Related papers: Flat bands in fractal-like geometry
Kagome lattice has been actively studied for the possible realization of frustration-induced two-dimensional flat bands and a number of correlation-induced phases. Currently, the search for kagome systems with a nearly dispersionless flat…
'Magic'-angle twisted bilayer graphene has received a lot of interest due to its flat bands with potentially non-trivial topology that lead to intricate correlated phases. A spectrum with flat bands, however, does not require a twist…
The topological properties of the flat band states of a one-electron Hamiltonian that describes a chain of atoms with $s-p$ orbitals are explored. This model is mapped onto a Kitaev-Creutz type model, providing a useful framework to…
We consider rectangular graph superlattices of sides l1, l2 with the wavefunction coupling at the junctions either of the delta type, when they are continuous and the sum of their derivatives is proportional to the common value at the…
Extensive recent research on Lieb and kagome lattices highlights their unique physics characterized by the coexistence of Dirac points, van Hove singularities, and flat bands. In these models, flat bands are typically pinned at the center…
Graphyne (GY) and graphdiyne (GDY)-based materials represent an intriguing class of two-dimensional (2D) carbon-rich networks with tunable structures and properties surpassing those of graphene. However, the challenge of fabricating…
Flat-band models have been of particular interest from both fundamental aspects and realization in materials. Beyond the canonical examples such as Lieb lattices and line graphs, a variety of tight-binding models are found to possess flat…
We demonstrate that a complete class of flat-band lattices with underlying commutative local symmetries exhibit a locally fragmented Hilbert space. The equitable partition theorem ensures distinct parities for the compact localized states…
A flat energy dispersion of electrons at the Fermi level of a material leads to instabilities in the electronic system and can drive phase transitions. Here we introduce a method to induce a flat band in two-dimensional (2D) materials. We…
We investigate the electronic structure of the kagome lattice model with first, second, and two kinds of third nearest-neighbor hoppings. We reveal that by tuning the third nearest-neighbor hoppings, not only single flat band but also…
The functional features of spatial networks depend upon a non-trivial relationship between the topological and physical structure. Here, we explore that relationship for spatial networks with radial symmetry and disordered fractal…
The collective electronic properties of various types of pseudospin-$1$ Dirac-cone materials with a flat band and finite bangaps in their energy spectra are the subject of our reported investigation. Specifically, we have calculated the…
The origin of non-dispersive flat band modes for a quasi-one dimensional square-kagome ladder network is explored analytically by virtue of the real space renormalization group (RSRG) technique. A section of the eigenstates is non-diffusive…
We show the existence of a flat band consisting of photonic zero modes in a gain and loss modulated lattice system, as a result of the underlying non-Hermitian particle-hole symmetry. This general finding explains the previous observation…
We consider quantum scattering of particles in media exhibiting strong dispersion degeneracy. In particular, we study flat-banded lattices and linearly dispersed energy bands. The former constitute a prime example of single-particle…
We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued self-adjoint operator, which is also…
We uncover the very rich graph topology of generic bounded non-Hermitian spectra, distinct from the topology of conventional band invariants and complex spectral winding. The graph configuration of complex spectra are characterized by the…
We describe a nonlinear kagome lattice with nonlinear dynamics described by Klein-Gordon interactions with a scalar unknown at each node, such as might occur in a nonlinear electrical lattice. We show that the dispersion relation has three…
We present a new approach to the theory of k-forms on self-similar fractals. We work out the details for two examples, the standard Sierpinski gasket and the 3-dimensional Sierpinski gasket, but the method is expected to be effective for…
We study localization and flat-band formation in lattices generated by repeated edge inflation of square, honeycomb, and triangular parent lattices. Replacing each bond by a finite tight-binding chain produces several distinct classes of…