific electronic state pairs [11].…”

Section: Introductionmentioning

confidence: 99%

Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals

Yang,

Zhou,

Yao

et al. 2021

Preprint

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We propose a way to create effective plane fractals for confined electrons by chemical surface doping in two-dimensional materials. In particular, for Sierpinski carpet (SC), we consider the adsorption of hydrogen or fluorine atoms on monolayer graphene, forming an effective fractional geometry (H-SC and F-SC). By calculating the spatial distribution of states and the fractal analysis of quantum conductance fluctuations of H-SC, F-SC, and real SC, we find there is a consistency of the electronic states in these different systems. Further optical calculations verified the fractional confinement of electrons in H-SC and F-SC. Our results indicate that the chemical surface doping on graphene is an efficient and accessible approach to confine the electrons roaming in a fractional dimension, and will stimulate further theoretical and experimental studies of fractals based on twodimensional materials.

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Localization in random fractal lattices

Cited by 31 publications

References 61 publications

Electro-optical properties of phosphorene quantum dots

Electro-optical properties of phosphorene quantum dots

Diffusive and arrested transport of atoms under tailored disorder

Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals

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