Related papers: Electronic fractal patterns in building Sierpinski…
In recent years, synthesis and experimental research of fractalized materials has evolved in a paradigmatic crossover with topological phases of matter. We present here a theoretical investigation of the helical edge transport in Sierpinski…
There is a growing interest in searching for topology in fractal dimensions with the aim of finding different properties and advantages compared to the integer dimensional case. It has previously been shown that the Laughlin state can be…
We prove that the hierarchical fractal model recently proposed for describing the stretched polymers [A. N. Samukhin et al, Phys. Rev. Lett.{\bf 78}, 326(1997)] is equivalent to a one-dimensional chain with hierarchical aperiodic structure.…
Recent progress in the design and fabrication of artificial two-dimensional (2D) materials paves the way for the experimental realization of electron systems moving on plane fractals. In this work, we present the results of computer…
Small-angle scattering (SAS) of X-rays, neutrons or light from ensembles of randomly oriented and placed deterministic fractal structures are studied theoretically. In the standard analysis, a very few parameters can be determined from SAS…
The checkerboard lattice has been proposed to host topological flat bands as a result of destructive interference among its various electronic hopping terms. However, it has proven challenging to realize experimentally due to the difficulty…
We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully…
The local structure of a fractal set is described by its dimension $D$, which is the exponent of a power-law relating the mass ${\cal N}$ in a ball to its radius $\epsilon$: ${\cal N}\sim \epsilon^D$. It is desirable to characterise the…
We present a comprehensive theory of spin transport in a non-degenerate semiconductor that is in contact with multiple ferromagnetic terminals. The spin dynamics in the semiconductor is studied during a perturbation of a general,…
Noncolinear magnetic texture breaks the spin-sublattice symmetry which gives rise to a spin-splitting effect. Inspired by this, we study the spin-dependent transport properties in a noncolinear antiferromagnetic fractal structure, namely,…
Electronic states with fractional spins arise in systems with large static correlation (strongly correlated systems). Such fractional-spin states are shown to be ensembles of degenerate ground states with normal spins. It is proven here…
Explicit predictions for Scanning Tunneling Microscopy (STM) on interacting one-dimensional electron systems are made using the Luttinger liquid formalism. The STM current changes with distance from an impurity or boundary in a…
The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two…
Fractal structures such as the Sierpi\'nski gasket have been predicted to enhance the critical temperature of s-wave superconductivity compared to regular crystals while maintaining macroscopic phase coherence of Cooper pairs. Here we…
We discuss the steady-state electronic transport in solid-state and molecular devices in the quantum regime. The decimation technique allows a comprehensive description of the electronic structure. Such a method is used, in conjunction with…
Land reclamation methods, indispensable for the proper development of modern coastal cities, are ecologically destructive. We present a fractal structure, similar to a Sierpinski triangle, which solves this problem by resting directly on…
We investigate the topological phases of the Haldane model on the Sierpi\'nski gasket. As a consequence of the fractal geometry, multiple fractal gaps arise. Additionally, a flat band appears, and due to a complex next-nearest neighbour…
Using the Sierpinski gasket (triangle) and carpet (square) lattices as examples, we theoretically study the properties of fractal superconductors. For that, we focus on the phenomenon of $s$-wave superconductivity in the Hubbard model with…
Theoretical quest of flat-band tight-binding models usually relies on lattice structures on which electrons reside. Typical examples of candidate lattice structures include the Lieb-type lattices and the line graphs. Meanwhile, there can be…
We show that transport in low-dimensional carbon structures with finite concentrations of scatterers can be modeled by utilising scaling theory and effective cross sections. Our reults are based on large scale numerical simulations of…