相关论文: Confined Electrons in Effective Plane Fractals
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…
Fractals are self-repeating patterns which have dimensions given by fractions rather than integers. While the dimension of a system unambiguously defines its properties, a fractional dimensional system can exhibit interesting properties.…
In view of promising applications of fractal nanostructures, we analyze the spectra of quantum particles in the Sierpinski carpet and study the non-correlated electron gas in this geometry. We show that the spectrum exhibits scale…
Recent progress in controllable functionalization of graphene surfaces enables the experimental realization of complex functionalized graphene nanostructures, such as Sierpinski carpet (SC) fractals. Herein, we model the SC fractals formed…
The dimensionality of an electronic quantum system is decisive for its properties. In 1D electrons form a Luttinger liquid and in 2D they exhibit the quantum Hall effect. However, very little is known about the behavior of electrons in…
The Sierpinski Triangle (ST) is a fractal mathematical structure that has been used to explore the emergence of flat bands in lattices of different geometries and dimensions in condensed matter. Here we look into fractal features in the…
Orbital magnetization (OM) in Sierpinski carpet (SC) and triangle (ST) fractal is theoretically investigated by using Haldane model as a prototypical example. The OM calculation is performed following two distinct approaches; employing the…
Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a…
We construct Sierpinski-carpet (SC) based on AA or AB bilayer graphene by atom vacancies, namely, SC-AA and SC-AB, to investigate the effects of interlayer coupling on the electronic properties of fractals. Compared with monolayer graphene…
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…
Deterministic fractal antennas are employed to realize multimodal plasmonic devices. Such structures show strongly enhanced localized electromagnetic fields typically in the infrared range with a hierarchical spatial distribution.…
Fractal lattices, with their self-similar and intricate structures, offer potential platforms for engineering physical properties on the nanoscale and also for realizing and manipulating high order topological insulator states in novel…
We introduce hybrid fractals as a class of fractals constructed by gluing several fractal pieces in a specific manner and study energy forms and Laplacians on them. We consider in particular a hybrid based on the $3$-level Sierpinski…
Theoretical progress in graphene physics has largely relied on the application of a simple nearest-neighbor tight-binding model capable of predicting many of the electronic properties of this material. However, important features that…
At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density…
In past decades, the application of fractals to electrode design for enhanced signaling and electrochemical performance was a popular subject and enabled the growth of consumer micro-electronics. Supercapacitors, which are energy storage…
Hofstadter's butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux…
Ground-plane cloaks, which transform a curved mirror into a flat one, and recently reported at wavelengths ranging from the optical to the visible spectrum, bring the realm of optical illusion a step closer to reality. However, all…
Inside the metals, semiconductors, and magnets of our everyday experience, electrons are uniformly distributed throughout the material. By contrast, electrons often form clumpy patterns inside of strongly correlated electronic systems…
We report the presence of multiple flat bands in a class of two-dimensional (2D) lattices formed by Sierpinski gasket (SPG) fractal geometries as the basic unit cells. Solving the tight-binding Hamiltonian for such lattices with different…